Translate all code to English (#1836)

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* Revisit the CN-to-EN translation for Java code using Claude-4.5

* Revisit the CN-to-EN translation for Cpp code using Claude-4.5.

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en/codes/go/chapter_array_and_linkedlist/array.go

@@ -0,0 +1,79 @@
+// File: array.go
+// Created Time: 2022-12-29
+// Author: GuoWei (gongguowei01@gmail.com), cathay (cathaycchen@gmail.com)
+
+package chapter_array_and_linkedlist
+
+import (
+	"math/rand"
+)
+
+/* Random access to element */
+func randomAccess(nums []int) (randomNum int) {
+	// Randomly select a number in the interval [0, nums.length)
+	randomIndex := rand.Intn(len(nums))
+	// Retrieve and return the random element
+	randomNum = nums[randomIndex]
+	return
+}
+
+/* Extend array length */
+func extend(nums []int, enlarge int) []int {
+	// Initialize an array with extended length
+	res := make([]int, len(nums)+enlarge)
+	// Copy all elements from the original array to the new array
+	for i, num := range nums {
+		res[i] = num
+	}
+	// Return the extended new array
+	return res
+}
+
+/* Insert element num at index index in the array */
+func insert(nums []int, num int, index int) {
+	// Move all elements at and after index index backward by one position
+	for i := len(nums) - 1; i > index; i-- {
+		nums[i] = nums[i-1]
+	}
+	// Assign num to the element at index index
+	nums[index] = num
+}
+
+/* Remove the element at index index */
+func remove(nums []int, index int) {
+	// Move all elements after index index forward by one position
+	for i := index; i < len(nums)-1; i++ {
+		nums[i] = nums[i+1]
+	}
+}
+
+/* Traverse array */
+func traverse(nums []int) {
+	count := 0
+	// Traverse array by index
+	for i := 0; i < len(nums); i++ {
+		count += nums[i]
+	}
+	count = 0
+	// Direct traversal of array elements
+	for _, num := range nums {
+		count += num
+	}
+	// Traverse simultaneously data index and elements
+	for i, num := range nums {
+		count += nums[i]
+		count += num
+	}
+}
+
+/* Find the specified element in the array */
+func find(nums []int, target int) (index int) {
+	index = -1
+	for i := 0; i < len(nums); i++ {
+		if nums[i] == target {
+			index = i
+			break
+		}
+	}
+	return
+}

en/codes/go/chapter_array_and_linkedlist/array_test.go

@@ -0,0 +1,50 @@
+// File: array_test.go
+// Created Time: 2022-12-29
+// Author: GuoWei (gongguowei01@gmail.com), cathay (cathaycchen@gmail.com)
+
+package chapter_array_and_linkedlist
+
+/**
+We treat Go Slice as Array here. This reduces
+the learning cost and allows us to focus on data structures and algorithms.
+*/
+
+import (
+	"fmt"
+	"testing"
+)
+
+/* Driver Code */
+func TestArray(t *testing.T) {
+	/* Initialize array */
+	var arr [5]int
+	fmt.Println("Array arr =", arr)
+	// In Go, specifying length ([5]int) creates an array, not specifying length ([]int) creates a slice
+	// Since Go arrays are designed to have their length determined at compile time, only constants can be used to specify the length
+	// For convenience in implementing the extend() function, slices are treated as arrays below
+	nums := []int{1, 3, 2, 5, 4}
+	fmt.Println("Array nums =", nums)
+
+	/* Insert element */
+	randomNum := randomAccess(nums)
+	fmt.Println("Get random element in nums", randomNum)
+
+	/* Traverse array */
+	nums = extend(nums, 3)
+	fmt.Println("Extend array length to 8, get nums =", nums)
+
+	/* Insert element */
+	insert(nums, 6, 3)
+	fmt.Println("Insert number 6 at index 3, get nums =", nums)
+
+	/* Remove element */
+	remove(nums, 2)
+	fmt.Println("Remove element at index 2, get nums =", nums)
+
+	/* Traverse array */
+	traverse(nums)
+
+	/* Find element */
+	index := find(nums, 3)
+	fmt.Println("Find element 3 in nums, get index =", index)
+}

en/codes/go/chapter_array_and_linkedlist/linked_list.go

@@ -0,0 +1,51 @@
+// File: linked_list.go
+// Created Time: 2022-12-29
+// Author: cathay (cathaycchen@gmail.com)
+
+package chapter_array_and_linkedlist
+
+import (
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+/* Insert node P after node n0 in the linked list */
+func insertNode(n0 *ListNode, P *ListNode) {
+	n1 := n0.Next
+	P.Next = n1
+	n0.Next = P
+}
+
+/* Remove the first node after node n0 in the linked list */
+func removeItem(n0 *ListNode) {
+	if n0.Next == nil {
+		return
+	}
+	// n0 -> P -> n1
+	P := n0.Next
+	n1 := P.Next
+	n0.Next = n1
+}
+
+/* Access the node at index index in the linked list */
+func access(head *ListNode, index int) *ListNode {
+	for i := 0; i < index; i++ {
+		if head == nil {
+			return nil
+		}
+		head = head.Next
+	}
+	return head
+}
+
+/* Find the first node with value target in the linked list */
+func findNode(head *ListNode, target int) int {
+	index := 0
+	for head != nil {
+		if head.Val == target {
+			return index
+		}
+		head = head.Next
+		index++
+	}
+	return -1
+}

en/codes/go/chapter_array_and_linkedlist/linked_list_test.go

@@ -0,0 +1,48 @@
+// File: linked_list_test.go
+// Created Time: 2022-12-29
+// Author: cathay (cathaycchen@gmail.com)
+
+package chapter_array_and_linkedlist
+
+import (
+	"fmt"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestLinkedList(t *testing.T) {
+	/* Initialize linked list 1 -> 3 -> 2 -> 5 -> 4 */
+	// Initialize each node
+	n0 := NewListNode(1)
+	n1 := NewListNode(3)
+	n2 := NewListNode(2)
+	n3 := NewListNode(5)
+	n4 := NewListNode(4)
+
+	// Build references between nodes
+	n0.Next = n1
+	n1.Next = n2
+	n2.Next = n3
+	n3.Next = n4
+	fmt.Println("Initialized linked list is")
+	PrintLinkedList(n0)
+
+	/* Insert node */
+	insertNode(n0, NewListNode(0))
+	fmt.Println("Linked list after inserting node is")
+	PrintLinkedList(n0)
+
+	/* Remove node */
+	removeItem(n0)
+	fmt.Println("Linked list after removing node is")
+	PrintLinkedList(n0)
+
+	/* Access node */
+	node := access(n0, 3)
+	fmt.Println("Value of node at index 3 in linked list =", node)
+
+	/* Search node */
+	index := findNode(n0, 2)
+	fmt.Println("Index of node with value 2 in linked list =", index)
+}

en/codes/go/chapter_array_and_linkedlist/list_test.go

@@ -0,0 +1,66 @@
+// File: list_test.go
+// Created Time: 2022-12-18
+// Author: msk397 (machangxinq@gmail.com)
+
+package chapter_array_and_linkedlist
+
+import (
+	"fmt"
+	"sort"
+	"testing"
+)
+
+/* Driver Code */
+func TestList(t *testing.T) {
+	/* Initialize list */
+	nums := []int{1, 3, 2, 5, 4}
+	fmt.Println("List nums =", nums)
+
+	/* Update element */
+	num := nums[1] // Access element at index 1
+	fmt.Println("Access element at index 1, get num =", num)
+
+	/* Add elements at the end */
+	nums[1] = 0 // Update element at index 1 to 0
+	fmt.Println("Update element at index 1 to 0, get nums =", nums)
+
+	/* Remove element */
+	nums = nil
+	fmt.Println("After clearing list, nums =", nums)
+
+	/* Direct traversal of list elements */
+	nums = append(nums, 1)
+	nums = append(nums, 3)
+	nums = append(nums, 2)
+	nums = append(nums, 5)
+	nums = append(nums, 4)
+	fmt.Println("After adding elements, nums =", nums)
+
+	/* Sort list */
+	nums = append(nums[:3], append([]int{6}, nums[3:]...)...) // Insert number 6 at index 3
+	fmt.Println("Insert number 6 at index 3, get nums =", nums)
+
+	/* Remove element */
+	nums = append(nums[:3], nums[4:]...) // Remove element at index 3
+	fmt.Println("Remove element at index 3, get nums =", nums)
+
+	/* Traverse list by index */
+	count := 0
+	for i := 0; i < len(nums); i++ {
+		count += nums[i]
+	}
+	/* Directly traverse list elements */
+	count = 0
+	for _, x := range nums {
+		count += x
+	}
+
+	/* Concatenate two lists */
+	nums1 := []int{6, 8, 7, 10, 9}
+	nums = append(nums, nums1...) // Concatenate list nums1 to nums
+	fmt.Println("Concatenate list nums1 to nums, get nums =", nums)
+
+	/* Sort list */
+	sort.Ints(nums) // After sorting, list elements are arranged from smallest to largest
+	fmt.Println("After sorting list, nums =", nums)
+}

en/codes/go/chapter_array_and_linkedlist/my_list.go

@@ -0,0 +1,109 @@
+// File: my_list.go
+// Created Time: 2022-12-18
+// Author: msk397 (machangxinq@gmail.com)
+
+package chapter_array_and_linkedlist
+
+/* List class */
+type myList struct {
+	arrCapacity int
+	arr         []int
+	arrSize     int
+	extendRatio int
+}
+
+/* Constructor */
+func newMyList() *myList {
+	return &myList{
+		arrCapacity: 10,              // List capacity
+		arr:         make([]int, 10), // Array (stores list elements)
+		arrSize:     0,               // List length (current number of elements)
+		extendRatio: 2,               // Multiple by which the list capacity is extended each time
+	}
+}
+
+/* Get list length (current number of elements) */
+func (l *myList) size() int {
+	return l.arrSize
+}
+
+/* Get list capacity */
+func (l *myList) capacity() int {
+	return l.arrCapacity
+}
+
+/* Update element */
+func (l *myList) get(index int) int {
+	// If the index is out of bounds, throw an exception, as below
+	if index < 0 || index >= l.arrSize {
+		panic("Index out of bounds")
+	}
+	return l.arr[index]
+}
+
+/* Add elements at the end */
+func (l *myList) set(num, index int) {
+	if index < 0 || index >= l.arrSize {
+		panic("Index out of bounds")
+	}
+	l.arr[index] = num
+}
+
+/* Direct traversal of list elements */
+func (l *myList) add(num int) {
+	// When the number of elements exceeds capacity, trigger the extension mechanism
+	if l.arrSize == l.arrCapacity {
+		l.extendCapacity()
+	}
+	l.arr[l.arrSize] = num
+	// Update the number of elements
+	l.arrSize++
+}
+
+/* Sort list */
+func (l *myList) insert(num, index int) {
+	if index < 0 || index >= l.arrSize {
+		panic("Index out of bounds")
+	}
+	// When the number of elements exceeds capacity, trigger the extension mechanism
+	if l.arrSize == l.arrCapacity {
+		l.extendCapacity()
+	}
+	// Move all elements after index index forward by one position
+	for j := l.arrSize - 1; j >= index; j-- {
+		l.arr[j+1] = l.arr[j]
+	}
+	l.arr[index] = num
+	// Update the number of elements
+	l.arrSize++
+}
+
+/* Remove element */
+func (l *myList) remove(index int) int {
+	if index < 0 || index >= l.arrSize {
+		panic("Index out of bounds")
+	}
+	num := l.arr[index]
+	// Create a new array with length _extend_ratio times the original array, and copy the original array to the new array
+	for j := index; j < l.arrSize-1; j++ {
+		l.arr[j] = l.arr[j+1]
+	}
+	// Update the number of elements
+	l.arrSize--
+	// Return the removed element
+	return num
+}
+
+/* Driver Code */
+func (l *myList) extendCapacity() {
+	// Create a new array with length extendRatio times the original array and copy the original array to the new array
+	l.arr = append(l.arr, make([]int, l.arrCapacity*(l.extendRatio-1))...)
+	// Add elements at the end
+	l.arrCapacity = len(l.arr)
+}
+
+/* Return list with valid length */
+func (l *myList) toArray() []int {
+	// Elements enqueue
+	return l.arr[:l.arrSize]
+}

en/codes/go/chapter_array_and_linkedlist/my_list_test.go

@@ -0,0 +1,46 @@
+// File: my_list_test.go
+// Created Time: 2022-12-18
+// Author: msk397 (machangxinq@gmail.com)
+
+package chapter_array_and_linkedlist
+
+import (
+	"fmt"
+	"testing"
+)
+
+/* Driver Code */
+func TestMyList(t *testing.T) {
+	/* Initialize list */
+	nums := newMyList()
+	/* Direct traversal of list elements */
+	nums.add(1)
+	nums.add(3)
+	nums.add(2)
+	nums.add(5)
+	nums.add(4)
+	fmt.Printf("List nums = %v, capacity = %v, length = %v\n", nums.toArray(), nums.capacity(), nums.size())
+
+	/* Sort list */
+	nums.insert(6, 3)
+	fmt.Printf("Insert number 6 at index 3, get nums = %v\n", nums.toArray())
+
+	/* Remove element */
+	nums.remove(3)
+	fmt.Printf("Remove element at index 3, get nums = %v\n", nums.toArray())
+
+	/* Update element */
+	num := nums.get(1)
+	fmt.Printf("Access element at index 1, get num = %v\n", num)
+
+	/* Add elements at the end */
+	nums.set(0, 1)
+	fmt.Printf("Update element at index 1 to 0, get nums = %v\n", nums.toArray())
+
+	/* Test capacity expansion mechanism */
+	for i := 0; i < 10; i++ {
+		// At i = 5, the list length will exceed the list capacity, triggering the expansion mechanism
+		nums.add(i)
+	}
+	fmt.Printf("After expansion, list nums = %v, capacity = %v, length = %v\n", nums.toArray(), nums.capacity(), nums.size())
+}

en/codes/go/chapter_backtracking/n_queens.go

@@ -0,0 +1,57 @@
+// File: n_queens.go
+// Created Time: 2023-05-09
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+/* Backtracking algorithm: N queens */
+func backtrack(row, n int, state *[][]string, res *[][][]string, cols, diags1, diags2 *[]bool) {
+	// When all rows are placed, record the solution
+	if row == n {
+		newState := make([][]string, len(*state))
+		for i, _ := range newState {
+			newState[i] = make([]string, len((*state)[0]))
+			copy(newState[i], (*state)[i])
+
+		}
+		*res = append(*res, newState)
+		return
+	}
+	// Traverse all columns
+	for col := 0; col < n; col++ {
+		// Calculate the main diagonal and anti-diagonal corresponding to this cell
+		diag1 := row - col + n - 1
+		diag2 := row + col
+		// Pruning: do not allow queens to exist in the column, main diagonal, and anti-diagonal of this cell
+		if !(*cols)[col] && !(*diags1)[diag1] && !(*diags2)[diag2] {
+			// Attempt: place the queen in this cell
+			(*state)[row][col] = "Q"
+			(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = true, true, true
+			// Place the next row
+			backtrack(row+1, n, state, res, cols, diags1, diags2)
+			// Backtrack: restore this cell to an empty cell
+			(*state)[row][col] = "#"
+			(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = false, false, false
+		}
+	}
+}
+
+/* Solve N queens */
+func nQueens(n int) [][][]string {
+	// Initialize an n*n chessboard, where 'Q' represents a queen and '#' represents an empty cell
+	state := make([][]string, n)
+	for i := 0; i < n; i++ {
+		row := make([]string, n)
+		for i := 0; i < n; i++ {
+			row[i] = "#"
+		}
+		state[i] = row
+	}
+	// Record whether there is a queen in the column
+	cols := make([]bool, n)
+	diags1 := make([]bool, 2*n-1)
+	diags2 := make([]bool, 2*n-1)
+	res := make([][][]string, 0)
+	backtrack(0, n, &state, &res, &cols, &diags1, &diags2)
+	return res
+}

en/codes/go/chapter_backtracking/n_queens_test.go

@@ -0,0 +1,24 @@
+// File: n_queens_test.go
+// Created Time: 2023-05-14
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestNQueens(t *testing.T) {
+	n := 4
+	res := nQueens(n)
+
+	fmt.Println("Input board size is ", n)
+	fmt.Println("Total queen placement solutions: ", len(res), " solutions")
+	for _, state := range res {
+		fmt.Println("--------------------")
+		for _, row := range state {
+			fmt.Println(row)
+		}
+	}
+}

en/codes/go/chapter_backtracking/permutation_test.go

@@ -0,0 +1,33 @@
+// File: permutation_test.go
+// Created Time: 2023-05-09
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+import (
+	"fmt"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestPermutationI(t *testing.T) {
+	/* Permutations I */
+	nums := []int{1, 2, 3}
+	fmt.Printf("Input array nums = ")
+	PrintSlice(nums)
+
+	res := permutationsI(nums)
+	fmt.Printf("All permutations res = ")
+	fmt.Println(res)
+}
+
+func TestPermutationII(t *testing.T) {
+	nums := []int{1, 2, 2}
+	fmt.Printf("Input array nums = ")
+	PrintSlice(nums)
+
+	res := permutationsII(nums)
+	fmt.Printf("All permutations res = ")
+	fmt.Println(res)
+}

en/codes/go/chapter_backtracking/permutations_i.go

@@ -0,0 +1,38 @@
+// File: permutations_i.go
+// Created Time: 2023-05-14
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+/* Backtracking algorithm: Permutations I */
+func backtrackI(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {
+	// When the state length equals the number of elements, record the solution
+	if len(*state) == len(*choices) {
+		newState := append([]int{}, *state...)
+		*res = append(*res, newState)
+	}
+	// Traverse all choices
+	for i := 0; i < len(*choices); i++ {
+		choice := (*choices)[i]
+		// Pruning: do not allow repeated selection of elements
+		if !(*selected)[i] {
+			// Attempt: make choice, update state
+			(*selected)[i] = true
+			*state = append(*state, choice)
+			// Proceed to the next round of selection
+			backtrackI(state, choices, selected, res)
+			// Backtrack: undo choice, restore to previous state
+			(*selected)[i] = false
+			*state = (*state)[:len(*state)-1]
+		}
+	}
+}
+
+/* Permutations I */
+func permutationsI(nums []int) [][]int {
+	res := make([][]int, 0)
+	state := make([]int, 0)
+	selected := make([]bool, len(nums))
+	backtrackI(&state, &nums, &selected, &res)
+	return res
+}

en/codes/go/chapter_backtracking/permutations_ii.go

@@ -0,0 +1,41 @@
+// File: permutations_ii.go
+// Created Time: 2023-05-14
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+/* Backtracking algorithm: Permutations II */
+func backtrackII(state *[]int, choices *[]int, selected *[]bool, res *[][]int) {
+	// When the state length equals the number of elements, record the solution
+	if len(*state) == len(*choices) {
+		newState := append([]int{}, *state...)
+		*res = append(*res, newState)
+	}
+	// Traverse all choices
+	duplicated := make(map[int]struct{}, 0)
+	for i := 0; i < len(*choices); i++ {
+		choice := (*choices)[i]
+		// Pruning: do not allow repeated selection of elements and do not allow repeated selection of equal elements
+		if _, ok := duplicated[choice]; !ok && !(*selected)[i] {
+			// Attempt: make choice, update state
+			// Record the selected element value
+			duplicated[choice] = struct{}{}
+			(*selected)[i] = true
+			*state = append(*state, choice)
+			// Proceed to the next round of selection
+			backtrackII(state, choices, selected, res)
+			// Backtrack: undo choice, restore to previous state
+			(*selected)[i] = false
+			*state = (*state)[:len(*state)-1]
+		}
+	}
+}
+
+/* Permutations II */
+func permutationsII(nums []int) [][]int {
+	res := make([][]int, 0)
+	state := make([]int, 0)
+	selected := make([]bool, len(nums))
+	backtrackII(&state, &nums, &selected, &res)
+	return res
+}

en/codes/go/chapter_backtracking/preorder_traversal_i_compact.go

@@ -0,0 +1,22 @@
+// File: preorder_traversal_i_compact.go
+// Created Time: 2023-05-09
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+import (
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+/* Preorder traversal: Example 1 */
+func preOrderI(root *TreeNode, res *[]*TreeNode) {
+	if root == nil {
+		return
+	}
+	if (root.Val).(int) == 7 {
+		// Record solution
+		*res = append(*res, root)
+	}
+	preOrderI(root.Left, res)
+	preOrderI(root.Right, res)
+}

en/codes/go/chapter_backtracking/preorder_traversal_ii_compact.go

@@ -0,0 +1,26 @@
+// File: preorder_traversal_ii_compact.go
+// Created Time: 2023-05-09
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+import (
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+/* Preorder traversal: Example 2 */
+func preOrderII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {
+	if root == nil {
+		return
+	}
+	// Attempt
+	*path = append(*path, root)
+	if root.Val.(int) == 7 {
+		// Record solution
+		*res = append(*res, append([]*TreeNode{}, *path...))
+	}
+	preOrderII(root.Left, res, path)
+	preOrderII(root.Right, res, path)
+	// Backtrack
+	*path = (*path)[:len(*path)-1]
+}

en/codes/go/chapter_backtracking/preorder_traversal_iii_compact.go

@@ -0,0 +1,27 @@
+// File: preorder_traversal_iii_compact.go
+// Created Time: 2023-05-09
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+import (
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+/* Preorder traversal: Example 3 */
+func preOrderIII(root *TreeNode, res *[][]*TreeNode, path *[]*TreeNode) {
+	// Pruning
+	if root == nil || root.Val == 3 {
+		return
+	}
+	// Attempt
+	*path = append(*path, root)
+	if root.Val.(int) == 7 {
+		// Record solution
+		*res = append(*res, append([]*TreeNode{}, *path...))
+	}
+	preOrderIII(root.Left, res, path)
+	preOrderIII(root.Right, res, path)
+	// Backtrack
+	*path = (*path)[:len(*path)-1]
+}

en/codes/go/chapter_backtracking/preorder_traversal_iii_template.go

@@ -0,0 +1,57 @@
+// File: preorder_traversal_iii_template.go
+// Created Time: 2023-05-09
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+import (
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+/* Check if the current state is a solution */
+func isSolution(state *[]*TreeNode) bool {
+	return len(*state) != 0 && (*state)[len(*state)-1].Val == 7
+}
+
+/* Record solution */
+func recordSolution(state *[]*TreeNode, res *[][]*TreeNode) {
+	*res = append(*res, append([]*TreeNode{}, *state...))
+}
+
+/* Check if the choice is valid under the current state */
+func isValid(state *[]*TreeNode, choice *TreeNode) bool {
+	return choice != nil && choice.Val != 3
+}
+
+/* Update state */
+func makeChoice(state *[]*TreeNode, choice *TreeNode) {
+	*state = append(*state, choice)
+}
+
+/* Restore state */
+func undoChoice(state *[]*TreeNode, choice *TreeNode) {
+	*state = (*state)[:len(*state)-1]
+}
+
+/* Backtracking algorithm: Example 3 */
+func backtrackIII(state *[]*TreeNode, choices *[]*TreeNode, res *[][]*TreeNode) {
+	// Check if it is a solution
+	if isSolution(state) {
+		// Record solution
+		recordSolution(state, res)
+	}
+	// Traverse all choices
+	for _, choice := range *choices {
+		// Pruning: check if the choice is valid
+		if isValid(state, choice) {
+			// Attempt: make choice, update state
+			makeChoice(state, choice)
+			// Proceed to the next round of selection
+			temp := make([]*TreeNode, 0)
+			temp = append(temp, choice.Left, choice.Right)
+			backtrackIII(state, &temp, res)
+			// Backtrack: undo choice, restore to previous state
+			undoChoice(state, choice)
+		}
+	}
+}

en/codes/go/chapter_backtracking/preorder_traversal_test.go

@@ -0,0 +1,91 @@
+// File: preorder_traversal_i_compact_test.go
+// Created Time: 2023-05-09
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+import (
+	"fmt"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestPreorderTraversalICompact(t *testing.T) {
+	/* Initialize binary tree */
+	root := SliceToTree([]any{1, 7, 3, 4, 5, 6, 7})
+	fmt.Println("\nInitialize binary tree")
+	PrintTree(root)
+
+	// Preorder traversal
+	res := make([]*TreeNode, 0)
+	preOrderI(root, &res)
+
+	fmt.Println("\nOutput all nodes with value 7")
+	for _, node := range res {
+		fmt.Printf("%v ", node.Val)
+	}
+	fmt.Println()
+}
+
+func TestPreorderTraversalIICompact(t *testing.T) {
+	/* Initialize binary tree */
+	root := SliceToTree([]any{1, 7, 3, 4, 5, 6, 7})
+	fmt.Println("\nInitialize binary tree")
+	PrintTree(root)
+
+	// Preorder traversal
+	path := make([]*TreeNode, 0)
+	res := make([][]*TreeNode, 0)
+	preOrderII(root, &res, &path)
+
+	fmt.Println("\nOutput all paths from root node to node 7")
+	for _, path := range res {
+		for _, node := range path {
+			fmt.Printf("%v ", node.Val)
+		}
+		fmt.Println()
+	}
+}
+
+func TestPreorderTraversalIIICompact(t *testing.T) {
+	/* Initialize binary tree */
+	root := SliceToTree([]any{1, 7, 3, 4, 5, 6, 7})
+	fmt.Println("\nInitialize binary tree")
+	PrintTree(root)
+
+	// Preorder traversal
+	path := make([]*TreeNode, 0)
+	res := make([][]*TreeNode, 0)
+	preOrderIII(root, &res, &path)
+
+	fmt.Println("\nOutput all paths from root node to node 7, paths do not include nodes with value 3")
+	for _, path := range res {
+		for _, node := range path {
+			fmt.Printf("%v ", node.Val)
+		}
+		fmt.Println()
+	}
+}
+
+func TestPreorderTraversalIIITemplate(t *testing.T) {
+	/* Initialize binary tree */
+	root := SliceToTree([]any{1, 7, 3, 4, 5, 6, 7})
+	fmt.Println("\nInitialize binary tree")
+	PrintTree(root)
+
+	// Backtracking algorithm
+	res := make([][]*TreeNode, 0)
+	state := make([]*TreeNode, 0)
+	choices := make([]*TreeNode, 0)
+	choices = append(choices, root)
+	backtrackIII(&state, &choices, &res)
+
+	fmt.Println("\nOutput all paths from root node to node 7, paths do not include nodes with value 3")
+	for _, path := range res {
+		for _, node := range path {
+			fmt.Printf("%v ", node.Val)
+		}
+		fmt.Println()
+	}
+}

en/codes/go/chapter_backtracking/subset_sum_i.go

@@ -0,0 +1,42 @@
+// File: subset_sum_i.go
+// Created Time: 2023-06-24
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+import "sort"
+
+/* Backtracking algorithm: Subset sum I */
+func backtrackSubsetSumI(start, target int, state, choices *[]int, res *[][]int) {
+	// When the subset sum equals target, record the solution
+	if target == 0 {
+		newState := append([]int{}, *state...)
+		*res = append(*res, newState)
+		return
+	}
+	// Traverse all choices
+	// Pruning 2: start traversing from start to avoid generating duplicate subsets
+	for i := start; i < len(*choices); i++ {
+		// Pruning 1: if the subset sum exceeds target, end the loop directly
+		// This is because the array is sorted, and later elements are larger, so the subset sum will definitely exceed target
+		if target-(*choices)[i] < 0 {
+			break
+		}
+		// Attempt: make choice, update target, start
+		*state = append(*state, (*choices)[i])
+		// Proceed to the next round of selection
+		backtrackSubsetSumI(i, target-(*choices)[i], state, choices, res)
+		// Backtrack: undo choice, restore to previous state
+		*state = (*state)[:len(*state)-1]
+	}
+}
+
+/* Solve subset sum I */
+func subsetSumI(nums []int, target int) [][]int {
+	state := make([]int, 0) // State (subset)
+	sort.Ints(nums)         // Sort nums
+	start := 0              // Start point for traversal
+	res := make([][]int, 0) // Result list (subset list)
+	backtrackSubsetSumI(start, target, &state, &nums, &res)
+	return res
+}

en/codes/go/chapter_backtracking/subset_sum_i_naive.go

@@ -0,0 +1,37 @@
+// File: subset_sum_i_naive.go
+// Created Time: 2023-06-24
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+/* Backtracking algorithm: Subset sum I */
+func backtrackSubsetSumINaive(total, target int, state, choices *[]int, res *[][]int) {
+	// When the subset sum equals target, record the solution
+	if target == total {
+		newState := append([]int{}, *state...)
+		*res = append(*res, newState)
+		return
+	}
+	// Traverse all choices
+	for i := 0; i < len(*choices); i++ {
+		// Pruning: if the subset sum exceeds target, skip this choice
+		if total+(*choices)[i] > target {
+			continue
+		}
+		// Attempt: make choice, update element sum total
+		*state = append(*state, (*choices)[i])
+		// Proceed to the next round of selection
+		backtrackSubsetSumINaive(total+(*choices)[i], target, state, choices, res)
+		// Backtrack: undo choice, restore to previous state
+		*state = (*state)[:len(*state)-1]
+	}
+}
+
+/* Solve subset sum I (including duplicate subsets) */
+func subsetSumINaive(nums []int, target int) [][]int {
+	state := make([]int, 0) // State (subset)
+	total := 0              // Subset sum
+	res := make([][]int, 0) // Result list (subset list)
+	backtrackSubsetSumINaive(total, target, &state, &nums, &res)
+	return res
+}

en/codes/go/chapter_backtracking/subset_sum_ii.go

@@ -0,0 +1,47 @@
+// File: subset_sum_ii.go
+// Created Time: 2023-06-24
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+import "sort"
+
+/* Backtracking algorithm: Subset sum II */
+func backtrackSubsetSumII(start, target int, state, choices *[]int, res *[][]int) {
+	// When the subset sum equals target, record the solution
+	if target == 0 {
+		newState := append([]int{}, *state...)
+		*res = append(*res, newState)
+		return
+	}
+	// Traverse all choices
+	// Pruning 2: start traversing from start to avoid generating duplicate subsets
+	// Pruning 3: start traversing from start to avoid repeatedly selecting the same element
+	for i := start; i < len(*choices); i++ {
+		// Pruning 1: if the subset sum exceeds target, end the loop directly
+		// This is because the array is sorted, and later elements are larger, so the subset sum will definitely exceed target
+		if target-(*choices)[i] < 0 {
+			break
+		}
+		// Pruning 4: if this element equals the left element, it means this search branch is duplicate, skip it directly
+		if i > start && (*choices)[i] == (*choices)[i-1] {
+			continue
+		}
+		// Attempt: make choice, update target, start
+		*state = append(*state, (*choices)[i])
+		// Proceed to the next round of selection
+		backtrackSubsetSumII(i+1, target-(*choices)[i], state, choices, res)
+		// Backtrack: undo choice, restore to previous state
+		*state = (*state)[:len(*state)-1]
+	}
+}
+
+/* Solve subset sum II */
+func subsetSumII(nums []int, target int) [][]int {
+	state := make([]int, 0) // State (subset)
+	sort.Ints(nums)         // Sort nums
+	start := 0              // Start point for traversal
+	res := make([][]int, 0) // Result list (subset list)
+	backtrackSubsetSumII(start, target, &state, &nums, &res)
+	return res
+}

en/codes/go/chapter_backtracking/subset_sum_test.go

@@ -0,0 +1,56 @@
+// File: subset_sum_test.go
+// Created Time: 2023-06-24
+// Author: Reanon (793584285@qq.com)
+
+package chapter_backtracking
+
+import (
+	"fmt"
+	"strconv"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestSubsetSumINaive(t *testing.T) {
+	nums := []int{3, 4, 5}
+	target := 9
+	res := subsetSumINaive(nums, target)
+
+	fmt.Printf("target = " + strconv.Itoa(target) + ", input array nums = ")
+	PrintSlice(nums)
+
+	fmt.Println("All subsets with sum equal to " + strconv.Itoa(target) + " are res = ")
+	for i := range res {
+		PrintSlice(res[i])
+	}
+	fmt.Println("Please note that this method outputs results containing duplicate sets")
+}
+
+func TestSubsetSumI(t *testing.T) {
+	nums := []int{3, 4, 5}
+	target := 9
+	res := subsetSumI(nums, target)
+
+	fmt.Printf("target = " + strconv.Itoa(target) + ", input array nums = ")
+	PrintSlice(nums)
+
+	fmt.Println("All subsets with sum equal to " + strconv.Itoa(target) + " are res = ")
+	for i := range res {
+		PrintSlice(res[i])
+	}
+}
+
+func TestSubsetSumII(t *testing.T) {
+	nums := []int{4, 4, 5}
+	target := 9
+	res := subsetSumII(nums, target)
+
+	fmt.Printf("target = " + strconv.Itoa(target) + ", input array nums = ")
+	PrintSlice(nums)
+
+	fmt.Println("All subsets with sum equal to " + strconv.Itoa(target) + " are res = ")
+	for i := range res {
+		PrintSlice(res[i])
+	}
+}

en/codes/go/chapter_computational_complexity/iteration.go

@@ -0,0 +1,59 @@
+// File: iteration.go
+// Created Time: 2023-08-28
+// Author: Reanon (793584285@qq.com)
+
+package chapter_computational_complexity
+
+import "fmt"
+
+/* for loop */
+func forLoop(n int) int {
+	res := 0
+	// Sum 1, 2, ..., n-1, n
+	for i := 1; i <= n; i++ {
+		res += i
+	}
+	return res
+}
+
+/* while loop */
+func whileLoop(n int) int {
+	res := 0
+	// Initialize condition variable
+	i := 1
+	// Sum 1, 2, ..., n-1, n
+	for i <= n {
+		res += i
+		// Update condition variable
+		i++
+	}
+	return res
+}
+
+/* while loop (two updates) */
+func whileLoopII(n int) int {
+	res := 0
+	// Initialize condition variable
+	i := 1
+	// Sum 1, 4, 10, ...
+	for i <= n {
+		res += i
+		// Update condition variable
+		i++
+		i *= 2
+	}
+	return res
+}
+
+/* Nested for loop */
+func nestedForLoop(n int) string {
+	res := ""
+	// Loop i = 1, 2, ..., n-1, n
+	for i := 1; i <= n; i++ {
+		for j := 1; j <= n; j++ {
+			// Loop j = 1, 2, ..., n-1, n
+			res += fmt.Sprintf("(%d, %d), ", i, j)
+		}
+	}
+	return res
+}

en/codes/go/chapter_computational_complexity/iteration_test.go

@@ -0,0 +1,26 @@
+// File: iteration_test.go
+// Created Time: 2023-08-28
+// Author: Reanon (793584285@qq.com)
+
+package chapter_computational_complexity
+
+import (
+	"fmt"
+	"testing"
+)
+
+/* Driver Code */
+func TestIteration(t *testing.T) {
+	n := 5
+	res := forLoop(n)
+	fmt.Println("\nfor loop sum result res = ", res)
+
+	res = whileLoop(n)
+	fmt.Println("\nwhile loop sum result res = ", res)
+
+	res = whileLoopII(n)
+	fmt.Println("\nwhile loop (two updates) sum result res = ", res)
+
+	resStr := nestedForLoop(n)
+	fmt.Println("\nDouble for loop traversal result ", resStr)
+}

en/codes/go/chapter_computational_complexity/recursion.go

@@ -0,0 +1,61 @@
+// File: recursion.go
+// Created Time: 2023-08-28
+// Author: Reanon (793584285@qq.com)
+
+package chapter_computational_complexity
+
+import "container/list"
+
+/* Recursion */
+func recur(n int) int {
+	// Termination condition
+	if n == 1 {
+		return 1
+	}
+	// Recurse: recursive call
+	res := recur(n - 1)
+	// Return: return result
+	return n + res
+}
+
+/* Simulate recursion using iteration */
+func forLoopRecur(n int) int {
+	// Use an explicit stack to simulate the system call stack
+	stack := list.New()
+	res := 0
+	// Recurse: recursive call
+	for i := n; i > 0; i-- {
+		// Simulate "recurse" with "push"
+		stack.PushBack(i)
+	}
+	// Return: return result
+	for stack.Len() != 0 {
+		// Simulate "return" with "pop"
+		res += stack.Back().Value.(int)
+		stack.Remove(stack.Back())
+	}
+	// res = 1+2+3+...+n
+	return res
+}
+
+/* Tail recursion */
+func tailRecur(n int, res int) int {
+	// Termination condition
+	if n == 0 {
+		return res
+	}
+	// Tail recursive call
+	return tailRecur(n-1, res+n)
+}
+
+/* Fibonacci sequence: recursion */
+func fib(n int) int {
+	// Termination condition f(1) = 0, f(2) = 1
+	if n == 1 || n == 2 {
+		return n - 1
+	}
+	// Recursive call f(n) = f(n-1) + f(n-2)
+	res := fib(n-1) + fib(n-2)
+	// Return result f(n)
+	return res
+}

en/codes/go/chapter_computational_complexity/recursion_test.go

@@ -0,0 +1,26 @@
+// File: recursion_test.go
+// Created Time: 2023-08-28
+// Author: Reanon (793584285@qq.com)
+
+package chapter_computational_complexity
+
+import (
+	"fmt"
+	"testing"
+)
+
+/* Driver Code */
+func TestRecursion(t *testing.T) {
+	n := 5
+	res := recur(n)
+	fmt.Println("\nRecursive function sum result res = ", res)
+
+	res = forLoopRecur(n)
+	fmt.Println("\nUsing iteration to simulate recursive sum result res = ", res)
+
+	res = tailRecur(n, 0)
+	fmt.Println("\nTail recursive function sum result res = ", res)
+
+	res = fib(n)
+	fmt.Println("\nThe ", n, "th term of Fibonacci sequence is", res)
+}

en/codes/go/chapter_computational_complexity/space_complexity.go

@@ -0,0 +1,106 @@
+// File: space_complexity.go
+// Created Time: 2022-12-15
+// Author: cathay (cathaycchen@gmail.com)
+
+package chapter_computational_complexity
+
+import (
+	"fmt"
+	"strconv"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+/* Struct */
+type node struct {
+	val  int
+	next *node
+}
+
+/* Create node struct */
+func newNode(val int) *node {
+	return &node{val: val}
+}
+
+/* Function */
+func function() int {
+	// Perform some operations...
+	return 0
+}
+
+/* Constant order */
+func spaceConstant(n int) {
+	// Constants, variables, objects occupy O(1) space
+	const a = 0
+	b := 0
+	nums := make([]int, 10000)
+	node := newNode(0)
+	// Variables in the loop occupy O(1) space
+	var c int
+	for i := 0; i < n; i++ {
+		c = 0
+	}
+	// Functions in the loop occupy O(1) space
+	for i := 0; i < n; i++ {
+		function()
+	}
+	b += 0
+	c += 0
+	nums[0] = 0
+	node.val = 0
+}
+
+/* Linear order */
+func spaceLinear(n int) {
+	// Array of length n uses O(n) space
+	_ = make([]int, n)
+	// A list of length n occupies O(n) space
+	var nodes []*node
+	for i := 0; i < n; i++ {
+		nodes = append(nodes, newNode(i))
+	}
+	// A hash table of length n occupies O(n) space
+	m := make(map[int]string, n)
+	for i := 0; i < n; i++ {
+		m[i] = strconv.Itoa(i)
+	}
+}
+
+/* Linear order (recursive implementation) */
+func spaceLinearRecur(n int) {
+	fmt.Println("Recursion n =", n)
+	if n == 1 {
+		return
+	}
+	spaceLinearRecur(n - 1)
+}
+
+/* Exponential order */
+func spaceQuadratic(n int) {
+	// Matrix uses O(n^2) space
+	numMatrix := make([][]int, n)
+	for i := 0; i < n; i++ {
+		numMatrix[i] = make([]int, n)
+	}
+}
+
+/* Quadratic order (recursive implementation) */
+func spaceQuadraticRecur(n int) int {
+	if n <= 0 {
+		return 0
+	}
+	nums := make([]int, n)
+	fmt.Printf("In recursion n = %d, nums length = %d \n", n, len(nums))
+	return spaceQuadraticRecur(n - 1)
+}
+
+/* Driver Code */
+func buildTree(n int) *TreeNode {
+	if n == 0 {
+		return nil
+	}
+	root := NewTreeNode(0)
+	root.Left = buildTree(n - 1)
+	root.Right = buildTree(n - 1)
+	return root
+}

en/codes/go/chapter_computational_complexity/space_complexity_test.go

@@ -0,0 +1,26 @@
+// File: space_complexity_test.go
+// Created Time: 2022-12-15
+// Author: cathay (cathaycchen@gmail.com)
+
+package chapter_computational_complexity
+
+import (
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestSpaceComplexity(t *testing.T) {
+	n := 5
+	// Constant order
+	spaceConstant(n)
+	// Linear order
+	spaceLinear(n)
+	spaceLinearRecur(n)
+	// Exponential order
+	spaceQuadratic(n)
+	spaceQuadraticRecur(n)
+	// Exponential order
+	root := buildTree(n)
+	PrintTree(root)
+}

en/codes/go/chapter_computational_complexity/time_complexity.go

@@ -0,0 +1,130 @@
+// File: time_complexity.go
+// Created Time: 2022-12-13
+// Author: msk397 (machangxinq@gmail.com)
+
+package chapter_computational_complexity
+
+/* Constant order */
+func constant(n int) int {
+	count := 0
+	size := 100000
+	for i := 0; i < size; i++ {
+		count++
+	}
+	return count
+}
+
+/* Linear order */
+func linear(n int) int {
+	count := 0
+	for i := 0; i < n; i++ {
+		count++
+	}
+	return count
+}
+
+/* Linear order (traversing array) */
+func arrayTraversal(nums []int) int {
+	count := 0
+	// Number of iterations is proportional to the array length
+	for range nums {
+		count++
+	}
+	return count
+}
+
+/* Exponential order */
+func quadratic(n int) int {
+	count := 0
+	// Number of iterations is quadratically related to the data size n
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			count++
+		}
+	}
+	return count
+}
+
+/* Quadratic order (bubble sort) */
+func bubbleSort(nums []int) int {
+	count := 0 // Counter
+	// Outer loop: unsorted range is [0, i]
+	for i := len(nums) - 1; i > 0; i-- {
+		// Inner loop: swap the largest element in the unsorted range [0, i] to the rightmost end of that range
+		for j := 0; j < i; j++ {
+			if nums[j] > nums[j+1] {
+				// Swap nums[j] and nums[j + 1]
+				tmp := nums[j]
+				nums[j] = nums[j+1]
+				nums[j+1] = tmp
+				count += 3 // Element swap includes 3 unit operations
+			}
+		}
+	}
+	return count
+}
+
+/* Exponential order (loop implementation) */
+func exponential(n int) int {
+	count, base := 0, 1
+	// Cells divide into two every round, forming sequence 1, 2, 4, 8, ..., 2^(n-1)
+	for i := 0; i < n; i++ {
+		for j := 0; j < base; j++ {
+			count++
+		}
+		base *= 2
+	}
+	// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
+	return count
+}
+
+/* Exponential order (recursive implementation) */
+func expRecur(n int) int {
+	if n == 1 {
+		return 1
+	}
+	return expRecur(n-1) + expRecur(n-1) + 1
+}
+
+/* Logarithmic order (loop implementation) */
+func logarithmic(n int) int {
+	count := 0
+	for n > 1 {
+		n = n / 2
+		count++
+	}
+	return count
+}
+
+/* Logarithmic order (recursive implementation) */
+func logRecur(n int) int {
+	if n <= 1 {
+		return 0
+	}
+	return logRecur(n/2) + 1
+}
+
+/* Linearithmic order */
+func linearLogRecur(n int) int {
+	if n <= 1 {
+		return 1
+	}
+	count := linearLogRecur(n/2) + linearLogRecur(n/2)
+	for i := 0; i < n; i++ {
+		count++
+	}
+	return count
+}
+
+/* Factorial order (recursive implementation) */
+func factorialRecur(n int) int {
+	if n == 0 {
+		return 1
+	}
+	count := 0
+	// Split from 1 into n
+	for i := 0; i < n; i++ {
+		count += factorialRecur(n - 1)
+	}
+	return count
+}

en/codes/go/chapter_computational_complexity/time_complexity_test.go

@@ -0,0 +1,48 @@
+// File: time_complexity_test.go
+// Created Time: 2022-12-13
+// Author: msk397 (machangxinq@gmail.com)
+
+package chapter_computational_complexity
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestTimeComplexity(t *testing.T) {
+	n := 8
+	fmt.Println("Input data size n =", n)
+
+	count := constant(n)
+	fmt.Println("Number of constant-order operations =", count)
+
+	count = linear(n)
+	fmt.Println("Number of linear-order operations =", count)
+	count = arrayTraversal(make([]int, n))
+	fmt.Println("Number of linear-order (array traversal) operations =", count)
+
+	count = quadratic(n)
+	fmt.Println("Number of quadratic-order operations =", count)
+	nums := make([]int, n)
+	for i := 0; i < n; i++ {
+		nums[i] = n - i
+	}
+	count = bubbleSort(nums)
+	fmt.Println("Number of quadratic-order (bubble sort) operations =", count)
+
+	count = exponential(n)
+	fmt.Println("Number of exponential-order (loop implementation) operations =", count)
+	count = expRecur(n)
+	fmt.Println("Number of exponential-order (recursive implementation) operations =", count)
+
+	count = logarithmic(n)
+	fmt.Println("Number of logarithmic-order (loop implementation) operations =", count)
+	count = logRecur(n)
+	fmt.Println("Number of logarithmic-order (recursive implementation) operations =", count)
+
+	count = linearLogRecur(n)
+	fmt.Println("Number of linearithmic-order (recursive implementation) operations =", count)
+
+	count = factorialRecur(n)
+	fmt.Println("Number of factorial-order (recursive implementation) operations =", count)
+}

en/codes/go/chapter_computational_complexity/worst_best_time_complexity.go

@@ -0,0 +1,35 @@
+// File: worst_best_time_complexity.go
+// Created Time: 2022-12-13
+// Author: msk397 (machangxinq@gmail.com), cathay (cathaycchen@gmail.com)
+
+package chapter_computational_complexity
+
+import (
+	"math/rand"
+)
+
+/* Generate an array with elements { 1, 2, ..., n }, order shuffled */
+func randomNumbers(n int) []int {
+	nums := make([]int, n)
+	// Generate array nums = { 1, 2, 3, ..., n }
+	for i := 0; i < n; i++ {
+		nums[i] = i + 1
+	}
+	// Randomly shuffle array elements
+	rand.Shuffle(len(nums), func(i, j int) {
+		nums[i], nums[j] = nums[j], nums[i]
+	})
+	return nums
+}
+
+/* Find the index of number 1 in array nums */
+func findOne(nums []int) int {
+	for i := 0; i < len(nums); i++ {
+		// When element 1 is at the head of the array, best time complexity O(1) is achieved
+		// When element 1 is at the tail of the array, worst time complexity O(n) is achieved
+		if nums[i] == 1 {
+			return i
+		}
+	}
+	return -1
+}

en/codes/go/chapter_computational_complexity/worst_best_time_complexity_test.go

@@ -0,0 +1,20 @@
+// File: worst_best_time_complexity_test.go
+// Created Time: 2022-12-13
+// Author: msk397 (machangxinq@gmail.com), cathay (cathaycchen@gmail.com)
+
+package chapter_computational_complexity
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestWorstBestTimeComplexity(t *testing.T) {
+	for i := 0; i < 10; i++ {
+		n := 100
+		nums := randomNumbers(n)
+		index := findOne(nums)
+		fmt.Println("\nAfter shuffling array [ 1, 2, ..., n ] =", nums)
+		fmt.Println("Index of number 1 is", index)
+	}
+}

en/codes/go/chapter_divide_and_conquer/binary_search_recur.go

@@ -0,0 +1,34 @@
+// File: binary_search_recur.go
+// Created Time: 2023-07-19
+// Author: hongyun-robot (1836017030@qq.com)
+
+package chapter_divide_and_conquer
+
+/* Binary search: problem f(i, j) */
+func dfs(nums []int, target, i, j int) int {
+	// If interval is empty, indicating no target element, return -1
+	if i > j {
+		return -1
+	}
+	// Calculate midpoint index
+	m := i + ((j - i) >> 1)
+	// Compare midpoint with target element
+	if nums[m] < target {
+		// If smaller, recurse on right half of array
+		// Recursion subproblem f(m+1, j)
+		return dfs(nums, target, m+1, j)
+	} else if nums[m] > target {
+		// If larger, recurse on left half of array
+		// Recursion subproblem f(i, m-1)
+		return dfs(nums, target, i, m-1)
+	} else {
+		// Found the target element, return its index
+		return m
+	}
+}
+
+/* Binary search */
+func binarySearch(nums []int, target int) int {
+	n := len(nums)
+	return dfs(nums, target, 0, n-1)
+}

en/codes/go/chapter_divide_and_conquer/binary_search_recur_test.go

@@ -0,0 +1,20 @@
+// File: binary_search_recur_test.go
+// Created Time: 2023-07-19
+// Author: hongyun-robot (1836017030@qq.com)
+
+package chapter_divide_and_conquer
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestBinarySearch(t *testing.T) {
+	nums := []int{1, 3, 6, 8, 12, 15, 23, 26, 31, 35}
+	target := 6
+	noTarget := 99
+	targetIndex := binarySearch(nums, target)
+	fmt.Println("Index of target element 6 = ", targetIndex)
+	noTargetIndex := binarySearch(nums, noTarget)
+	fmt.Println("Index of non-existent target element = ", noTargetIndex)
+}

en/codes/go/chapter_divide_and_conquer/build_tree.go

@@ -0,0 +1,37 @@
+// File: build_tree.go
+// Created Time: 2023-07-20
+// Author: hongyun-robot (1836017030@qq.com)
+
+package chapter_divide_and_conquer
+
+import . "github.com/krahets/hello-algo/pkg"
+
+/* Build binary tree: divide and conquer */
+func dfsBuildTree(preorder []int, inorderMap map[int]int, i, l, r int) *TreeNode {
+	// Terminate when the subtree interval is empty
+	if r-l < 0 {
+		return nil
+	}
+	// Initialize the root node
+	root := NewTreeNode(preorder[i])
+	// Query m to divide the left and right subtrees
+	m := inorderMap[preorder[i]]
+	// Subproblem: build the left subtree
+	root.Left = dfsBuildTree(preorder, inorderMap, i+1, l, m-1)
+	// Subproblem: build the right subtree
+	root.Right = dfsBuildTree(preorder, inorderMap, i+1+m-l, m+1, r)
+	// Return the root node
+	return root
+}
+
+/* Build binary tree */
+func buildTree(preorder, inorder []int) *TreeNode {
+	// Initialize hash map, storing the mapping from inorder elements to indices
+	inorderMap := make(map[int]int, len(inorder))
+	for i := 0; i < len(inorder); i++ {
+		inorderMap[inorder[i]] = i
+	}
+
+	root := dfsBuildTree(preorder, inorderMap, 0, 0, len(inorder)-1)
+	return root
+}

en/codes/go/chapter_divide_and_conquer/build_tree_test.go

@@ -0,0 +1,25 @@
+// File: build_tree_test.go
+// Created Time: 2023-07-20
+// Author: hongyun-robot (1836017030@qq.com)
+
+package chapter_divide_and_conquer
+
+import (
+	"fmt"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestBuildTree(t *testing.T) {
+	preorder := []int{3, 9, 2, 1, 7}
+	inorder := []int{9, 3, 1, 2, 7}
+	fmt.Print("Preorder traversal = ")
+	PrintSlice(preorder)
+	fmt.Print("Inorder traversal = ")
+	PrintSlice(inorder)
+
+	root := buildTree(preorder, inorder)
+	fmt.Println("The constructed binary tree is:")
+	PrintTree(root)
+}

en/codes/go/chapter_divide_and_conquer/hanota.go

@@ -0,0 +1,39 @@
+// File: hanota.go
+// Created Time: 2023-07-21
+// Author: hongyun-robot (1836017030@qq.com)
+
+package chapter_divide_and_conquer
+
+import "container/list"
+
+/* Move a disk */
+func move(src, tar *list.List) {
+	// Take out a disk from the top of src
+	pan := src.Back()
+	// Place the disk on top of tar
+	tar.PushBack(pan.Value)
+	// Remove top disk from src
+	src.Remove(pan)
+}
+
+/* Solve the Tower of Hanoi problem f(i) */
+func dfsHanota(i int, src, buf, tar *list.List) {
+	// If there is only one disk left in src, move it directly to tar
+	if i == 1 {
+		move(src, tar)
+		return
+	}
+	// Subproblem f(i-1): move the top i-1 disks from src to buf using tar
+	dfsHanota(i-1, src, tar, buf)
+	// Subproblem f(1): move the remaining disk from src to tar
+	move(src, tar)
+	// Subproblem f(i-1): move the top i-1 disks from buf to tar using src
+	dfsHanota(i-1, buf, src, tar)
+}
+
+/* Solve the Tower of Hanoi problem */
+func solveHanota(A, B, C *list.List) {
+	n := A.Len()
+	// Move the top n disks from A to C using B
+	dfsHanota(n, A, B, C)
+}

en/codes/go/chapter_divide_and_conquer/hanota_test.go

@@ -0,0 +1,40 @@
+// File: hanota_test.go
+// Created Time: 2023-07-21
+// Author: hongyun-robot (1836017030@qq.com)
+
+package chapter_divide_and_conquer
+
+import (
+	"container/list"
+	"fmt"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestHanota(t *testing.T) {
+	// The tail of the list is the top of the rod
+	A := list.New()
+	for i := 5; i > 0; i-- {
+		A.PushBack(i)
+	}
+	B := list.New()
+	C := list.New()
+	fmt.Println("In initial state:")
+	fmt.Print("A = ")
+	PrintList(A)
+	fmt.Print("B = ")
+	PrintList(B)
+	fmt.Print("C = ")
+	PrintList(C)
+
+	solveHanota(A, B, C)
+
+	fmt.Println("After disk movement is complete:")
+	fmt.Print("A = ")
+	PrintList(A)
+	fmt.Print("B = ")
+	PrintList(B)
+	fmt.Print("C = ")
+	PrintList(C)
+}

en/codes/go/chapter_dynamic_programming/climbing_stairs_backtrack.go

@@ -0,0 +1,36 @@
+// File: climbing_stairs_backtrack.go
+// Created Time: 2023-07-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* Backtracking */
+func backtrack(choices []int, state, n int, res []int) {
+	// When climbing to the n-th stair, add 1 to the solution count
+	if state == n {
+		res[0] = res[0] + 1
+	}
+	// Traverse all choices
+	for _, choice := range choices {
+		// Pruning: not allowed to go beyond the n-th stair
+		if state+choice > n {
+			continue
+		}
+		// Attempt: make choice, update state
+		backtrack(choices, state+choice, n, res)
+		// Backtrack
+	}
+}
+
+/* Climbing stairs: Backtracking */
+func climbingStairsBacktrack(n int) int {
+	// Can choose to climb up 1 or 2 stairs
+	choices := []int{1, 2}
+	// Start climbing from the 0-th stair
+	state := 0
+	res := make([]int, 1)
+	// Use res[0] to record the solution count
+	res[0] = 0
+	backtrack(choices, state, n, res)
+	return res[0]
+}

en/codes/go/chapter_dynamic_programming/climbing_stairs_constraint_dp.go

@@ -0,0 +1,25 @@
+// File: climbing_stairs_constraint_dp.go
+// Created Time: 2023-07-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* Climbing stairs with constraint: Dynamic programming */
+func climbingStairsConstraintDP(n int) int {
+	if n == 1 || n == 2 {
+		return 1
+	}
+	// Initialize dp table, used to store solutions to subproblems
+	dp := make([][3]int, n+1)
+	// Initial state: preset the solution to the smallest subproblem
+	dp[1][1] = 1
+	dp[1][2] = 0
+	dp[2][1] = 0
+	dp[2][2] = 1
+	// State transition: gradually solve larger subproblems from smaller ones
+	for i := 3; i <= n; i++ {
+		dp[i][1] = dp[i-1][2]
+		dp[i][2] = dp[i-2][1] + dp[i-2][2]
+	}
+	return dp[n][1] + dp[n][2]
+}

en/codes/go/chapter_dynamic_programming/climbing_stairs_dfs.go

@@ -0,0 +1,21 @@
+// File: climbing_stairs_dfs.go
+// Created Time: 2023-07-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* Search */
+func dfs(i int) int {
+	// Known dp[1] and dp[2], return them
+	if i == 1 || i == 2 {
+		return i
+	}
+	// dp[i] = dp[i-1] + dp[i-2]
+	count := dfs(i-1) + dfs(i-2)
+	return count
+}
+
+/* Climbing stairs: Search */
+func climbingStairsDFS(n int) int {
+	return dfs(n)
+}

en/codes/go/chapter_dynamic_programming/climbing_stairs_dfs_mem.go

@@ -0,0 +1,32 @@
+// File: climbing_stairs_dfs_mem.go
+// Created Time: 2023-07-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* Memoization search */
+func dfsMem(i int, mem []int) int {
+	// Known dp[1] and dp[2], return them
+	if i == 1 || i == 2 {
+		return i
+	}
+	// If record dp[i] exists, return it directly
+	if mem[i] != -1 {
+		return mem[i]
+	}
+	// dp[i] = dp[i-1] + dp[i-2]
+	count := dfsMem(i-1, mem) + dfsMem(i-2, mem)
+	// Record dp[i]
+	mem[i] = count
+	return count
+}
+
+/* Climbing stairs: Memoization search */
+func climbingStairsDFSMem(n int) int {
+	// mem[i] records the total number of solutions to climb to the i-th stair, -1 means no record
+	mem := make([]int, n+1)
+	for i := range mem {
+		mem[i] = -1
+	}
+	return dfsMem(n, mem)
+}

en/codes/go/chapter_dynamic_programming/climbing_stairs_dp.go

@@ -0,0 +1,35 @@
+// File: climbing_stairs_dp.go
+// Created Time: 2023-07-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* Climbing stairs: Dynamic programming */
+func climbingStairsDP(n int) int {
+	if n == 1 || n == 2 {
+		return n
+	}
+	// Initialize dp table, used to store solutions to subproblems
+	dp := make([]int, n+1)
+	// Initial state: preset the solution to the smallest subproblem
+	dp[1] = 1
+	dp[2] = 2
+	// State transition: gradually solve larger subproblems from smaller ones
+	for i := 3; i <= n; i++ {
+		dp[i] = dp[i-1] + dp[i-2]
+	}
+	return dp[n]
+}
+
+/* Climbing stairs: Space-optimized dynamic programming */
+func climbingStairsDPComp(n int) int {
+	if n == 1 || n == 2 {
+		return n
+	}
+	a, b := 1, 2
+	// State transition: gradually solve larger subproblems from smaller ones
+	for i := 3; i <= n; i++ {
+		a, b = b, a+b
+	}
+	return b
+}

en/codes/go/chapter_dynamic_programming/climbing_stairs_test.go

@@ -0,0 +1,57 @@
+// File: climbing_stairs_test.go
+// Created Time: 2023-07-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestClimbingStairsBacktrack(t *testing.T) {
+	n := 9
+	res := climbingStairsBacktrack(n)
+	fmt.Printf("Climbing %d stairs has %d solutions\n", n, res)
+}
+
+func TestClimbingStairsDFS(t *testing.T) {
+	n := 9
+	res := climbingStairsDFS(n)
+	fmt.Printf("Climbing %d stairs has %d solutions\n", n, res)
+}
+
+func TestClimbingStairsDFSMem(t *testing.T) {
+	n := 9
+	res := climbingStairsDFSMem(n)
+	fmt.Printf("Climbing %d stairs has %d solutions\n", n, res)
+}
+
+func TestClimbingStairsDP(t *testing.T) {
+	n := 9
+	res := climbingStairsDP(n)
+	fmt.Printf("Climbing %d stairs has %d solutions\n", n, res)
+}
+
+func TestClimbingStairsDPComp(t *testing.T) {
+	n := 9
+	res := climbingStairsDPComp(n)
+	fmt.Printf("Climbing %d stairs has %d solutions\n", n, res)
+}
+
+func TestClimbingStairsConstraintDP(t *testing.T) {
+	n := 9
+	res := climbingStairsConstraintDP(n)
+	fmt.Printf("Climbing %d stairs has %d solutions\n", n, res)
+}
+
+func TestMinCostClimbingStairsDPComp(t *testing.T) {
+	cost := []int{0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1}
+	fmt.Printf("Input stair cost list is %v\n", cost)
+
+	res := minCostClimbingStairsDP(cost)
+	fmt.Printf("Minimum cost to climb stairs is %d\n", res)
+
+	res = minCostClimbingStairsDPComp(cost)
+	fmt.Printf("Minimum cost to climb stairs is %d\n", res)
+}

en/codes/go/chapter_dynamic_programming/coin_change.go

@@ -0,0 +1,66 @@
+// File: coin_change.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import "math"
+
+/* Coin change: Dynamic programming */
+func coinChangeDP(coins []int, amt int) int {
+	n := len(coins)
+	max := amt + 1
+	// Initialize dp table
+	dp := make([][]int, n+1)
+	for i := 0; i <= n; i++ {
+		dp[i] = make([]int, amt+1)
+	}
+	// State transition: first row and first column
+	for a := 1; a <= amt; a++ {
+		dp[0][a] = max
+	}
+	// State transition: rest of the rows and columns
+	for i := 1; i <= n; i++ {
+		for a := 1; a <= amt; a++ {
+			if coins[i-1] > a {
+				// If exceeds target amount, don't select coin i
+				dp[i][a] = dp[i-1][a]
+			} else {
+				// The smaller value between not selecting and selecting coin i
+				dp[i][a] = int(math.Min(float64(dp[i-1][a]), float64(dp[i][a-coins[i-1]]+1)))
+			}
+		}
+	}
+	if dp[n][amt] != max {
+		return dp[n][amt]
+	}
+	return -1
+}
+
+/* Coin change: Dynamic programming */
+func coinChangeDPComp(coins []int, amt int) int {
+	n := len(coins)
+	max := amt + 1
+	// Initialize dp table
+	dp := make([]int, amt+1)
+	for i := 1; i <= amt; i++ {
+		dp[i] = max
+	}
+	// State transition
+	for i := 1; i <= n; i++ {
+		// Traverse in forward order
+		for a := 1; a <= amt; a++ {
+			if coins[i-1] > a {
+				// If exceeds target amount, don't select coin i
+				dp[a] = dp[a]
+			} else {
+				// The smaller value between not selecting and selecting coin i
+				dp[a] = int(math.Min(float64(dp[a]), float64(dp[a-coins[i-1]]+1)))
+			}
+		}
+	}
+	if dp[amt] != max {
+		return dp[amt]
+	}
+	return -1
+}

en/codes/go/chapter_dynamic_programming/coin_change_ii.go

@@ -0,0 +1,54 @@
+// File: coin_change_ii.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* Coin change II: Dynamic programming */
+func coinChangeIIDP(coins []int, amt int) int {
+	n := len(coins)
+	// Initialize dp table
+	dp := make([][]int, n+1)
+	for i := 0; i <= n; i++ {
+		dp[i] = make([]int, amt+1)
+	}
+	// Initialize first column
+	for i := 0; i <= n; i++ {
+		dp[i][0] = 1
+	}
+	// State transition: rest of the rows and columns
+	for i := 1; i <= n; i++ {
+		for a := 1; a <= amt; a++ {
+			if coins[i-1] > a {
+				// If exceeds target amount, don't select coin i
+				dp[i][a] = dp[i-1][a]
+			} else {
+				// Sum of the two options: not selecting and selecting coin i
+				dp[i][a] = dp[i-1][a] + dp[i][a-coins[i-1]]
+			}
+		}
+	}
+	return dp[n][amt]
+}
+
+/* Coin change II: Space-optimized dynamic programming */
+func coinChangeIIDPComp(coins []int, amt int) int {
+	n := len(coins)
+	// Initialize dp table
+	dp := make([]int, amt+1)
+	dp[0] = 1
+	// State transition
+	for i := 1; i <= n; i++ {
+		// Traverse in forward order
+		for a := 1; a <= amt; a++ {
+			if coins[i-1] > a {
+				// If exceeds target amount, don't select coin i
+				dp[a] = dp[a]
+			} else {
+				// Sum of the two options: not selecting and selecting coin i
+				dp[a] = dp[a] + dp[a-coins[i-1]]
+			}
+		}
+	}
+	return dp[amt]
+}

en/codes/go/chapter_dynamic_programming/coin_change_test.go

@@ -0,0 +1,23 @@
+// File: coin_change_test.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestCoinChange(t *testing.T) {
+	coins := []int{1, 2, 5}
+	amt := 4
+
+	// Dynamic programming
+	res := coinChangeDP(coins, amt)
+	fmt.Printf("Minimum number of coins needed to make target amount is %d\n", res)
+
+	// Space-optimized dynamic programming
+	res = coinChangeDPComp(coins, amt)
+	fmt.Printf("Minimum number of coins needed to make target amount is %d\n", res)
+}

en/codes/go/chapter_dynamic_programming/edit_distance.go

@@ -0,0 +1,129 @@
+// File: edit_distance.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* Edit distance: Brute-force search */
+func editDistanceDFS(s string, t string, i int, j int) int {
+	// If both s and t are empty, return 0
+	if i == 0 && j == 0 {
+		return 0
+	}
+	// If s is empty, return length of t
+	if i == 0 {
+		return j
+	}
+	// If t is empty, return length of s
+	if j == 0 {
+		return i
+	}
+	// If two characters are equal, skip both characters
+	if s[i-1] == t[j-1] {
+		return editDistanceDFS(s, t, i-1, j-1)
+	}
+	// Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+	insert := editDistanceDFS(s, t, i, j-1)
+	deleted := editDistanceDFS(s, t, i-1, j)
+	replace := editDistanceDFS(s, t, i-1, j-1)
+	// Return minimum edit steps
+	return MinInt(MinInt(insert, deleted), replace) + 1
+}
+
+/* Edit distance: Memoization search */
+func editDistanceDFSMem(s string, t string, mem [][]int, i int, j int) int {
+	// If both s and t are empty, return 0
+	if i == 0 && j == 0 {
+		return 0
+	}
+	// If s is empty, return length of t
+	if i == 0 {
+		return j
+	}
+	// If t is empty, return length of s
+	if j == 0 {
+		return i
+	}
+	// If there's a record, return it directly
+	if mem[i][j] != -1 {
+		return mem[i][j]
+	}
+	// If two characters are equal, skip both characters
+	if s[i-1] == t[j-1] {
+		return editDistanceDFSMem(s, t, mem, i-1, j-1)
+	}
+	// Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+	insert := editDistanceDFSMem(s, t, mem, i, j-1)
+	deleted := editDistanceDFSMem(s, t, mem, i-1, j)
+	replace := editDistanceDFSMem(s, t, mem, i-1, j-1)
+	// Record and return minimum edit steps
+	mem[i][j] = MinInt(MinInt(insert, deleted), replace) + 1
+	return mem[i][j]
+}
+
+/* Edit distance: Dynamic programming */
+func editDistanceDP(s string, t string) int {
+	n := len(s)
+	m := len(t)
+	dp := make([][]int, n+1)
+	for i := 0; i <= n; i++ {
+		dp[i] = make([]int, m+1)
+	}
+	// State transition: first row and first column
+	for i := 1; i <= n; i++ {
+		dp[i][0] = i
+	}
+	for j := 1; j <= m; j++ {
+		dp[0][j] = j
+	}
+	// State transition: rest of the rows and columns
+	for i := 1; i <= n; i++ {
+		for j := 1; j <= m; j++ {
+			if s[i-1] == t[j-1] {
+				// If two characters are equal, skip both characters
+				dp[i][j] = dp[i-1][j-1]
+			} else {
+				// Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+				dp[i][j] = MinInt(MinInt(dp[i][j-1], dp[i-1][j]), dp[i-1][j-1]) + 1
+			}
+		}
+	}
+	return dp[n][m]
+}
+
+/* Edit distance: Space-optimized dynamic programming */
+func editDistanceDPComp(s string, t string) int {
+	n := len(s)
+	m := len(t)
+	dp := make([]int, m+1)
+	// State transition: first row
+	for j := 1; j <= m; j++ {
+		dp[j] = j
+	}
+	// State transition: rest of the rows
+	for i := 1; i <= n; i++ {
+		// State transition: first column
+		leftUp := dp[0] // Temporarily store dp[i-1, j-1]
+		dp[0] = i
+		// State transition: rest of the columns
+		for j := 1; j <= m; j++ {
+			temp := dp[j]
+			if s[i-1] == t[j-1] {
+				// If two characters are equal, skip both characters
+				dp[j] = leftUp
+			} else {
+				// Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+				dp[j] = MinInt(MinInt(dp[j-1], dp[j]), leftUp) + 1
+			}
+			leftUp = temp // Update for next round's dp[i-1, j-1]
+		}
+	}
+	return dp[m]
+}
+
+func MinInt(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}

en/codes/go/chapter_dynamic_programming/edit_distance_test.go

@@ -0,0 +1,40 @@
+// File: edit_distance_test.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestEditDistanceDFS(test *testing.T) {
+	s := "bag"
+	t := "pack"
+	n := len(s)
+	m := len(t)
+
+	// Brute-force search
+	res := editDistanceDFS(s, t, n, m)
+	fmt.Printf("Changing %s to %s requires a minimum of %d edits\n", s, t, res)
+
+	// Memoization search
+	mem := make([][]int, n+1)
+	for i := 0; i <= n; i++ {
+		mem[i] = make([]int, m+1)
+		for j := 0; j <= m; j++ {
+			mem[i][j] = -1
+		}
+	}
+	res = editDistanceDFSMem(s, t, mem, n, m)
+	fmt.Printf("Changing %s to %s requires a minimum of %d edits\n", s, t, res)
+
+	// Dynamic programming
+	res = editDistanceDP(s, t)
+	fmt.Printf("Changing %s to %s requires a minimum of %d edits\n", s, t, res)
+
+	// Space-optimized dynamic programming
+	res = editDistanceDPComp(s, t)
+	fmt.Printf("Changing %s to %s requires a minimum of %d edits\n", s, t, res)
+}

en/codes/go/chapter_dynamic_programming/knapsack.go

@@ -0,0 +1,87 @@
+// File: knapsack.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import "math"
+
+/* 0-1 knapsack: Brute-force search */
+func knapsackDFS(wgt, val []int, i, c int) int {
+	// If all items have been selected or knapsack has no remaining capacity, return value 0
+	if i == 0 || c == 0 {
+		return 0
+	}
+	// If exceeds knapsack capacity, can only choose not to put it in
+	if wgt[i-1] > c {
+		return knapsackDFS(wgt, val, i-1, c)
+	}
+	// Calculate the maximum value of not putting in and putting in item i
+	no := knapsackDFS(wgt, val, i-1, c)
+	yes := knapsackDFS(wgt, val, i-1, c-wgt[i-1]) + val[i-1]
+	// Return the larger value of the two options
+	return int(math.Max(float64(no), float64(yes)))
+}
+
+/* 0-1 knapsack: Memoization search */
+func knapsackDFSMem(wgt, val []int, mem [][]int, i, c int) int {
+	// If all items have been selected or knapsack has no remaining capacity, return value 0
+	if i == 0 || c == 0 {
+		return 0
+	}
+	// If there's a record, return it directly
+	if mem[i][c] != -1 {
+		return mem[i][c]
+	}
+	// If exceeds knapsack capacity, can only choose not to put it in
+	if wgt[i-1] > c {
+		return knapsackDFSMem(wgt, val, mem, i-1, c)
+	}
+	// Calculate the maximum value of not putting in and putting in item i
+	no := knapsackDFSMem(wgt, val, mem, i-1, c)
+	yes := knapsackDFSMem(wgt, val, mem, i-1, c-wgt[i-1]) + val[i-1]
+	// Return the larger value of the two options
+	mem[i][c] = int(math.Max(float64(no), float64(yes)))
+	return mem[i][c]
+}
+
+/* 0-1 knapsack: Dynamic programming */
+func knapsackDP(wgt, val []int, cap int) int {
+	n := len(wgt)
+	// Initialize dp table
+	dp := make([][]int, n+1)
+	for i := 0; i <= n; i++ {
+		dp[i] = make([]int, cap+1)
+	}
+	// State transition
+	for i := 1; i <= n; i++ {
+		for c := 1; c <= cap; c++ {
+			if wgt[i-1] > c {
+				// If exceeds knapsack capacity, don't select item i
+				dp[i][c] = dp[i-1][c]
+			} else {
+				// The larger value between not selecting and selecting item i
+				dp[i][c] = int(math.Max(float64(dp[i-1][c]), float64(dp[i-1][c-wgt[i-1]]+val[i-1])))
+			}
+		}
+	}
+	return dp[n][cap]
+}
+
+/* 0-1 knapsack: Space-optimized dynamic programming */
+func knapsackDPComp(wgt, val []int, cap int) int {
+	n := len(wgt)
+	// Initialize dp table
+	dp := make([]int, cap+1)
+	// State transition
+	for i := 1; i <= n; i++ {
+		// Traverse in reverse order
+		for c := cap; c >= 1; c-- {
+			if wgt[i-1] <= c {
+				// The larger value between not selecting and selecting item i
+				dp[c] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))
+			}
+		}
+	}
+	return dp[cap]
+}

en/codes/go/chapter_dynamic_programming/knapsack_test.go

@@ -0,0 +1,54 @@
+// File: knapsack_test.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestKnapsack(t *testing.T) {
+	wgt := []int{10, 20, 30, 40, 50}
+	val := []int{50, 120, 150, 210, 240}
+	c := 50
+	n := len(wgt)
+
+	// Brute-force search
+	res := knapsackDFS(wgt, val, n, c)
+	fmt.Printf("Maximum item value not exceeding knapsack capacity is %d\n", res)
+
+	// Memoization search
+	mem := make([][]int, n+1)
+	for i := 0; i <= n; i++ {
+		mem[i] = make([]int, c+1)
+		for j := 0; j <= c; j++ {
+			mem[i][j] = -1
+		}
+	}
+	res = knapsackDFSMem(wgt, val, mem, n, c)
+	fmt.Printf("Maximum item value not exceeding knapsack capacity is %d\n", res)
+
+	// Dynamic programming
+	res = knapsackDP(wgt, val, c)
+	fmt.Printf("Maximum item value not exceeding knapsack capacity is %d\n", res)
+
+	// Space-optimized dynamic programming
+	res = knapsackDPComp(wgt, val, c)
+	fmt.Printf("Maximum item value not exceeding knapsack capacity is %d\n", res)
+}
+
+func TestUnboundedKnapsack(t *testing.T) {
+	wgt := []int{1, 2, 3}
+	val := []int{5, 11, 15}
+	c := 4
+
+	// Dynamic programming
+	res := unboundedKnapsackDP(wgt, val, c)
+	fmt.Printf("Maximum item value not exceeding knapsack capacity is %d\n", res)
+
+	// Space-optimized dynamic programming
+	res = unboundedKnapsackDPComp(wgt, val, c)
+	fmt.Printf("Maximum item value not exceeding knapsack capacity is %d\n", res)
+}

en/codes/go/chapter_dynamic_programming/min_cost_climbing_stairs_dp.go

@@ -0,0 +1,52 @@
+// File: min_cost_climbing_stairs_dp.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* Minimum cost climbing stairs: Dynamic programming */
+func minCostClimbingStairsDP(cost []int) int {
+	n := len(cost) - 1
+	if n == 1 || n == 2 {
+		return cost[n]
+	}
+	min := func(a, b int) int {
+		if a < b {
+			return a
+		}
+		return b
+	}
+	// Initialize dp table, used to store solutions to subproblems
+	dp := make([]int, n+1)
+	// Initial state: preset the solution to the smallest subproblem
+	dp[1] = cost[1]
+	dp[2] = cost[2]
+	// State transition: gradually solve larger subproblems from smaller ones
+	for i := 3; i <= n; i++ {
+		dp[i] = min(dp[i-1], dp[i-2]) + cost[i]
+	}
+	return dp[n]
+}
+
+/* Minimum cost climbing stairs: Space-optimized dynamic programming */
+func minCostClimbingStairsDPComp(cost []int) int {
+	n := len(cost) - 1
+	if n == 1 || n == 2 {
+		return cost[n]
+	}
+	min := func(a, b int) int {
+		if a < b {
+			return a
+		}
+		return b
+	}
+	// Initial state: preset the solution to the smallest subproblem
+	a, b := cost[1], cost[2]
+	// State transition: gradually solve larger subproblems from smaller ones
+	for i := 3; i <= n; i++ {
+		tmp := b
+		b = min(a, tmp) + cost[i]
+		a = tmp
+	}
+	return b
+}

en/codes/go/chapter_dynamic_programming/min_path_sum.go

@@ -0,0 +1,94 @@
+// File: min_path_sum.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import "math"
+
+/* Minimum path sum: Brute-force search */
+func minPathSumDFS(grid [][]int, i, j int) int {
+	// If it's the top-left cell, terminate the search
+	if i == 0 && j == 0 {
+		return grid[0][0]
+	}
+	// If row or column index is out of bounds, return +∞ cost
+	if i < 0 || j < 0 {
+		return math.MaxInt
+	}
+	// Calculate the minimum path cost from top-left to (i-1, j) and (i, j-1)
+	up := minPathSumDFS(grid, i-1, j)
+	left := minPathSumDFS(grid, i, j-1)
+	// Return the minimum path cost from top-left to (i, j)
+	return int(math.Min(float64(left), float64(up))) + grid[i][j]
+}
+
+/* Minimum path sum: Memoization search */
+func minPathSumDFSMem(grid, mem [][]int, i, j int) int {
+	// If it's the top-left cell, terminate the search
+	if i == 0 && j == 0 {
+		return grid[0][0]
+	}
+	// If row or column index is out of bounds, return +∞ cost
+	if i < 0 || j < 0 {
+		return math.MaxInt
+	}
+	// If there's a record, return it directly
+	if mem[i][j] != -1 {
+		return mem[i][j]
+	}
+	// Minimum path cost for left and upper cells
+	up := minPathSumDFSMem(grid, mem, i-1, j)
+	left := minPathSumDFSMem(grid, mem, i, j-1)
+	// Record and return the minimum path cost from top-left to (i, j)
+	mem[i][j] = int(math.Min(float64(left), float64(up))) + grid[i][j]
+	return mem[i][j]
+}
+
+/* Minimum path sum: Dynamic programming */
+func minPathSumDP(grid [][]int) int {
+	n, m := len(grid), len(grid[0])
+	// Initialize dp table
+	dp := make([][]int, n)
+	for i := 0; i < n; i++ {
+		dp[i] = make([]int, m)
+	}
+	dp[0][0] = grid[0][0]
+	// State transition: first row
+	for j := 1; j < m; j++ {
+		dp[0][j] = dp[0][j-1] + grid[0][j]
+	}
+	// State transition: first column
+	for i := 1; i < n; i++ {
+		dp[i][0] = dp[i-1][0] + grid[i][0]
+	}
+	// State transition: rest of the rows and columns
+	for i := 1; i < n; i++ {
+		for j := 1; j < m; j++ {
+			dp[i][j] = int(math.Min(float64(dp[i][j-1]), float64(dp[i-1][j]))) + grid[i][j]
+		}
+	}
+	return dp[n-1][m-1]
+}
+
+/* Minimum path sum: Space-optimized dynamic programming */
+func minPathSumDPComp(grid [][]int) int {
+	n, m := len(grid), len(grid[0])
+	// Initialize dp table
+	dp := make([]int, m)
+	// State transition: first row
+	dp[0] = grid[0][0]
+	for j := 1; j < m; j++ {
+		dp[j] = dp[j-1] + grid[0][j]
+	}
+	// State transition: rest of the rows and columns
+	for i := 1; i < n; i++ {
+		// State transition: first column
+		dp[0] = dp[0] + grid[i][0]
+		// State transition: rest of the columns
+		for j := 1; j < m; j++ {
+			dp[j] = int(math.Min(float64(dp[j-1]), float64(dp[j]))) + grid[i][j]
+		}
+	}
+	return dp[m-1]
+}

en/codes/go/chapter_dynamic_programming/min_path_sum_test.go

@@ -0,0 +1,43 @@
+// File: min_path_sum_test.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestMinPathSum(t *testing.T) {
+	grid := [][]int{
+		{1, 3, 1, 5},
+		{2, 2, 4, 2},
+		{5, 3, 2, 1},
+		{4, 3, 5, 2},
+	}
+	n, m := len(grid), len(grid[0])
+
+	// Brute-force search
+	res := minPathSumDFS(grid, n-1, m-1)
+	fmt.Printf("Minimum path sum from top-left to bottom-right is %d\n", res)
+
+	// Memoization search
+	mem := make([][]int, n)
+	for i := 0; i < n; i++ {
+		mem[i] = make([]int, m)
+		for j := 0; j < m; j++ {
+			mem[i][j] = -1
+		}
+	}
+	res = minPathSumDFSMem(grid, mem, n-1, m-1)
+	fmt.Printf("Minimum path sum from top-left to bottom-right is %d\n", res)
+
+	// Dynamic programming
+	res = minPathSumDP(grid)
+	fmt.Printf("Minimum path sum from top-left to bottom-right is %d\n", res)
+
+	// Space-optimized dynamic programming
+	res = minPathSumDPComp(grid)
+	fmt.Printf("Minimum path sum from top-left to bottom-right is %d\n", res)
+}

en/codes/go/chapter_dynamic_programming/unbounded_knapsack.go

@@ -0,0 +1,50 @@
+// File: unbounded_knapsack.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import "math"
+
+/* Unbounded knapsack: Dynamic programming */
+func unboundedKnapsackDP(wgt, val []int, cap int) int {
+	n := len(wgt)
+	// Initialize dp table
+	dp := make([][]int, n+1)
+	for i := 0; i <= n; i++ {
+		dp[i] = make([]int, cap+1)
+	}
+	// State transition
+	for i := 1; i <= n; i++ {
+		for c := 1; c <= cap; c++ {
+			if wgt[i-1] > c {
+				// If exceeds knapsack capacity, don't select item i
+				dp[i][c] = dp[i-1][c]
+			} else {
+				// The larger value between not selecting and selecting item i
+				dp[i][c] = int(math.Max(float64(dp[i-1][c]), float64(dp[i][c-wgt[i-1]]+val[i-1])))
+			}
+		}
+	}
+	return dp[n][cap]
+}
+
+/* Unbounded knapsack: Space-optimized dynamic programming */
+func unboundedKnapsackDPComp(wgt, val []int, cap int) int {
+	n := len(wgt)
+	// Initialize dp table
+	dp := make([]int, cap+1)
+	// State transition
+	for i := 1; i <= n; i++ {
+		for c := 1; c <= cap; c++ {
+			if wgt[i-1] > c {
+				// If exceeds knapsack capacity, don't select item i
+				dp[c] = dp[c]
+			} else {
+				// The larger value between not selecting and selecting item i
+				dp[c] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))
+			}
+		}
+	}
+	return dp[cap]
+}

en/codes/go/chapter_graph/graph_adjacency_list.go

@@ -0,0 +1,100 @@
+// File: graph_adjacency_list.go
+// Created Time: 2023-01-31
+// Author: Reanon (793584285@qq.com)
+
+package chapter_graph
+
+import (
+	"fmt"
+	"strconv"
+	"strings"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+/* Undirected graph class based on adjacency list */
+type graphAdjList struct {
+	// Adjacency list, key: vertex, value: all adjacent vertices of that vertex
+	adjList map[Vertex][]Vertex
+}
+
+/* Constructor */
+func newGraphAdjList(edges [][]Vertex) *graphAdjList {
+	g := &graphAdjList{
+		adjList: make(map[Vertex][]Vertex),
+	}
+	// Add all vertices and edges
+	for _, edge := range edges {
+		g.addVertex(edge[0])
+		g.addVertex(edge[1])
+		g.addEdge(edge[0], edge[1])
+	}
+	return g
+}
+
+/* Get the number of vertices */
+func (g *graphAdjList) size() int {
+	return len(g.adjList)
+}
+
+/* Add edge */
+func (g *graphAdjList) addEdge(vet1 Vertex, vet2 Vertex) {
+	_, ok1 := g.adjList[vet1]
+	_, ok2 := g.adjList[vet2]
+	if !ok1 || !ok2 || vet1 == vet2 {
+		panic("error")
+	}
+	// Add edge vet1 - vet2, add anonymous struct{},
+	g.adjList[vet1] = append(g.adjList[vet1], vet2)
+	g.adjList[vet2] = append(g.adjList[vet2], vet1)
+}
+
+/* Remove edge */
+func (g *graphAdjList) removeEdge(vet1 Vertex, vet2 Vertex) {
+	_, ok1 := g.adjList[vet1]
+	_, ok2 := g.adjList[vet2]
+	if !ok1 || !ok2 || vet1 == vet2 {
+		panic("error")
+	}
+	// Remove edge vet1 - vet2
+	g.adjList[vet1] = DeleteSliceElms(g.adjList[vet1], vet2)
+	g.adjList[vet2] = DeleteSliceElms(g.adjList[vet2], vet1)
+}
+
+/* Add vertex */
+func (g *graphAdjList) addVertex(vet Vertex) {
+	_, ok := g.adjList[vet]
+	if ok {
+		return
+	}
+	// Add a new linked list in the adjacency list
+	g.adjList[vet] = make([]Vertex, 0)
+}
+
+/* Remove vertex */
+func (g *graphAdjList) removeVertex(vet Vertex) {
+	_, ok := g.adjList[vet]
+	if !ok {
+		panic("error")
+	}
+	// Remove the linked list corresponding to vertex vet in the adjacency list
+	delete(g.adjList, vet)
+	// Traverse the linked lists of other vertices and remove all edges containing vet
+	for v, list := range g.adjList {
+		g.adjList[v] = DeleteSliceElms(list, vet)
+	}
+}
+
+/* Print adjacency list */
+func (g *graphAdjList) print() {
+	var builder strings.Builder
+	fmt.Printf("Adjacency list = \n")
+	for k, v := range g.adjList {
+		builder.WriteString("\t\t" + strconv.Itoa(k.Val) + ": ")
+		for _, vet := range v {
+			builder.WriteString(strconv.Itoa(vet.Val) + " ")
+		}
+		fmt.Println(builder.String())
+		builder.Reset()
+	}
+}

en/codes/go/chapter_graph/graph_adjacency_list_test.go

@@ -0,0 +1,45 @@
+// File: graph_adjacency_list_test.go
+// Created Time: 2023-01-31
+// Author: Reanon (793584285@qq.com)
+
+package chapter_graph
+
+import (
+	"fmt"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestGraphAdjList(t *testing.T) {
+	/* Add edge */
+	v := ValsToVets([]int{1, 3, 2, 5, 4})
+	edges := [][]Vertex{{v[0], v[1]}, {v[0], v[3]}, {v[1], v[2]}, {v[2], v[3]}, {v[2], v[4]}, {v[3], v[4]}}
+	graph := newGraphAdjList(edges)
+	fmt.Println("After initialization, graph is:")
+	graph.print()
+
+	/* Add edge */
+	// Vertices 1, 3 are v[0], v[1]
+	graph.addEdge(v[0], v[2])
+	fmt.Println("\nAfter adding edge 1-2, graph is")
+	graph.print()
+
+	/* Remove edge */
+	// Vertex 3 is v[1]
+	graph.removeEdge(v[0], v[1])
+	fmt.Println("\nAfter removing edge 1-3, graph is")
+	graph.print()
+
+	/* Add vertex */
+	v5 := NewVertex(6)
+	graph.addVertex(v5)
+	fmt.Println("\nAfter adding vertex 6, graph is")
+	graph.print()
+
+	/* Remove vertex */
+	// Vertex 3 is v[1]
+	graph.removeVertex(v[1])
+	fmt.Println("\nAfter removing vertex 3, graph is")
+	graph.print()
+}

en/codes/go/chapter_graph/graph_adjacency_matrix.go

@@ -0,0 +1,102 @@
+// File: graph_adjacency_matrix.go
+// Created Time: 2023-01-31
+// Author: Reanon (793584285@qq.com)
+
+package chapter_graph
+
+import "fmt"
+
+/* Undirected graph class based on adjacency matrix */
+type graphAdjMat struct {
+	// Vertex list, where the element represents the "vertex value" and the index represents the "vertex index"
+	vertices []int
+	// Adjacency matrix, where the row and column indices correspond to the "vertex index"
+	adjMat [][]int
+}
+
+/* Constructor */
+func newGraphAdjMat(vertices []int, edges [][]int) *graphAdjMat {
+	// Add vertex
+	n := len(vertices)
+	adjMat := make([][]int, n)
+	for i := range adjMat {
+		adjMat[i] = make([]int, n)
+	}
+	// Initialize graph
+	g := &graphAdjMat{
+		vertices: vertices,
+		adjMat:   adjMat,
+	}
+	// Add edge
+	// Note that the edges elements represent vertex indices, i.e., corresponding to the vertices element indices
+	for i := range edges {
+		g.addEdge(edges[i][0], edges[i][1])
+	}
+	return g
+}
+
+/* Get the number of vertices */
+func (g *graphAdjMat) size() int {
+	return len(g.vertices)
+}
+
+/* Add vertex */
+func (g *graphAdjMat) addVertex(val int) {
+	n := g.size()
+	// Add the value of the new vertex to the vertex list
+	g.vertices = append(g.vertices, val)
+	// Add a row to the adjacency matrix
+	newRow := make([]int, n)
+	g.adjMat = append(g.adjMat, newRow)
+	// Add a column to the adjacency matrix
+	for i := range g.adjMat {
+		g.adjMat[i] = append(g.adjMat[i], 0)
+	}
+}
+
+/* Remove vertex */
+func (g *graphAdjMat) removeVertex(index int) {
+	if index >= g.size() {
+		return
+	}
+	// Remove the vertex at index from the vertex list
+	g.vertices = append(g.vertices[:index], g.vertices[index+1:]...)
+	// Remove the row at index from the adjacency matrix
+	g.adjMat = append(g.adjMat[:index], g.adjMat[index+1:]...)
+	// Remove the column at index from the adjacency matrix
+	for i := range g.adjMat {
+		g.adjMat[i] = append(g.adjMat[i][:index], g.adjMat[i][index+1:]...)
+	}
+}
+
+/* Add edge */
+// Parameters i, j correspond to the vertices element indices
+func (g *graphAdjMat) addEdge(i, j int) {
+	// Handle index out of bounds and equality
+	if i < 0 || j < 0 || i >= g.size() || j >= g.size() || i == j {
+		fmt.Errorf("%s", "Index Out Of Bounds Exception")
+	}
+	// In an undirected graph, the adjacency matrix is symmetric about the main diagonal, i.e., (i, j) == (j, i)
+	g.adjMat[i][j] = 1
+	g.adjMat[j][i] = 1
+}
+
+/* Remove edge */
+// Parameters i, j correspond to the vertices element indices
+func (g *graphAdjMat) removeEdge(i, j int) {
+	// Handle index out of bounds and equality
+	if i < 0 || j < 0 || i >= g.size() || j >= g.size() || i == j {
+		fmt.Errorf("%s", "Index Out Of Bounds Exception")
+	}
+	g.adjMat[i][j] = 0
+	g.adjMat[j][i] = 0
+}
+
+/* Print adjacency matrix */
+func (g *graphAdjMat) print() {
+	fmt.Printf("\tVertex list = %v\n", g.vertices)
+	fmt.Printf("\tAdjacency matrix = \n")
+	for i := range g.adjMat {
+		fmt.Printf("\t\t\t%v\n", g.adjMat[i])
+	}
+}

en/codes/go/chapter_graph/graph_adjacency_matrix_test.go

@@ -0,0 +1,43 @@
+// File: graph_adjacency_matrix_test.go
+// Created Time: 2023-01-31
+// Author: Reanon (793584285@qq.com)
+
+package chapter_graph
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestGraphAdjMat(t *testing.T) {
+	/* Add edge */
+	// Note that the edges elements represent vertex indices, i.e., corresponding to the vertices element indices
+	vertices := []int{1, 3, 2, 5, 4}
+	edges := [][]int{{0, 1}, {1, 2}, {2, 3}, {0, 3}, {2, 4}, {3, 4}}
+	graph := newGraphAdjMat(vertices, edges)
+	fmt.Println("After initialization, graph is:")
+	graph.print()
+
+	/* Add edge */
+	// Add vertex
+	graph.addEdge(0, 2)
+	fmt.Println("After adding edge 1-2, graph is")
+	graph.print()
+
+	/* Remove edge */
+	// Vertices 1, 3 have indices 0, 1 respectively
+	graph.removeEdge(0, 1)
+	fmt.Println("After removing edge 1-3, graph is")
+	graph.print()
+
+	/* Add vertex */
+	graph.addVertex(6)
+	fmt.Println("After adding vertex 6, graph is")
+	graph.print()
+
+	/* Remove vertex */
+	// Vertex 3 has index 1
+	graph.removeVertex(1)
+	fmt.Println("After removing vertex 3, graph is")
+	graph.print()
+}

en/codes/go/chapter_graph/graph_bfs.go

@@ -0,0 +1,41 @@
+// File: graph_bfs.go
+// Created Time: 2023-02-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_graph
+
+import (
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+/* Breadth-first traversal */
+// Use adjacency list to represent the graph, in order to obtain all adjacent vertices of a specified vertex
+func graphBFS(g *graphAdjList, startVet Vertex) []Vertex {
+	// Vertex traversal sequence
+	res := make([]Vertex, 0)
+	// Hash set for recording vertices that have been visited
+	visited := make(map[Vertex]struct{})
+	visited[startVet] = struct{}{}
+	// Queue used to implement BFS, using slice to simulate queue
+	queue := make([]Vertex, 0)
+	queue = append(queue, startVet)
+	// Starting from vertex vet, loop until all vertices are visited
+	for len(queue) > 0 {
+		// Dequeue the front vertex
+		vet := queue[0]
+		queue = queue[1:]
+		// Record visited vertex
+		res = append(res, vet)
+		// Traverse all adjacent vertices of this vertex
+		for _, adjVet := range g.adjList[vet] {
+			_, isExist := visited[adjVet]
+			// Only enqueue unvisited vertices
+			if !isExist {
+				queue = append(queue, adjVet)
+				visited[adjVet] = struct{}{}
+			}
+		}
+	}
+	// Return vertex traversal sequence
+	return res
+}

en/codes/go/chapter_graph/graph_bfs_test.go

@@ -0,0 +1,29 @@
+// File: graph_bfs_test.go
+// Created Time: 2023-02-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_graph
+
+import (
+	"fmt"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestGraphBFS(t *testing.T) {
+	/* Add edge */
+	vets := ValsToVets([]int{0, 1, 2, 3, 4, 5, 6, 7, 8, 9})
+	edges := [][]Vertex{
+		{vets[0], vets[1]}, {vets[0], vets[3]}, {vets[1], vets[2]}, {vets[1], vets[4]},
+		{vets[2], vets[5]}, {vets[3], vets[4]}, {vets[3], vets[6]}, {vets[4], vets[5]},
+		{vets[4], vets[7]}, {vets[5], vets[8]}, {vets[6], vets[7]}, {vets[7], vets[8]}}
+	graph := newGraphAdjList(edges)
+	fmt.Println("After initialization, graph is:")
+	graph.print()
+
+	/* Breadth-first traversal */
+	res := graphBFS(graph, vets[0])
+	fmt.Println("Breadth-first traversal (BFS) vertex sequence is:")
+	PrintSlice(VetsToVals(res))
+}

en/codes/go/chapter_graph/graph_dfs.go

@@ -0,0 +1,36 @@
+// File: graph_dfs.go
+// Created Time: 2023-02-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_graph
+
+import (
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+/* Depth-first traversal helper function */
+func dfs(g *graphAdjList, visited map[Vertex]struct{}, res *[]Vertex, vet Vertex) {
+	// append operation returns a new reference, must reassign original reference to new slice's reference
+	*res = append(*res, vet)
+	visited[vet] = struct{}{}
+	// Traverse all adjacent vertices of this vertex
+	for _, adjVet := range g.adjList[vet] {
+		_, isExist := visited[adjVet]
+		// Recursively visit adjacent vertices
+		if !isExist {
+			dfs(g, visited, res, adjVet)
+		}
+	}
+}
+
+/* Depth-first traversal */
+// Use adjacency list to represent the graph, in order to obtain all adjacent vertices of a specified vertex
+func graphDFS(g *graphAdjList, startVet Vertex) []Vertex {
+	// Vertex traversal sequence
+	res := make([]Vertex, 0)
+	// Hash set for recording vertices that have been visited
+	visited := make(map[Vertex]struct{})
+	dfs(g, visited, &res, startVet)
+	// Return vertex traversal sequence
+	return res
+}

en/codes/go/chapter_graph/graph_dfs_test.go

@@ -0,0 +1,28 @@
+// File: graph_dfs_test.go
+// Created Time: 2023-02-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_graph
+
+import (
+	"fmt"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestGraphDFS(t *testing.T) {
+	/* Add edge */
+	vets := ValsToVets([]int{0, 1, 2, 3, 4, 5, 6})
+	edges := [][]Vertex{
+		{vets[0], vets[1]}, {vets[0], vets[3]}, {vets[1], vets[2]},
+		{vets[2], vets[5]}, {vets[4], vets[5]}, {vets[5], vets[6]}}
+	graph := newGraphAdjList(edges)
+	fmt.Println("After initialization, graph is:")
+	graph.print()
+
+	/* Depth-first traversal */
+	res := graphDFS(graph, vets[0])
+	fmt.Println("Depth-first traversal (DFS) vertex sequence is:")
+	PrintSlice(VetsToVals(res))
+}

en/codes/go/chapter_greedy/coin_change_greedy.go

@@ -0,0 +1,27 @@
+// File: coin_change_greedy.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_greedy
+
+/* Coin change: Greedy algorithm */
+func coinChangeGreedy(coins []int, amt int) int {
+	// Assume coins list is sorted
+	i := len(coins) - 1
+	count := 0
+	// Loop to make greedy choices until no remaining amount
+	for amt > 0 {
+		// Find the coin that is less than and closest to the remaining amount
+		for i > 0 && coins[i] > amt {
+			i--
+		}
+		// Choose coins[i]
+		amt -= coins[i]
+		count++
+	}
+	// If no feasible solution is found, return -1
+	if amt != 0 {
+		return -1
+	}
+	return count
+}

en/codes/go/chapter_greedy/coin_change_greedy_test.go

@@ -0,0 +1,35 @@
+// File: coin_change_greedy_test.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_greedy
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestCoinChangeGreedy(t *testing.T) {
+	// Greedy algorithm: Can guarantee finding the global optimal solution
+	coins := []int{1, 5, 10, 20, 50, 100}
+	amt := 186
+	res := coinChangeGreedy(coins, amt)
+	fmt.Printf("coins = %v, amt = %d\n", coins, amt)
+	fmt.Printf("Minimum number of coins needed to make %d is %d\n", amt, res)
+
+	// Greedy algorithm: Cannot guarantee finding the global optimal solution
+	coins = []int{1, 20, 50}
+	amt = 60
+	res = coinChangeGreedy(coins, amt)
+	fmt.Printf("coins = %v, amt = %d\n", coins, amt)
+	fmt.Printf("Minimum number of coins needed to make %d is %d\n", amt, res)
+	fmt.Println("Actually the minimum number needed is 3, i.e., 20 + 20 + 20")
+
+	// Greedy algorithm: Cannot guarantee finding the global optimal solution
+	coins = []int{1, 49, 50}
+	amt = 98
+	res = coinChangeGreedy(coins, amt)
+	fmt.Printf("coins = %v, amt = %d\n", coins, amt)
+	fmt.Printf("Minimum number of coins needed to make %d is %d\n", amt, res)
+	fmt.Println("Actually the minimum number needed is 2, i.e., 49 + 49")
+}

en/codes/go/chapter_greedy/fractional_knapsack.go

@@ -0,0 +1,41 @@
+// File: fractional_knapsack.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_greedy
+
+import "sort"
+
+/* Item */
+type Item struct {
+	w int // Item weight
+	v int // Item value
+}
+
+/* Fractional knapsack: Greedy algorithm */
+func fractionalKnapsack(wgt []int, val []int, cap int) float64 {
+	// Create item list with two attributes: weight, value
+	items := make([]Item, len(wgt))
+	for i := 0; i < len(wgt); i++ {
+		items[i] = Item{wgt[i], val[i]}
+	}
+	// Sort by unit value item.v / item.w from high to low
+	sort.Slice(items, func(i, j int) bool {
+		return float64(items[i].v)/float64(items[i].w) > float64(items[j].v)/float64(items[j].w)
+	})
+	// Loop for greedy selection
+	res := 0.0
+	for _, item := range items {
+		if item.w <= cap {
+			// If remaining capacity is sufficient, put the entire current item into the knapsack
+			res += float64(item.v)
+			cap -= item.w
+		} else {
+			// If remaining capacity is insufficient, put part of the current item into the knapsack
+			res += float64(item.v) / float64(item.w) * float64(cap)
+			// No remaining capacity, so break out of the loop
+			break
+		}
+	}
+	return res
+}

en/codes/go/chapter_greedy/fractional_knapsack_test.go

@@ -0,0 +1,20 @@
+// File: fractional_knapsack_test.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_greedy
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestFractionalKnapsack(t *testing.T) {
+	wgt := []int{10, 20, 30, 40, 50}
+	val := []int{50, 120, 150, 210, 240}
+	capacity := 50
+
+	// Greedy algorithm
+	res := fractionalKnapsack(wgt, val, capacity)
+	fmt.Println("Maximum item value not exceeding knapsack capacity is", res)
+}

en/codes/go/chapter_greedy/max_capacity.go

@@ -0,0 +1,28 @@
+// File: max_capacity.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_greedy
+
+import "math"
+
+/* Max capacity: Greedy algorithm */
+func maxCapacity(ht []int) int {
+	// Initialize i, j to be at both ends of the array
+	i, j := 0, len(ht)-1
+	// Initial max capacity is 0
+	res := 0
+	// Loop for greedy selection until the two boards meet
+	for i < j {
+		// Update max capacity
+		capacity := int(math.Min(float64(ht[i]), float64(ht[j]))) * (j - i)
+		res = int(math.Max(float64(res), float64(capacity)))
+		// Move the shorter board inward
+		if ht[i] < ht[j] {
+			i++
+		} else {
+			j--
+		}
+	}
+	return res
+}

en/codes/go/chapter_greedy/max_capacity_test.go

@@ -0,0 +1,18 @@
+// File: max_capacity_test.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_greedy
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestMaxCapacity(t *testing.T) {
+	ht := []int{3, 8, 5, 2, 7, 7, 3, 4}
+
+	// Greedy algorithm
+	res := maxCapacity(ht)
+	fmt.Println("Maximum capacity is", res)
+}

en/codes/go/chapter_greedy/max_product_cutting.go

@@ -0,0 +1,28 @@
+// File: max_product_cutting.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_greedy
+
+import "math"
+
+/* Max product cutting: Greedy algorithm */
+func maxProductCutting(n int) int {
+	// When n <= 3, must cut out a 1
+	if n <= 3 {
+		return 1 * (n - 1)
+	}
+	// Greedily cut out 3, a is the number of 3s, b is the remainder
+	a := n / 3
+	b := n % 3
+	if b == 1 {
+		// When the remainder is 1, convert a pair of 1 * 3 to 2 * 2
+		return int(math.Pow(3, float64(a-1))) * 2 * 2
+	}
+	if b == 2 {
+		// When the remainder is 2, do nothing
+		return int(math.Pow(3, float64(a))) * 2
+	}
+	// When the remainder is 0, do nothing
+	return int(math.Pow(3, float64(a)))
+}

en/codes/go/chapter_greedy/max_product_cutting_test.go

@@ -0,0 +1,17 @@
+// File: max_product_cutting_test.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_greedy
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestMaxProductCutting(t *testing.T) {
+	n := 58
+	// Greedy algorithm
+	res := maxProductCutting(n)
+	fmt.Println("Maximum cutting product is", res)
+}

en/codes/go/chapter_hashing/array_hash_map.go

@@ -0,0 +1,97 @@
+// File: array_hash_map.go
+// Created Time: 2022-12-14
+// Author: msk397 (machangxinq@gmail.com)
+
+package chapter_hashing
+
+import "fmt"
+
+/* Key-value pair */
+type pair struct {
+	key int
+	val string
+}
+
+/* Hash table based on array implementation */
+type arrayHashMap struct {
+	buckets []*pair
+}
+
+/* Initialize hash table */
+func newArrayHashMap() *arrayHashMap {
+	// Initialize array with 100 buckets
+	buckets := make([]*pair, 100)
+	return &arrayHashMap{buckets: buckets}
+}
+
+/* Hash function */
+func (a *arrayHashMap) hashFunc(key int) int {
+	index := key % 100
+	return index
+}
+
+/* Query operation */
+func (a *arrayHashMap) get(key int) string {
+	index := a.hashFunc(key)
+	pair := a.buckets[index]
+	if pair == nil {
+		return "Not Found"
+	}
+	return pair.val
+}
+
+/* Add operation */
+func (a *arrayHashMap) put(key int, val string) {
+	pair := &pair{key: key, val: val}
+	index := a.hashFunc(key)
+	a.buckets[index] = pair
+}
+
+/* Remove operation */
+func (a *arrayHashMap) remove(key int) {
+	index := a.hashFunc(key)
+	// Set to nil to delete
+	a.buckets[index] = nil
+}
+
+/* Get all key pairs */
+func (a *arrayHashMap) pairSet() []*pair {
+	var pairs []*pair
+	for _, pair := range a.buckets {
+		if pair != nil {
+			pairs = append(pairs, pair)
+		}
+	}
+	return pairs
+}
+
+/* Get all keys */
+func (a *arrayHashMap) keySet() []int {
+	var keys []int
+	for _, pair := range a.buckets {
+		if pair != nil {
+			keys = append(keys, pair.key)
+		}
+	}
+	return keys
+}
+
+/* Get all values */
+func (a *arrayHashMap) valueSet() []string {
+	var values []string
+	for _, pair := range a.buckets {
+		if pair != nil {
+			values = append(values, pair.val)
+		}
+	}
+	return values
+}
+
+/* Print hash table */
+func (a *arrayHashMap) print() {
+	for _, pair := range a.buckets {
+		if pair != nil {
+			fmt.Println(pair.key, "->", pair.val)
+		}
+	}
+}

en/codes/go/chapter_hashing/array_hash_map_test.go

@@ -0,0 +1,52 @@
+// File: array_hash_map_test.go
+// Created Time: 2022-12-14
+// Author: msk397 (machangxinq@gmail.com)
+
+package chapter_hashing
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestArrayHashMap(t *testing.T) {
+	/* Initialize hash table */
+	hmap := newArrayHashMap()
+
+	/* Add operation */
+	// Add key-value pair (key, value) to the hash table
+	hmap.put(12836, "Xiao Ha")
+	hmap.put(15937, "Xiao Luo")
+	hmap.put(16750, "Xiao Suan")
+	hmap.put(13276, "Xiao Fa")
+	hmap.put(10583, "Xiao Ya")
+	fmt.Println("\nAfter adding is complete, hash table is\nKey -> Value")
+	hmap.print()
+
+	/* Query operation */
+	// Input key into hash table to get value
+	name := hmap.get(15937)
+	fmt.Println("\nInput student ID 15937, query name " + name)
+
+	/* Remove operation */
+	// Remove key-value pair (key, value) from hash table
+	hmap.remove(10583)
+	fmt.Println("\nAfter removing 10583, hash table is\nKey -> Value")
+	hmap.print()
+
+	/* Traverse hash table */
+	fmt.Println("\nTraverse key-value pairs Key->Value")
+	for _, kv := range hmap.pairSet() {
+		fmt.Println(kv.key, " -> ", kv.val)
+	}
+
+	fmt.Println("\nTraverse keys only Key")
+	for _, key := range hmap.keySet() {
+		fmt.Println(key)
+	}
+
+	fmt.Println("\nTraverse values only Value")
+	for _, val := range hmap.valueSet() {
+		fmt.Println(val)
+	}
+}

en/codes/go/chapter_hashing/hash_collision_test.go

@@ -0,0 +1,62 @@
+// File: hash_collision_test.go
+// Created Time: 2022-12-14
+// Author: msk397 (machangxinq@gmail.com)
+
+package chapter_hashing
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestHashMapChaining(t *testing.T) {
+	/* Initialize hash table */
+	hmap := newHashMapChaining()
+
+	/* Add operation */
+	// Add key-value pair (key, value) to the hash table
+	hmap.put(12836, "Xiao Ha")
+	hmap.put(15937, "Xiao Luo")
+	hmap.put(16750, "Xiao Suan")
+	hmap.put(13276, "Xiao Fa")
+	hmap.put(10583, "Xiao Ya")
+	fmt.Println("\nAfter adding is complete, hash table is\nKey -> Value")
+	hmap.print()
+
+	/* Query operation */
+	// Input key into hash table to get value
+	name := hmap.get(15937)
+	fmt.Println("\nInput student ID 15937, found name", name)
+
+	/* Remove operation */
+	// Remove key-value pair (key, value) from hash table
+	hmap.remove(12836)
+	fmt.Println("\nAfter removing 12836, hash table is\nKey -> Value")
+	hmap.print()
+}
+
+func TestHashMapOpenAddressing(t *testing.T) {
+	/* Initialize hash table */
+	hmap := newHashMapOpenAddressing()
+
+	/* Add operation */
+	// Add key-value pair (key, value) to the hash table
+	hmap.put(12836, "Xiao Ha")
+	hmap.put(15937, "Xiao Luo")
+	hmap.put(16750, "Xiao Suan")
+	hmap.put(13276, "Xiao Fa")
+	hmap.put(10583, "Xiao Ya")
+	fmt.Println("\nAfter adding is complete, hash table is\nKey -> Value")
+	hmap.print()
+
+	/* Query operation */
+	// Input key into hash table to get value
+	name := hmap.get(13276)
+	fmt.Println("\nInput student ID 13276, query name ", name)
+
+	/* Remove operation */
+	// Remove key-value pair (key, value) from hash table
+	hmap.remove(16750)
+	fmt.Println("\nAfter removing 16750, hash table is\nKey -> Value")
+	hmap.print()
+}

en/codes/go/chapter_hashing/hash_map_chaining.go

@@ -0,0 +1,134 @@
+// File: hash_map_chaining.go
+// Created Time: 2023-06-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_hashing
+
+import (
+	"fmt"
+	"strconv"
+	"strings"
+)
+
+/* Hash table with separate chaining */
+type hashMapChaining struct {
+	size        int      // Number of key-value pairs
+	capacity    int      // Hash table capacity
+	loadThres   float64  // Load factor threshold for triggering expansion
+	extendRatio int      // Expansion multiplier
+	buckets     [][]pair // Bucket array
+}
+
+/* Constructor */
+func newHashMapChaining() *hashMapChaining {
+	buckets := make([][]pair, 4)
+	for i := 0; i < 4; i++ {
+		buckets[i] = make([]pair, 0)
+	}
+	return &hashMapChaining{
+		size:        0,
+		capacity:    4,
+		loadThres:   2.0 / 3.0,
+		extendRatio: 2,
+		buckets:     buckets,
+	}
+}
+
+/* Hash function */
+func (m *hashMapChaining) hashFunc(key int) int {
+	return key % m.capacity
+}
+
+/* Load factor */
+func (m *hashMapChaining) loadFactor() float64 {
+	return float64(m.size) / float64(m.capacity)
+}
+
+/* Query operation */
+func (m *hashMapChaining) get(key int) string {
+	idx := m.hashFunc(key)
+	bucket := m.buckets[idx]
+	// Traverse bucket, if key is found, return corresponding val
+	for _, p := range bucket {
+		if p.key == key {
+			return p.val
+		}
+	}
+	// Return empty string if key not found
+	return ""
+}
+
+/* Add operation */
+func (m *hashMapChaining) put(key int, val string) {
+	// When load factor exceeds threshold, perform expansion
+	if m.loadFactor() > m.loadThres {
+		m.extend()
+	}
+	idx := m.hashFunc(key)
+	// Traverse bucket, if specified key is encountered, update corresponding val and return
+	for i := range m.buckets[idx] {
+		if m.buckets[idx][i].key == key {
+			m.buckets[idx][i].val = val
+			return
+		}
+	}
+	// If key does not exist, append key-value pair to the end
+	p := pair{
+		key: key,
+		val: val,
+	}
+	m.buckets[idx] = append(m.buckets[idx], p)
+	m.size += 1
+}
+
+/* Remove operation */
+func (m *hashMapChaining) remove(key int) {
+	idx := m.hashFunc(key)
+	// Traverse bucket and remove key-value pair from it
+	for i, p := range m.buckets[idx] {
+		if p.key == key {
+			// Slice deletion
+			m.buckets[idx] = append(m.buckets[idx][:i], m.buckets[idx][i+1:]...)
+			m.size -= 1
+			break
+		}
+	}
+}
+
+/* Expand hash table */
+func (m *hashMapChaining) extend() {
+	// Temporarily store the original hash table
+	tmpBuckets := make([][]pair, len(m.buckets))
+	for i := 0; i < len(m.buckets); i++ {
+		tmpBuckets[i] = make([]pair, len(m.buckets[i]))
+		copy(tmpBuckets[i], m.buckets[i])
+	}
+	// Initialize expanded new hash table
+	m.capacity *= m.extendRatio
+	m.buckets = make([][]pair, m.capacity)
+	for i := 0; i < m.capacity; i++ {
+		m.buckets[i] = make([]pair, 0)
+	}
+	m.size = 0
+	// Move key-value pairs from original hash table to new hash table
+	for _, bucket := range tmpBuckets {
+		for _, p := range bucket {
+			m.put(p.key, p.val)
+		}
+	}
+}
+
+/* Print hash table */
+func (m *hashMapChaining) print() {
+	var builder strings.Builder
+
+	for _, bucket := range m.buckets {
+		builder.WriteString("[")
+		for _, p := range bucket {
+			builder.WriteString(strconv.Itoa(p.key) + " -> " + p.val + " ")
+		}
+		builder.WriteString("]")
+		fmt.Println(builder.String())
+		builder.Reset()
+	}
+}

en/codes/go/chapter_hashing/hash_map_open_addressing.go

@@ -0,0 +1,126 @@
+// File: hash_map_open_addressing.go
+// Created Time: 2023-06-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_hashing
+
+import (
+	"fmt"
+)
+
+/* Hash table with open addressing */
+type hashMapOpenAddressing struct {
+	size        int     // Number of key-value pairs
+	capacity    int     // Hash table capacity
+	loadThres   float64 // Load factor threshold for triggering expansion
+	extendRatio int     // Expansion multiplier
+	buckets     []*pair // Bucket array
+	TOMBSTONE   *pair   // Removal marker
+}
+
+/* Constructor */
+func newHashMapOpenAddressing() *hashMapOpenAddressing {
+	return &hashMapOpenAddressing{
+		size:        0,
+		capacity:    4,
+		loadThres:   2.0 / 3.0,
+		extendRatio: 2,
+		buckets:     make([]*pair, 4),
+		TOMBSTONE:   &pair{-1, "-1"},
+	}
+}
+
+/* Hash function */
+func (h *hashMapOpenAddressing) hashFunc(key int) int {
+	return key % h.capacity // Calculate hash value based on key
+}
+
+/* Load factor */
+func (h *hashMapOpenAddressing) loadFactor() float64 {
+	return float64(h.size) / float64(h.capacity) // Calculate current load factor
+}
+
+/* Search for bucket index corresponding to key */
+func (h *hashMapOpenAddressing) findBucket(key int) int {
+	index := h.hashFunc(key) // Get initial index
+	firstTombstone := -1     // Record position of first TOMBSTONE encountered
+	for h.buckets[index] != nil {
+		if h.buckets[index].key == key {
+			if firstTombstone != -1 {
+				// If a removal marker was encountered before, move the key-value pair to that index
+				h.buckets[firstTombstone] = h.buckets[index]
+				h.buckets[index] = h.TOMBSTONE
+				return firstTombstone // Return the moved bucket index
+			}
+			return index // Return found index
+		}
+		if firstTombstone == -1 && h.buckets[index] == h.TOMBSTONE {
+			firstTombstone = index // Record position of first deletion marker encountered
+		}
+		index = (index + 1) % h.capacity // Linear probing, wrap around to head if past tail
+	}
+	// If key does not exist, return the index for insertion
+	if firstTombstone != -1 {
+		return firstTombstone
+	}
+	return index
+}
+
+/* Query operation */
+func (h *hashMapOpenAddressing) get(key int) string {
+	index := h.findBucket(key) // Search for bucket index corresponding to key
+	if h.buckets[index] != nil && h.buckets[index] != h.TOMBSTONE {
+		return h.buckets[index].val // If key-value pair is found, return corresponding val
+	}
+	return "" // Return "" if key-value pair does not exist
+}
+
+/* Add operation */
+func (h *hashMapOpenAddressing) put(key int, val string) {
+	if h.loadFactor() > h.loadThres {
+		h.extend() // When load factor exceeds threshold, perform expansion
+	}
+	index := h.findBucket(key) // Search for bucket index corresponding to key
+	if h.buckets[index] == nil || h.buckets[index] == h.TOMBSTONE {
+		h.buckets[index] = &pair{key, val} // If key-value pair does not exist, add the key-value pair
+		h.size++
+	} else {
+		h.buckets[index].val = val // If key-value pair found, overwrite val
+	}
+}
+
+/* Remove operation */
+func (h *hashMapOpenAddressing) remove(key int) {
+	index := h.findBucket(key) // Search for bucket index corresponding to key
+	if h.buckets[index] != nil && h.buckets[index] != h.TOMBSTONE {
+		h.buckets[index] = h.TOMBSTONE // If key-value pair is found, overwrite it with removal marker
+		h.size--
+	}
+}
+
+/* Expand hash table */
+func (h *hashMapOpenAddressing) extend() {
+	oldBuckets := h.buckets               // Temporarily store the original hash table
+	h.capacity *= h.extendRatio           // Update capacity
+	h.buckets = make([]*pair, h.capacity) // Initialize expanded new hash table
+	h.size = 0                            // Reset size
+	// Move key-value pairs from original hash table to new hash table
+	for _, pair := range oldBuckets {
+		if pair != nil && pair != h.TOMBSTONE {
+			h.put(pair.key, pair.val)
+		}
+	}
+}
+
+/* Print hash table */
+func (h *hashMapOpenAddressing) print() {
+	for _, pair := range h.buckets {
+		if pair == nil {
+			fmt.Println("nil")
+		} else if pair == h.TOMBSTONE {
+			fmt.Println("TOMBSTONE")
+		} else {
+			fmt.Printf("%d -> %s\n", pair.key, pair.val)
+		}
+	}
+}

en/codes/go/chapter_hashing/hash_map_test.go

@@ -0,0 +1,74 @@
+// File: hash_map_test.go
+// Created Time: 2022-12-14
+// Author: msk397 (machangxinq@gmail.com)
+
+package chapter_hashing
+
+import (
+	"fmt"
+	"strconv"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestHashMap(t *testing.T) {
+	/* Initialize hash table */
+	hmap := make(map[int]string)
+
+	/* Add operation */
+	// Add key-value pair (key, value) to the hash table
+	hmap[12836] = "Xiao Ha"
+	hmap[15937] = "Xiao Luo"
+	hmap[16750] = "Xiao Suan"
+	hmap[13276] = "Xiao Fa"
+	hmap[10583] = "Xiao Ya"
+	fmt.Println("\nAfter adding is complete, hash table is\nKey -> Value")
+	PrintMap(hmap)
+
+	/* Query operation */
+	// Input key into hash table to get value
+	name := hmap[15937]
+	fmt.Println("\nInput student ID 15937, query name ", name)
+
+	/* Remove operation */
+	// Remove key-value pair (key, value) from hash table
+	delete(hmap, 10583)
+	fmt.Println("\nAfter removing 10583, hash table is\nKey -> Value")
+	PrintMap(hmap)
+
+	/* Traverse hash table */
+	// Traverse key-value pairs
+	fmt.Println("\nTraverse key-value pairs Key->Value")
+	for key, value := range hmap {
+		fmt.Println(key, "->", value)
+	}
+	// Traverse keys only
+	fmt.Println("\nTraverse keys only Key")
+	for key := range hmap {
+		fmt.Println(key)
+	}
+	// Traverse values only
+	fmt.Println("\nTraverse values only Value")
+	for _, value := range hmap {
+		fmt.Println(value)
+	}
+}
+
+func TestSimpleHash(t *testing.T) {
+	var hash int
+
+	key := "Hello Algo"
+
+	hash = addHash(key)
+	fmt.Println("Additive hash value is " + strconv.Itoa(hash))
+
+	hash = mulHash(key)
+	fmt.Println("Multiplicative hash value is " + strconv.Itoa(hash))
+
+	hash = xorHash(key)
+	fmt.Println("XOR hash value is " + strconv.Itoa(hash))
+
+	hash = rotHash(key)
+	fmt.Println("Rotational hash value is " + strconv.Itoa(hash))
+}

en/codes/go/chapter_hashing/simple_hash.go

@@ -0,0 +1,55 @@
+// File: simple_hash.go
+// Created Time: 2023-06-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_hashing
+
+import "fmt"
+
+/* Additive hash */
+func addHash(key string) int {
+	var hash int64
+	var modulus int64
+
+	modulus = 1000000007
+	for _, b := range []byte(key) {
+		hash = (hash + int64(b)) % modulus
+	}
+	return int(hash)
+}
+
+/* Multiplicative hash */
+func mulHash(key string) int {
+	var hash int64
+	var modulus int64
+
+	modulus = 1000000007
+	for _, b := range []byte(key) {
+		hash = (31*hash + int64(b)) % modulus
+	}
+	return int(hash)
+}
+
+/* XOR hash */
+func xorHash(key string) int {
+	hash := 0
+	modulus := 1000000007
+	for _, b := range []byte(key) {
+		fmt.Println(int(b))
+		hash ^= int(b)
+		hash = (31*hash + int(b)) % modulus
+	}
+	return hash & modulus
+}
+
+/* Rotational hash */
+func rotHash(key string) int {
+	var hash int64
+	var modulus int64
+
+	modulus = 1000000007
+	for _, b := range []byte(key) {
+		hash = ((hash << 4) ^ (hash >> 28) ^ int64(b)) % modulus
+	}
+	return int(hash)
+}

en/codes/go/chapter_heap/heap.go

@@ -0,0 +1,45 @@
+// File: heap.go
+// Created Time: 2023-01-12
+// Author: Reanon (793584285@qq.com)
+
+package chapter_heap
+
+// In Go, integer max heap can be built by implementing heap.Interface
+// Implementing heap.Interface requires also implementing sort.Interface
+type intHeap []any
+
+// Push function of heap.Interface, implements pushing element to heap
+func (h *intHeap) Push(x any) {
+	// Push and Pop use pointer receiver as parameter
+	// Because they not only adjust the slice content, but also modify the slice length.
+	*h = append(*h, x.(int))
+}
+
+// Pop function of heap.Interface, implements popping heap top element
+func (h *intHeap) Pop() any {
+	// Element to be popped is stored at the end
+	last := (*h)[len(*h)-1]
+	*h = (*h)[:len(*h)-1]
+	return last
+}
+
+// Len function of sort.Interface
+func (h *intHeap) Len() int {
+	return len(*h)
+}
+
+// Less function of sort.Interface
+func (h *intHeap) Less(i, j int) bool {
+	// If implementing min heap, need to change to less than sign
+	return (*h)[i].(int) > (*h)[j].(int)
+}
+
+// Swap function of sort.Interface
+func (h *intHeap) Swap(i, j int) {
+	(*h)[i], (*h)[j] = (*h)[j], (*h)[i]
+}
+
+// Top gets heap top element
+func (h *intHeap) Top() any {
+	return (*h)[0]
+}

en/codes/go/chapter_heap/heap_test.go

@@ -0,0 +1,101 @@
+// File: heap_test.go
+// Created Time: 2023-01-12
+// Author: Reanon (793584285@qq.com)
+
+package chapter_heap
+
+import (
+	"container/heap"
+	"fmt"
+	"strconv"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func testPush(h *intHeap, val int) {
+	// Call heap.Interface function to add element
+	heap.Push(h, val)
+	fmt.Printf("\nAfter element %d pushes to heap \n", val)
+	PrintHeap(*h)
+}
+
+func testPop(h *intHeap) {
+	// Call heap.Interface function to remove element
+	val := heap.Pop(h)
+	fmt.Printf("\nAfter heap top element %d pops from heap \n", val)
+	PrintHeap(*h)
+}
+
+func TestHeap(t *testing.T) {
+	/* Initialize heap */
+	// Consider negating the elements before entering the heap, which can reverse the size relationship, thus implementing max heap
+	maxHeap := &intHeap{}
+	heap.Init(maxHeap)
+	/* Element enters heap */
+	testPush(maxHeap, 1)
+	testPush(maxHeap, 3)
+	testPush(maxHeap, 2)
+	testPush(maxHeap, 5)
+	testPush(maxHeap, 4)
+
+	/* Check if heap is empty */
+	top := maxHeap.Top()
+	fmt.Printf("Heap top element is %d\n", top)
+
+	/* Time complexity is O(n), not O(nlogn) */
+	testPop(maxHeap)
+	testPop(maxHeap)
+	testPop(maxHeap)
+	testPop(maxHeap)
+	testPop(maxHeap)
+
+	/* Get heap size */
+	size := len(*maxHeap)
+	fmt.Printf("Heap size is %d\n", size)
+
+	/* Check if heap is empty */
+	isEmpty := len(*maxHeap) == 0
+	fmt.Printf("Is heap empty %t\n", isEmpty)
+}
+
+func TestMyHeap(t *testing.T) {
+	/* Initialize heap */
+	// Consider negating the elements before entering the heap, which can reverse the size relationship, thus implementing max heap
+	maxHeap := newMaxHeap([]any{9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2})
+	fmt.Printf("After input array and building heap\n")
+	maxHeap.print()
+
+	/* Check if heap is empty */
+	peek := maxHeap.peek()
+	fmt.Printf("\nHeap top element is %d\n", peek)
+
+	/* Element enters heap */
+	val := 7
+	maxHeap.push(val)
+	fmt.Printf("\nAfter element %d enters heap\n", val)
+	maxHeap.print()
+
+	/* Time complexity is O(n), not O(nlogn) */
+	peek = maxHeap.pop()
+	fmt.Printf("\nAfter heap top element %d exits heap\n", peek)
+	maxHeap.print()
+
+	/* Get heap size */
+	size := maxHeap.size()
+	fmt.Printf("\nHeap element count is %d\n", size)
+
+	/* Check if heap is empty */
+	isEmpty := maxHeap.isEmpty()
+	fmt.Printf("\nIs heap empty %t\n", isEmpty)
+}
+
+func TestTopKHeap(t *testing.T) {
+	/* Initialize heap */
+	// Consider negating the elements before entering the heap, which can reverse the size relationship, thus implementing max heap
+	nums := []int{1, 7, 6, 3, 2}
+	k := 3
+	res := topKHeap(nums, k)
+	fmt.Printf("The largest " + strconv.Itoa(k) + " elements are")
+	PrintHeap(*res)
+}

en/codes/go/chapter_heap/my_heap.go

@@ -0,0 +1,140 @@
+// File: my_heap.go
+// Created Time: 2023-01-12
+// Author: Reanon (793584285@qq.com)
+
+package chapter_heap
+
+import (
+	"fmt"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+type maxHeap struct {
+	// Use slice instead of array to avoid expansion issues
+	data []any
+}
+
+/* Constructor, build empty heap */
+func newHeap() *maxHeap {
+	return &maxHeap{
+		data: make([]any, 0),
+	}
+}
+
+/* Constructor, build heap from slice */
+func newMaxHeap(nums []any) *maxHeap {
+	// Add list elements to heap as is
+	h := &maxHeap{data: nums}
+	for i := h.parent(len(h.data) - 1); i >= 0; i-- {
+		// Heapify all nodes except leaf nodes
+		h.siftDown(i)
+	}
+	return h
+}
+
+/* Get index of left child node */
+func (h *maxHeap) left(i int) int {
+	return 2*i + 1
+}
+
+/* Get index of right child node */
+func (h *maxHeap) right(i int) int {
+	return 2*i + 2
+}
+
+/* Get index of parent node */
+func (h *maxHeap) parent(i int) int {
+	// Floor division
+	return (i - 1) / 2
+}
+
+/* Swap elements */
+func (h *maxHeap) swap(i, j int) {
+	h.data[i], h.data[j] = h.data[j], h.data[i]
+}
+
+/* Get heap size */
+func (h *maxHeap) size() int {
+	return len(h.data)
+}
+
+/* Check if heap is empty */
+func (h *maxHeap) isEmpty() bool {
+	return len(h.data) == 0
+}
+
+/* Access top element */
+func (h *maxHeap) peek() any {
+	return h.data[0]
+}
+
+/* Element enters heap */
+func (h *maxHeap) push(val any) {
+	// Add node
+	h.data = append(h.data, val)
+	// Heapify from bottom to top
+	h.siftUp(len(h.data) - 1)
+}
+
+/* Starting from node i, heapify from bottom to top */
+func (h *maxHeap) siftUp(i int) {
+	for true {
+		// Get parent node of node i
+		p := h.parent(i)
+		// When "crossing root node" or "node needs no repair", end heapify
+		if p < 0 || h.data[i].(int) <= h.data[p].(int) {
+			break
+		}
+		// Swap two nodes
+		h.swap(i, p)
+		// Loop upward heapify
+		i = p
+	}
+}
+
+/* Element exits heap */
+func (h *maxHeap) pop() any {
+	// Handle empty case
+	if h.isEmpty() {
+		fmt.Println("error")
+		return nil
+	}
+	// Delete node
+	h.swap(0, h.size()-1)
+	// Remove node
+	val := h.data[len(h.data)-1]
+	h.data = h.data[:len(h.data)-1]
+	// Return top element
+	h.siftDown(0)
+
+	// Return heap top element
+	return val
+}
+
+/* Starting from node i, heapify from top to bottom */
+func (h *maxHeap) siftDown(i int) {
+	for true {
+		// Find node with maximum value among nodes i, l, r, denoted as max
+		l, r, max := h.left(i), h.right(i), i
+		if l < h.size() && h.data[l].(int) > h.data[max].(int) {
+			max = l
+		}
+		if r < h.size() && h.data[r].(int) > h.data[max].(int) {
+			max = r
+		}
+		// Swap two nodes
+		if max == i {
+			break
+		}
+		// Swap two nodes
+		h.swap(i, max)
+		// Loop downwards heapification
+		i = max
+	}
+}
+
+/* Driver Code */
+func (h *maxHeap) print() {
+	PrintHeap(h.data)
+}

en/codes/go/chapter_heap/top_k.go

@@ -0,0 +1,51 @@
+// File: top_k.go
+// Created Time: 2023-06-24
+// Author: Reanon (793584285@qq.com)
+
+package chapter_heap
+
+import "container/heap"
+
+type minHeap []any
+
+func (h *minHeap) Len() int           { return len(*h) }
+func (h *minHeap) Less(i, j int) bool { return (*h)[i].(int) < (*h)[j].(int) }
+func (h *minHeap) Swap(i, j int)      { (*h)[i], (*h)[j] = (*h)[j], (*h)[i] }
+
+// Push method of heap.Interface, implements pushing element to heap
+func (h *minHeap) Push(x any) {
+	*h = append(*h, x.(int))
+}
+
+// Pop method of heap.Interface, implements popping heap top element
+func (h *minHeap) Pop() any {
+	// Element to be popped is stored at the end
+	last := (*h)[len(*h)-1]
+	*h = (*h)[:len(*h)-1]
+	return last
+}
+
+// Top gets heap top element
+func (h *minHeap) Top() any {
+	return (*h)[0]
+}
+
+/* Find the largest k elements in array based on heap */
+func topKHeap(nums []int, k int) *minHeap {
+	// Python's heapq module implements min heap by default
+	h := &minHeap{}
+	heap.Init(h)
+	// Enter the first k elements of array into heap
+	for i := 0; i < k; i++ {
+		heap.Push(h, nums[i])
+	}
+	// Starting from the (k+1)th element, maintain heap length as k
+	for i := k; i < len(nums); i++ {
+		// If current element is greater than top element, top element exits heap, current element enters heap
+		if nums[i] > h.Top().(int) {
+			heap.Pop(h)
+			heap.Push(h, nums[i])
+		}
+	}
+	return h
+}

en/codes/go/chapter_searching/binary_search.go

@@ -0,0 +1,43 @@
+// File: binary_search.go
+// Created Time: 2022-12-05
+// Author: Slone123c (274325721@qq.com)
+
+package chapter_searching
+
+/* Binary search (closed interval on both sides) */
+func binarySearch(nums []int, target int) int {
+	// Initialize closed interval [0, n-1], i.e., i, j point to the first and last elements of the array
+	i, j := 0, len(nums)-1
+	// Loop, exit when the search interval is empty (empty when i > j)
+	for i <= j {
+		m := i + (j-i)/2      // Calculate the midpoint index m
+		if nums[m] < target { // This means target is in the interval [m+1, j]
+			i = m + 1
+		} else if nums[m] > target { // This means target is in the interval [i, m-1]
+			j = m - 1
+		} else { // Found the target element, return its index
+			return m
+		}
+	}
+	// Target element not found, return -1
+	return -1
+}
+
+/* Binary search (left-closed right-open interval) */
+func binarySearchLCRO(nums []int, target int) int {
+	// Initialize left-closed right-open interval [0, n), i.e., i, j point to the first element and last element+1
+	i, j := 0, len(nums)
+	// Loop, exit when the search interval is empty (empty when i = j)
+	for i < j {
+		m := i + (j-i)/2      // Calculate the midpoint index m
+		if nums[m] < target { // This means target is in the interval [m+1, j)
+			i = m + 1
+		} else if nums[m] > target { // This means target is in the interval [i, m)
+			j = m
+		} else { // Found the target element, return its index
+			return m
+		}
+	}
+	// Target element not found, return -1
+	return -1
+}

en/codes/go/chapter_searching/binary_search_edge.go

@@ -0,0 +1,31 @@
+// File: binary_search_edge.go
+// Created Time: 2023-08-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_searching
+
+/* Binary search for the leftmost target */
+func binarySearchLeftEdge(nums []int, target int) int {
+	// Equivalent to finding the insertion point of target
+	i := binarySearchInsertion(nums, target)
+	// Target not found, return -1
+	if i == len(nums) || nums[i] != target {
+		return -1
+	}
+	// Found target, return index i
+	return i
+}
+
+/* Binary search for the rightmost target */
+func binarySearchRightEdge(nums []int, target int) int {
+	// Convert to finding the leftmost target + 1
+	i := binarySearchInsertion(nums, target+1)
+	// j points to the rightmost target, i points to the first element greater than target
+	j := i - 1
+	// Target not found, return -1
+	if j == -1 || nums[j] != target {
+		return -1
+	}
+	// Found target, return index j
+	return j
+}

en/codes/go/chapter_searching/binary_search_insertion.go

@@ -0,0 +1,49 @@
+// File: binary_search_insertion.go
+// Created Time: 2023-08-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_searching
+
+/* Binary search for insertion point (no duplicate elements) */
+func binarySearchInsertionSimple(nums []int, target int) int {
+	// Initialize closed interval [0, n-1]
+	i, j := 0, len(nums)-1
+	for i <= j {
+		// Calculate the midpoint index m
+		m := i + (j-i)/2
+		if nums[m] < target {
+			// target is in the interval [m+1, j]
+			i = m + 1
+		} else if nums[m] > target {
+			// target is in the interval [i, m-1]
+			j = m - 1
+		} else {
+			// Found target, return insertion point m
+			return m
+		}
+	}
+	// Target not found, return insertion point i
+	return i
+}
+
+/* Binary search for insertion point (with duplicate elements) */
+func binarySearchInsertion(nums []int, target int) int {
+	// Initialize closed interval [0, n-1]
+	i, j := 0, len(nums)-1
+	for i <= j {
+		// Calculate the midpoint index m
+		m := i + (j-i)/2
+		if nums[m] < target {
+			// target is in the interval [m+1, j]
+			i = m + 1
+		} else if nums[m] > target {
+			// target is in the interval [i, m-1]
+			j = m - 1
+		} else {
+			// The first element less than target is in the interval [i, m-1]
+			j = m - 1
+		}
+	}
+	// Return insertion point i
+	return i
+}

en/codes/go/chapter_searching/binary_search_test.go

@@ -0,0 +1,61 @@
+// File: binary_search_test.go
+// Created Time: 2022-12-05
+// Author: Slone123c (274325721@qq.com)
+
+package chapter_searching
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestBinarySearch(t *testing.T) {
+	var (
+		target   = 6
+		nums     = []int{1, 3, 6, 8, 12, 15, 23, 26, 31, 35}
+		expected = 2
+	)
+	// Perform binary search in array
+	actual := binarySearch(nums, target)
+	fmt.Println("Index of target element 6 =", actual)
+	if actual != expected {
+		t.Errorf("Index of target element 6 = %d, should be %d", actual, expected)
+	}
+}
+
+func TestBinarySearchEdge(t *testing.T) {
+	// Array with duplicate elements
+	nums := []int{1, 3, 6, 8, 12, 15, 23, 26, 31, 35}
+	fmt.Println("\nArray nums = ", nums)
+
+	// Binary search left and right boundaries
+	for _, target := range []int{6, 7} {
+		index := binarySearchLeftEdge(nums, target)
+		fmt.Println("Leftmost element", target, " index is", index)
+
+		index = binarySearchRightEdge(nums, target)
+		fmt.Println("Rightmost element", target, " index is", index)
+	}
+}
+
+func TestBinarySearchInsertion(t *testing.T) {
+	// Array without duplicate elements
+	nums := []int{1, 3, 6, 8, 12, 15, 23, 26, 31, 35}
+	fmt.Println("Array nums =", nums)
+
+	// Binary search for insertion point
+	for _, target := range []int{6, 9} {
+		index := binarySearchInsertionSimple(nums, target)
+		fmt.Println("Element", target, " insertion point index is", index)
+	}
+
+	// Array with duplicate elements
+	nums = []int{1, 3, 6, 6, 6, 6, 6, 10, 12, 15}
+	fmt.Println("\nArray nums =", nums)
+
+	// Binary search for insertion point
+	for _, target := range []int{2, 6, 20} {
+		index := binarySearchInsertion(nums, target)
+		fmt.Println("Element", target, " insertion point index is", index)
+	}
+}

en/codes/go/chapter_searching/hashing_search.go

@@ -0,0 +1,29 @@
+// File: hashing_search.go
+// Created Time: 2022-12-12
+// Author: Slone123c (274325721@qq.com)
+
+package chapter_searching
+
+import . "github.com/krahets/hello-algo/pkg"
+
+/* Hash search (array) */
+func hashingSearchArray(m map[int]int, target int) int {
+	// Hash table's key: target element, value: index
+	// If this key does not exist in the hash table, return -1
+	if index, ok := m[target]; ok {
+		return index
+	} else {
+		return -1
+	}
+}
+
+/* Hash search (linked list) */
+func hashingSearchLinkedList(m map[int]*ListNode, target int) *ListNode {
+	// Hash table key: target node value, value: node object
+	// Return nil if key does not exist in hash table
+	if node, ok := m[target]; ok {
+		return node
+	} else {
+		return nil
+	}
+}

en/codes/go/chapter_searching/hashing_search_test.go

@@ -0,0 +1,36 @@
+// File: hashing_search_test.go
+// Created Time: 2022-12-12
+// Author: Slone123c (274325721@qq.com)
+
+package chapter_searching
+
+import (
+	"fmt"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestHashingSearch(t *testing.T) {
+	target := 3
+	/* Hash search (array) */
+	nums := []int{1, 5, 3, 2, 4, 7, 5, 9, 10, 8}
+	// Initialize hash table
+	m := make(map[int]int)
+	for i := 0; i < len(nums); i++ {
+		m[nums[i]] = i
+	}
+	index := hashingSearchArray(m, target)
+	fmt.Println("Index of target element 3 = ", index)
+
+	/* Hash search (linked list) */
+	head := ArrayToLinkedList(nums)
+	// Initialize hash table
+	m1 := make(map[int]*ListNode)
+	for head != nil {
+		m1[head.Val] = head
+		head = head.Next
+	}
+	node := hashingSearchLinkedList(m1, target)
+	fmt.Println("Node object corresponding to target node value 3 is ", node)
+}

en/codes/go/chapter_searching/linear_search.go

@@ -0,0 +1,36 @@
+// File: linear_search.go
+// Created Time: 2022-11-25
+// Author: Reanon (793584285@qq.com)
+
+package chapter_searching
+
+import (
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+/* Linear search (array) */
+func linearSearchArray(nums []int, target int) int {
+	// Traverse array
+	for i := 0; i < len(nums); i++ {
+		// Found the target element, return its index
+		if nums[i] == target {
+			return i
+		}
+	}
+	// Target element not found, return -1
+	return -1
+}
+
+/* Linear search (linked list) */
+func linearSearchLinkedList(node *ListNode, target int) *ListNode {
+	// Traverse the linked list
+	for node != nil {
+		// Found the target node, return it
+		if node.Val == target {
+			return node
+		}
+		node = node.Next
+	}
+	// Target element not found, return nil
+	return nil
+}

en/codes/go/chapter_searching/linear_search_test.go

@@ -0,0 +1,26 @@
+// File: linear_search_test.go
+// Created Time: 2022-11-25
+// Author: Reanon (793584285@qq.com)
+
+package chapter_searching
+
+import (
+	"fmt"
+	"testing"
+
+	. "github.com/krahets/hello-algo/pkg"
+)
+
+func TestLinearSearch(t *testing.T) {
+	target := 3
+	nums := []int{1, 5, 3, 2, 4, 7, 5, 9, 10, 8}
+
+	// Perform linear search in array
+	index := linearSearchArray(nums, target)
+	fmt.Println("Index of target element 3 =", index)
+
+	// Perform linear search in linked list
+	head := ArrayToLinkedList(nums)
+	node := linearSearchLinkedList(head, target)
+	fmt.Println("Node object with target value 3 is", node)
+}

en/codes/go/chapter_searching/two_sum.go

@@ -0,0 +1,33 @@
+// File: two_sum.go
+// Created Time: 2022-11-25
+// Author: reanon (793584285@qq.com)
+
+package chapter_searching
+
+/* Method 1: Brute force enumeration */
+func twoSumBruteForce(nums []int, target int) []int {
+	size := len(nums)
+	// Two nested loops, time complexity is O(n^2)
+	for i := 0; i < size-1; i++ {
+		for j := i + 1; j < size; j++ {
+			if nums[i]+nums[j] == target {
+				return []int{i, j}
+			}
+		}
+	}
+	return nil
+}
+
+/* Method 2: Auxiliary hash table */
+func twoSumHashTable(nums []int, target int) []int {
+	// Auxiliary hash table, space complexity is O(n)
+	hashTable := map[int]int{}
+	// Single loop, time complexity is O(n)
+	for idx, val := range nums {
+		if preIdx, ok := hashTable[target-val]; ok {
+			return []int{preIdx, idx}
+		}
+		hashTable[val] = idx
+	}
+	return nil
+}

en/codes/go/chapter_searching/two_sum_test.go

@@ -0,0 +1,24 @@
+// File: two_sum_test.go
+// Created Time: 2022-11-25
+// Author: reanon (793584285@qq.com)
+
+package chapter_searching
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestTwoSum(t *testing.T) {
+	// ======= Test Case =======
+	nums := []int{2, 7, 11, 15}
+	target := 13
+
+	// ====== Driver Code ======
+	// Method 1: Brute-force approach
+	res := twoSumBruteForce(nums, target)
+	fmt.Println("Method 1 res =", res)
+	// Method 2: Hash table
+	res = twoSumHashTable(nums, target)
+	fmt.Println("Method 2 res =", res)
+}

en/codes/go/chapter_sorting/bubble_sort.go

@@ -0,0 +1,38 @@
+// File: bubble_sort.go
+// Created Time: 2022-12-06
+// Author: Slone123c (274325721@qq.com)
+
+package chapter_sorting
+
+/* Bubble sort */
+func bubbleSort(nums []int) {
+	// Outer loop: unsorted range is [0, i]
+	for i := len(nums) - 1; i > 0; i-- {
+		// Inner loop: swap the largest element in the unsorted range [0, i] to the rightmost end of that range
+		for j := 0; j < i; j++ {
+			if nums[j] > nums[j+1] {
+				// Swap nums[j] and nums[j + 1]
+				nums[j], nums[j+1] = nums[j+1], nums[j]
+			}
+		}
+	}
+}
+
+/* Bubble sort (flag optimization) */
+func bubbleSortWithFlag(nums []int) {
+	// Outer loop: unsorted range is [0, i]
+	for i := len(nums) - 1; i > 0; i-- {
+		flag := false // Initialize flag
+		// Inner loop: swap the largest element in the unsorted range [0, i] to the rightmost end of that range
+		for j := 0; j < i; j++ {
+			if nums[j] > nums[j+1] {
+				// Swap nums[j] and nums[j + 1]
+				nums[j], nums[j+1] = nums[j+1], nums[j]
+				flag = true // Record element swap
+			}
+		}
+		if flag == false { // No elements were swapped in this round of "bubbling", exit directly
+			break
+		}
+	}
+}

en/codes/go/chapter_sorting/bubble_sort_test.go

@@ -0,0 +1,20 @@
+// File: bubble_sort_test.go
+// Created Time: 2022-12-06
+// Author: Slone123c (274325721@qq.com)
+
+package chapter_sorting
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestBubbleSort(t *testing.T) {
+	nums := []int{4, 1, 3, 1, 5, 2}
+	bubbleSort(nums)
+	fmt.Println("After bubble sort completes, nums = ", nums)
+
+	nums1 := []int{4, 1, 3, 1, 5, 2}
+	bubbleSortWithFlag(nums1)
+	fmt.Println("After bubble sort completes, nums1 = ", nums1)
+}

en/codes/go/chapter_sorting/bucket_sort.go

@@ -0,0 +1,37 @@
+// File: bucket_sort.go
+// Created Time: 2023-03-27
+// Author: Reanon (793584285@qq.com)
+
+package chapter_sorting
+
+import "sort"
+
+/* Bucket sort */
+func bucketSort(nums []float64) {
+	// Initialize k = n/2 buckets, expected to allocate 2 elements per bucket
+	k := len(nums) / 2
+	buckets := make([][]float64, k)
+	for i := 0; i < k; i++ {
+		buckets[i] = make([]float64, 0)
+	}
+	// 1. Distribute array elements into various buckets
+	for _, num := range nums {
+		// Input data range is [0, 1), use num * k to map to index range [0, k-1]
+		i := int(num * float64(k))
+		// Add num to bucket i
+		buckets[i] = append(buckets[i], num)
+	}
+	// 2. Sort each bucket
+	for i := 0; i < k; i++ {
+		// Use built-in slice sorting function, can also be replaced with other sorting algorithms
+		sort.Float64s(buckets[i])
+	}
+	// 3. Traverse buckets to merge results
+	i := 0
+	for _, bucket := range buckets {
+		for _, num := range bucket {
+			nums[i] = num
+			i++
+		}
+	}
+}

en/codes/go/chapter_sorting/bucket_sort_test.go

@@ -0,0 +1,17 @@
+// File: bucket_sort_test.go
+// Created Time: 2023-03-27
+// Author: Reanon (793584285@qq.com)
+
+package chapter_sorting
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestBucketSort(t *testing.T) {
+	// Assume input data is floating point, interval [0, 1)
+	nums := []float64{0.49, 0.96, 0.82, 0.09, 0.57, 0.43, 0.91, 0.75, 0.15, 0.37}
+	bucketSort(nums)
+	fmt.Println("After bucket sort completes, nums = ", nums)
+}

en/codes/go/chapter_sorting/counting_sort.go

@@ -0,0 +1,68 @@
+// File: counting_sort.go
+// Created Time: 2023-03-20
+// Author: Reanon (793584285@qq.com)
+
+package chapter_sorting
+
+type CountingSort struct{}
+
+/* Counting sort */
+// Simple implementation, cannot be used for sorting objects
+func countingSortNaive(nums []int) {
+	// 1. Count the maximum element m in the array
+	m := 0
+	for _, num := range nums {
+		if num > m {
+			m = num
+		}
+	}
+	// 2. Count the occurrence of each number
+	// counter[num] represents the occurrence of num
+	counter := make([]int, m+1)
+	for _, num := range nums {
+		counter[num]++
+	}
+	// 3. Traverse counter, filling each element back into the original array nums
+	for i, num := 0, 0; num < m+1; num++ {
+		for j := 0; j < counter[num]; j++ {
+			nums[i] = num
+			i++
+		}
+	}
+}
+
+/* Counting sort */
+// Complete implementation, can sort objects and is a stable sort
+func countingSort(nums []int) {
+	// 1. Count the maximum element m in the array
+	m := 0
+	for _, num := range nums {
+		if num > m {
+			m = num
+		}
+	}
+	// 2. Count the occurrence of each number
+	// counter[num] represents the occurrence of num
+	counter := make([]int, m+1)
+	for _, num := range nums {
+		counter[num]++
+	}
+	// 3. Calculate the prefix sum of counter, converting "occurrence count" to "tail index"
+	// counter[num]-1 is the last index where num appears in res
+	for i := 0; i < m; i++ {
+		counter[i+1] += counter[i]
+	}
+	// 4. Traverse nums in reverse order, placing each element into the result array res
+	// Initialize the array res to record results
+	n := len(nums)
+	res := make([]int, n)
+	for i := n - 1; i >= 0; i-- {
+		num := nums[i]
+		// Place num at the corresponding index
+		res[counter[num]-1] = num
+		// Decrement the prefix sum by 1, getting the next index to place num
+		counter[num]--
+	}
+	// Use result array res to overwrite the original array nums
+	copy(nums, res)
+}

en/codes/go/chapter_sorting/counting_sort_test.go

@@ -0,0 +1,20 @@
+// File: counting_sort_test.go
+// Created Time: 2023-03-20
+// Author: Reanon (793584285@qq.com)
+
+package chapter_sorting
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestCountingSort(t *testing.T) {
+	nums := []int{1, 0, 1, 2, 0, 4, 0, 2, 2, 4}
+	countingSortNaive(nums)
+	fmt.Println("After counting sort (cannot sort objects) completes, nums = ", nums)
+
+	nums1 := []int{1, 0, 1, 2, 0, 4, 0, 2, 2, 4}
+	countingSort(nums1)
+	fmt.Println("After counting sort completes, nums1 = ", nums1)
+}

en/codes/go/chapter_sorting/heap_sort.go

@@ -0,0 +1,44 @@
+// File: heap_sort.go
+// Created Time: 2023-05-29
+// Author: Reanon (793584285@qq.com)
+
+package chapter_sorting
+
+/* Heap length is n, start heapifying node i, from top to bottom */
+func siftDown(nums *[]int, n, i int) {
+	for true {
+		// If node i is largest or indices l, r are out of bounds, no need to continue heapify, break
+		l := 2*i + 1
+		r := 2*i + 2
+		ma := i
+		if l < n && (*nums)[l] > (*nums)[ma] {
+			ma = l
+		}
+		if r < n && (*nums)[r] > (*nums)[ma] {
+			ma = r
+		}
+		// Swap two nodes
+		if ma == i {
+			break
+		}
+		// Swap two nodes
+		(*nums)[i], (*nums)[ma] = (*nums)[ma], (*nums)[i]
+		// Loop downwards heapification
+		i = ma
+	}
+}
+
+/* Heap sort */
+func heapSort(nums *[]int) {
+	// Build heap operation: heapify all nodes except leaves
+	for i := len(*nums)/2 - 1; i >= 0; i-- {
+		siftDown(nums, len(*nums), i)
+	}
+	// Extract the largest element from the heap and repeat for n-1 rounds
+	for i := len(*nums) - 1; i > 0; i-- {
+		// Delete node
+		(*nums)[0], (*nums)[i] = (*nums)[i], (*nums)[0]
+		// Start heapifying the root node, from top to bottom
+		siftDown(nums, i, 0)
+	}
+}

en/codes/go/chapter_sorting/heap_sort_test.go

@@ -0,0 +1,16 @@
+// File: heap_sort_test.go
+// Created Time: 2023-05-29
+// Author: Reanon (793584285@qq.com)
+
+package chapter_sorting
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestHeapSort(t *testing.T) {
+	nums := []int{4, 1, 3, 1, 5, 2}
+	heapSort(&nums)
+	fmt.Println("After heap sort completes, nums = ", nums)
+}

en/codes/go/chapter_sorting/insertion_sort.go

@@ -0,0 +1,20 @@
+// File: insertion_sort.go
+// Created Time: 2022-12-12
+// Author: msk397 (machangxinq@gmail.com)
+
+package chapter_sorting
+
+/* Insertion sort */
+func insertionSort(nums []int) {
+	// Outer loop: sorted interval is [0, i-1]
+	for i := 1; i < len(nums); i++ {
+		base := nums[i]
+		j := i - 1
+		// Inner loop: insert base into the correct position within the sorted interval [0, i-1]
+		for j >= 0 && nums[j] > base {
+			nums[j+1] = nums[j] // Move nums[j] to the right by one position
+			j--
+		}
+		nums[j+1] = base // Assign base to the correct position
+	}
+}