Translate all code to English (#1836)

* Review the EN heading format.

* Fix pythontutor headings.

* Fix pythontutor headings.

* bug fixes

* Fix headings in **/summary.md

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

* 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.

* Fix the dictionary.

* Fix cpp code translation for the multipart strings.

* Translate Go code to English.

* Update workflows to test EN code.

* Add EN translation for C.

* Add EN translation for CSharp.

* Add EN translation for Swift.

* Trigger the CI check.

* Revert.

* Update en/hash_map.md

* Add the EN version of Dart code.

* Add the EN version of Kotlin code.

* Add missing code files.

* Add the EN version of JavaScript code.

* Add the EN version of TypeScript code.

* Fix the workflows.

* Add the EN version of Ruby code.

* Add the EN version of Rust code.

* Update the CI check for the English version  code.

* Update Python CI check.

* Fix cmakelists for en/C code.

* Fix Ruby comments

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]
+}