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en/codes/kotlin/chapter_dynamic_programming/climbing_stairs_backtrack.kt

@@ -0,0 +1,45 @@
+/**
+ * File: climbing_stairs_backtrack.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+/* Backtracking */
+fun backtrack(
+    choices: MutableList<Int>,
+    state: Int,
+    n: Int,
+    res: MutableList<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 in 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 */
+fun climbingStairsBacktrack(n: Int): Int {
+    val choices = mutableListOf(1, 2) // Can choose to climb up 1 or 2 stairs
+    val state = 0 // Start climbing from the 0-th stair
+    val res = mutableListOf<Int>()
+    res.add(0) // Use res[0] to record the solution count
+    backtrack(choices, state, n, res)
+    return res[0]
+}
+
+/* Driver Code */
+fun main() {
+    val n = 9
+
+    val res = climbingStairsBacktrack(n)
+    println("Climbing $n stairs has $res solutions")
+}

en/codes/kotlin/chapter_dynamic_programming/climbing_stairs_constraint_dp.kt

@@ -0,0 +1,35 @@
+/**
+ * File: climbing_stairs_constraint_dp.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+/* Climbing stairs with constraint: Dynamic programming */
+fun climbingStairsConstraintDP(n: Int): Int {
+    if (n == 1 || n == 2) {
+        return 1
+    }
+    // Initialize dp table, used to store solutions to subproblems
+    val dp = Array(n + 1) { IntArray(3) }
+    // 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 in 3..n) {
+        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]
+}
+
+/* Driver Code */
+fun main() {
+    val n = 9
+
+    val res = climbingStairsConstraintDP(n)
+    println("Climbing $n stairs has $res solutions")
+}

en/codes/kotlin/chapter_dynamic_programming/climbing_stairs_dfs.kt

@@ -0,0 +1,29 @@
+/**
+ * File: climbing_stairs_dfs.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+/* Search */
+fun 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]
+    val count = dfs(i - 1) + dfs(i - 2)
+    return count
+}
+
+/* Climbing stairs: Search */
+fun climbingStairsDFS(n: Int): Int {
+    return dfs(n)
+}
+
+/* Driver Code */
+fun main() {
+    val n = 9
+
+    val res = climbingStairsDFS(n)
+    println("Climbing $n stairs has $res solutions")
+}

en/codes/kotlin/chapter_dynamic_programming/climbing_stairs_dfs_mem.kt

@@ -0,0 +1,36 @@
+/**
+ * File: climbing_stairs_dfs_mem.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+/* Memoization search */
+fun dfs(i: Int, mem: IntArray): 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]
+    val count = dfs(i - 1, mem) + dfs(i - 2, mem)
+    // Record dp[i]
+    mem[i] = count
+    return count
+}
+
+/* Climbing stairs: Memoization search */
+fun climbingStairsDFSMem(n: Int): Int {
+    // mem[i] records the total number of solutions to climb to the i-th stair, -1 means no record
+    val mem = IntArray(n + 1)
+    mem.fill(-1)
+    return dfs(n, mem)
+}
+
+/* Driver Code */
+fun main() {
+    val n = 9
+
+    val res = climbingStairsDFSMem(n)
+    println("Climbing $n stairs has $res solutions")
+}

en/codes/kotlin/chapter_dynamic_programming/climbing_stairs_dp.kt

@@ -0,0 +1,46 @@
+/**
+ * File: climbing_stairs_dp.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+/* Climbing stairs: Dynamic programming */
+fun climbingStairsDP(n: Int): Int {
+    if (n == 1 || n == 2) return n
+    // Initialize dp table, used to store solutions to subproblems
+    val dp = IntArray(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 in 3..n) {
+        dp[i] = dp[i - 1] + dp[i - 2]
+    }
+    return dp[n]
+}
+
+/* Climbing stairs: Space-optimized dynamic programming */
+fun climbingStairsDPComp(n: Int): Int {
+    if (n == 1 || n == 2) return n
+    var a = 1
+    var b = 2
+    for (i in 3..n) {
+        val temp = b
+        b += a
+        a = temp
+    }
+    return b
+}
+
+/* Driver Code */
+fun main() {
+    val n = 9
+
+    var res = climbingStairsDP(n)
+    println("Climbing $n stairs has $res solutions")
+
+    res = climbingStairsDPComp(n)
+    println("Climbing $n stairs has $res solutions")
+}

en/codes/kotlin/chapter_dynamic_programming/coin_change.kt

@@ -0,0 +1,71 @@
+/**
+ * File: coin_change.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+import kotlin.math.min
+
+/* Coin change: Dynamic programming */
+fun coinChangeDP(coins: IntArray, amt: Int): Int {
+    val n = coins.size
+    val MAX = amt + 1
+    // Initialize dp table
+    val dp = Array(n + 1) { IntArray(amt + 1) }
+    // State transition: first row and first column
+    for (a in 1..amt) {
+        dp[0][a] = MAX
+    }
+    // State transition: rest of the rows and columns
+    for (i in 1..n) {
+        for (a in 1..amt) {
+            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] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)
+            }
+        }
+    }
+    return if (dp[n][amt] != MAX) dp[n][amt] else -1
+}
+
+/* Coin change: Space-optimized dynamic programming */
+fun coinChangeDPComp(coins: IntArray, amt: Int): Int {
+    val n = coins.size
+    val MAX = amt + 1
+    // Initialize dp table
+    val dp = IntArray(amt + 1)
+    dp.fill(MAX)
+    dp[0] = 0
+    // State transition
+    for (i in 1..n) {
+        for (a in 1..amt) {
+            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] = min(dp[a], dp[a - coins[i - 1]] + 1)
+            }
+        }
+    }
+    return if (dp[amt] != MAX) dp[amt] else -1
+}
+
+/* Driver Code */
+fun main() {
+    val coins = intArrayOf(1, 2, 5)
+    val amt = 4
+
+    // Dynamic programming
+    var res = coinChangeDP(coins, amt)
+    println("Minimum coins needed to make target amount is $res")
+
+    // Space-optimized dynamic programming
+    res = coinChangeDPComp(coins, amt)
+    println("Minimum coins needed to make target amount is $res")
+}

en/codes/kotlin/chapter_dynamic_programming/coin_change_ii.kt

@@ -0,0 +1,66 @@
+/**
+ * File: coin_change_ii.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+/* Coin change II: Dynamic programming */
+fun coinChangeIIDP(coins: IntArray, amt: Int): Int {
+    val n = coins.size
+    // Initialize dp table
+    val dp = Array(n + 1) { IntArray(amt + 1) }
+    // Initialize first column
+    for (i in 0..n) {
+        dp[i][0] = 1
+    }
+    // State transition
+    for (i in 1..n) {
+        for (a in 1..amt) {
+            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 */
+fun coinChangeIIDPComp(coins: IntArray, amt: Int): Int {
+    val n = coins.size
+    // Initialize dp table
+    val dp = IntArray(amt + 1)
+    dp[0] = 1
+    // State transition
+    for (i in 1..n) {
+        for (a in 1..amt) {
+            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]
+}
+
+/* Driver Code */
+fun main() {
+    val coins = intArrayOf(1, 2, 5)
+    val amt = 5
+
+    // Dynamic programming
+    var res = coinChangeIIDP(coins, amt)
+    println("Number of coin combinations to make target amount is $res")
+
+    // Space-optimized dynamic programming
+    res = coinChangeIIDPComp(coins, amt)
+    println("Number of coin combinations to make target amount is $res")
+}

en/codes/kotlin/chapter_dynamic_programming/edit_distance.kt

@@ -0,0 +1,143 @@
+/**
+ * File: edit_distance.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+import kotlin.math.min
+
+/* Edit distance: Brute-force search */
+fun 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
+    val insert = editDistanceDFS(s, t, i, j - 1)
+    val delete = editDistanceDFS(s, t, i - 1, j)
+    val replace = editDistanceDFS(s, t, i - 1, j - 1)
+    // Return minimum edit steps
+    return min(min(insert, delete), replace) + 1
+}
+
+/* Edit distance: Memoization search */
+fun editDistanceDFSMem(
+    s: String,
+    t: String,
+    mem: Array<IntArray>,
+    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
+    val insert = editDistanceDFSMem(s, t, mem, i, j - 1)
+    val delete = editDistanceDFSMem(s, t, mem, i - 1, j)
+    val replace = editDistanceDFSMem(s, t, mem, i - 1, j - 1)
+    // Record and return minimum edit steps
+    mem[i][j] = min(min(insert, delete), replace) + 1
+    return mem[i][j]
+}
+
+/* Edit distance: Dynamic programming */
+fun editDistanceDP(s: String, t: String): Int {
+    val n = s.length
+    val m = t.length
+    val dp = Array(n + 1) { IntArray(m + 1) }
+    // State transition: first row and first column
+    for (i in 1..n) {
+        dp[i][0] = i
+    }
+    for (j in 1..m) {
+        dp[0][j] = j
+    }
+    // State transition: rest of the rows and columns
+    for (i in 1..n) {
+        for (j in 1..m) {
+            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] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1
+            }
+        }
+    }
+    return dp[n][m]
+}
+
+/* Edit distance: Space-optimized dynamic programming */
+fun editDistanceDPComp(s: String, t: String): Int {
+    val n = s.length
+    val m = t.length
+    val dp = IntArray(m + 1)
+    // State transition: first row
+    for (j in 1..m) {
+        dp[j] = j
+    }
+    // State transition: rest of the rows
+    for (i in 1..n) {
+        // State transition: first column
+        var leftup = dp[0] // Temporarily store dp[i-1, j-1]
+        dp[0] = i
+        // State transition: rest of the columns
+        for (j in 1..m) {
+            val 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] = min(min(dp[j - 1], dp[j]), leftup) + 1
+            }
+            leftup = temp // Update for next round's dp[i-1, j-1]
+        }
+    }
+    return dp[m]
+}
+
+/* Driver Code */
+fun main() {
+    val s = "bag"
+    val t = "pack"
+    val n = s.length
+    val m = t.length
+
+    // Brute-force search
+    var res = editDistanceDFS(s, t, n, m)
+    println("Changing $s to $t requires minimum $res edits")
+
+    // Memoization search
+    val mem = Array(n + 1) { IntArray(m + 1) }
+    for (row in mem)
+        row.fill(-1)
+    res = editDistanceDFSMem(s, t, mem, n, m)
+    println("Changing $s to $t requires minimum $res edits")
+
+    // Dynamic programming
+    res = editDistanceDP(s, t)
+    println("Changing $s to $t requires minimum $res edits")
+
+    // Space-optimized dynamic programming
+    res = editDistanceDPComp(s, t)
+    println("Changing $s to $t requires minimum $res edits")
+}

en/codes/kotlin/chapter_dynamic_programming/knapsack.kt

@@ -0,0 +1,125 @@
+/**
+ * File: knapsack.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+import kotlin.math.max
+
+/* 0-1 knapsack: Brute-force search */
+fun knapsackDFS(
+    wgt: IntArray,
+    _val: IntArray,
+    i: Int,
+    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
+    val no = knapsackDFS(wgt, _val, i - 1, c)
+    val yes = knapsackDFS(wgt, _val, i - 1, c - wgt[i - 1]) + _val[i - 1]
+    // Return the larger value of the two options
+    return max(no, yes)
+}
+
+/* 0-1 knapsack: Memoization search */
+fun knapsackDFSMem(
+    wgt: IntArray,
+    _val: IntArray,
+    mem: Array<IntArray>,
+    i: Int,
+    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
+    val no = knapsackDFSMem(wgt, _val, mem, i - 1, c)
+    val yes = knapsackDFSMem(wgt, _val, mem, i - 1, c - wgt[i - 1]) + _val[i - 1]
+    // Record and return the larger value of the two options
+    mem[i][c] = max(no, yes)
+    return mem[i][c]
+}
+
+/* 0-1 knapsack: Dynamic programming */
+fun knapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {
+    val n = wgt.size
+    // Initialize dp table
+    val dp = Array(n + 1) { IntArray(cap + 1) }
+    // State transition
+    for (i in 1..n) {
+        for (c in 1..cap) {
+            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] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + _val[i - 1])
+            }
+        }
+    }
+    return dp[n][cap]
+}
+
+/* 0-1 knapsack: Space-optimized dynamic programming */
+fun knapsackDPComp(wgt: IntArray, _val: IntArray, cap: Int): Int {
+    val n = wgt.size
+    // Initialize dp table
+    val dp = IntArray(cap + 1)
+    // State transition
+    for (i in 1..n) {
+        // Traverse in reverse order
+        for (c in cap downTo 1) {
+            if (wgt[i - 1] <= c) {
+                // The larger value between not selecting and selecting item i
+                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])
+            }
+        }
+    }
+    return dp[cap]
+}
+
+/* Driver Code */
+fun main() {
+    val wgt = intArrayOf(10, 20, 30, 40, 50)
+    val _val = intArrayOf(50, 120, 150, 210, 240)
+    val cap = 50
+    val n = wgt.size
+
+    // Brute-force search
+    var res = knapsackDFS(wgt, _val, n, cap)
+    println("Maximum item value not exceeding knapsack capacity is $res")
+
+    // Memoization search
+    val mem = Array(n + 1) { IntArray(cap + 1) }
+    for (row in mem) {
+        row.fill(-1)
+    }
+    res = knapsackDFSMem(wgt, _val, mem, n, cap)
+    println("Maximum item value not exceeding knapsack capacity is $res")
+
+    // Dynamic programming
+    res = knapsackDP(wgt, _val, cap)
+    println("Maximum item value not exceeding knapsack capacity is $res")
+
+    // Space-optimized dynamic programming
+    res = knapsackDPComp(wgt, _val, cap)
+    println("Maximum item value not exceeding knapsack capacity is $res")
+}

en/codes/kotlin/chapter_dynamic_programming/min_cost_climbing_stairs_dp.kt

@@ -0,0 +1,51 @@
+/**
+ * File: min_cost_climbing_stairs_dp.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+import kotlin.math.min
+
+/* Minimum cost climbing stairs: Dynamic programming */
+fun minCostClimbingStairsDP(cost: IntArray): Int {
+    val n = cost.size - 1
+    if (n == 1 || n == 2) return cost[n]
+    // Initialize dp table, used to store solutions to subproblems
+    val dp = IntArray(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 in 3..n) {
+        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]
+    }
+    return dp[n]
+}
+
+/* Minimum cost climbing stairs: Space-optimized dynamic programming */
+fun minCostClimbingStairsDPComp(cost: IntArray): Int {
+    val n = cost.size - 1
+    if (n == 1 || n == 2) return cost[n]
+    var a = cost[1]
+    var b = cost[2]
+    for (i in 3..n) {
+        val tmp = b
+        b = min(a, tmp) + cost[i]
+        a = tmp
+    }
+    return b
+}
+
+/* Driver Code */
+fun main() {
+    val cost = intArrayOf(0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1)
+    println("Input stair cost list is ${cost.contentToString()}")
+
+    var res = minCostClimbingStairsDP(cost)
+    println("Minimum cost to climb stairs is $res")
+
+    res = minCostClimbingStairsDPComp(cost)
+    println("Minimum cost to climb stairs is $res")
+}

en/codes/kotlin/chapter_dynamic_programming/min_path_sum.kt

@@ -0,0 +1,132 @@
+/**
+ * File: min_path_sum.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+import kotlin.math.min
+
+/* Minimum path sum: Brute-force search */
+fun minPathSumDFS(grid: Array<IntArray>, i: Int, 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 Int.MAX_VALUE
+    }
+    // Calculate the minimum path cost from top-left to (i-1, j) and (i, j-1)
+    val up = minPathSumDFS(grid, i - 1, j)
+    val left = minPathSumDFS(grid, i, j - 1)
+    // Return the minimum path cost from top-left to (i, j)
+    return min(left, up) + grid[i][j]
+}
+
+/* Minimum path sum: Memoization search */
+fun minPathSumDFSMem(
+    grid: Array<IntArray>,
+    mem: Array<IntArray>,
+    i: Int,
+    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 Int.MAX_VALUE
+    }
+    // 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
+    val up = minPathSumDFSMem(grid, mem, i - 1, j)
+    val left = minPathSumDFSMem(grid, mem, i, j - 1)
+    // Record and return the minimum path cost from top-left to (i, j)
+    mem[i][j] = min(left, up) + grid[i][j]
+    return mem[i][j]
+}
+
+/* Minimum path sum: Dynamic programming */
+fun minPathSumDP(grid: Array<IntArray>): Int {
+    val n = grid.size
+    val m = grid[0].size
+    // Initialize dp table
+    val dp = Array(n) { IntArray(m) }
+    dp[0][0] = grid[0][0]
+    // State transition: first row
+    for (j in 1..<m) {
+        dp[0][j] = dp[0][j - 1] + grid[0][j]
+    }
+    // State transition: first column
+    for (i in 1..<n) {
+        dp[i][0] = dp[i - 1][0] + grid[i][0]
+    }
+    // State transition: rest of the rows and columns
+    for (i in 1..<n) {
+        for (j in 1..<m) {
+            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]
+        }
+    }
+    return dp[n - 1][m - 1]
+}
+
+/* Minimum path sum: Space-optimized dynamic programming */
+fun minPathSumDPComp(grid: Array<IntArray>): Int {
+    val n = grid.size
+    val m = grid[0].size
+    // Initialize dp table
+    val dp = IntArray(m)
+    // State transition: first row
+    dp[0] = grid[0][0]
+    for (j in 1..<m) {
+        dp[j] = dp[j - 1] + grid[0][j]
+    }
+    // State transition: rest of the rows
+    for (i in 1..<n) {
+        // State transition: first column
+        dp[0] = dp[0] + grid[i][0]
+        // State transition: rest of the columns
+        for (j in 1..<m) {
+            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]
+        }
+    }
+    return dp[m - 1]
+}
+
+/* Driver Code */
+fun main() {
+    val grid = arrayOf(
+        intArrayOf(1, 3, 1, 5),
+        intArrayOf(2, 2, 4, 2),
+        intArrayOf(5, 3, 2, 1),
+        intArrayOf(4, 3, 5, 2)
+    )
+    val n = grid.size
+    val m = grid[0].size
+
+    // Brute-force search
+    var res = minPathSumDFS(grid, n - 1, m - 1)
+    println("Minimum path sum from top-left to bottom-right is $res")
+
+    // Memoization search
+    val mem = Array(n) { IntArray(m) }
+    for (row in mem) {
+        row.fill(-1)
+    }
+    res = minPathSumDFSMem(grid, mem, n - 1, m - 1)
+    println("Minimum path sum from top-left to bottom-right is $res")
+
+    // Dynamic programming
+    res = minPathSumDP(grid)
+    println("Minimum path sum from top-left to bottom-right is $res")
+
+    // Space-optimized dynamic programming
+    res = minPathSumDPComp(grid)
+    println("Minimum path sum from top-left to bottom-right is $res")
+}

en/codes/kotlin/chapter_dynamic_programming/unbounded_knapsack.kt

@@ -0,0 +1,68 @@
+/**
+ * File: unbounded_knapsack.kt
+ * Created Time: 2024-01-25
+ * Author: curtishd (1023632660@qq.com)
+ */
+
+package chapter_dynamic_programming
+
+import kotlin.math.max
+
+/* Unbounded knapsack: Dynamic programming */
+fun unboundedKnapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {
+    val n = wgt.size
+    // Initialize dp table
+    val dp = Array(n + 1) { IntArray(cap + 1) }
+    // State transition
+    for (i in 1..n) {
+        for (c in 1..cap) {
+            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] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + _val[i - 1])
+            }
+        }
+    }
+    return dp[n][cap]
+}
+
+/* Unbounded knapsack: Space-optimized dynamic programming */
+fun unboundedKnapsackDPComp(
+    wgt: IntArray,
+    _val: IntArray,
+    cap: Int
+): Int {
+    val n = wgt.size
+    // Initialize dp table
+    val dp = IntArray(cap + 1)
+    // State transition
+    for (i in 1..n) {
+        for (c in 1..cap) {
+            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] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])
+            }
+        }
+    }
+    return dp[cap]
+}
+
+/* Driver Code */
+fun main() {
+    val wgt = intArrayOf(1, 2, 3)
+    val _val = intArrayOf(5, 11, 15)
+    val cap = 4
+
+    // Dynamic programming
+    var res = unboundedKnapsackDP(wgt, _val, cap)
+    println("Maximum item value not exceeding knapsack capacity is $res")
+
+    // Space-optimized dynamic programming
+    res = unboundedKnapsackDPComp(wgt, _val, cap)
+    println("Maximum item value not exceeding knapsack capacity is $res")
+}