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.

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* Add the EN version of Dart code.

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* Add missing code files.

* Add the EN version of JavaScript code.

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* 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/swift/chapter_dynamic_programming/climbing_stairs_backtrack.swift

@@ -0,0 +1,44 @@
+/**
+ * File: climbing_stairs_backtrack.swift
+ * Created Time: 2023-07-15
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* Backtracking */
+func backtrack(choices: [Int], state: Int, n: Int, res: inout [Int]) {
+    // When climbing to the n-th stair, add 1 to the solution count
+    if state == n {
+        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: choices, state: state + choice, n: n, res: &res)
+        // Backtrack
+    }
+}
+
+/* Climbing stairs: Backtracking */
+func climbingStairsBacktrack(n: Int) -> Int {
+    let choices = [1, 2] // Can choose to climb up 1 or 2 stairs
+    let state = 0 // Start climbing from the 0-th stair
+    var res: [Int] = []
+    res.append(0) // Use res[0] to record the solution count
+    backtrack(choices: choices, state: state, n: n, res: &res)
+    return res[0]
+}
+
+@main
+enum ClimbingStairsBacktrack {
+    /* Driver Code */
+    static func main() {
+        let n = 9
+
+        let res = climbingStairsBacktrack(n: n)
+        print("Climbing \(n) stairs has \(res) solutions")
+    }
+}

en/codes/swift/chapter_dynamic_programming/climbing_stairs_constraint_dp.swift

@@ -0,0 +1,36 @@
+/**
+ * File: climbing_stairs_constraint_dp.swift
+ * Created Time: 2023-07-15
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* 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
+    var dp = Array(repeating: Array(repeating: 0, count: 3), count: 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 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]
+}
+
+@main
+enum ClimbingStairsConstraintDP {
+    /* Driver Code */
+    static func main() {
+        let n = 9
+
+        let res = climbingStairsConstraintDP(n: n)
+        print("Climbing \(n) stairs has \(res) solutions")
+    }
+}

en/codes/swift/chapter_dynamic_programming/climbing_stairs_dfs.swift

@@ -0,0 +1,32 @@
+/**
+ * File: climbing_stairs_dfs.swift
+ * Created Time: 2023-07-15
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* 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]
+    let count = dfs(i: i - 1) + dfs(i: i - 2)
+    return count
+}
+
+/* Climbing stairs: Search */
+func climbingStairsDFS(n: Int) -> Int {
+    dfs(i: n)
+}
+
+@main
+enum ClimbingStairsDFS {
+    /* Driver Code */
+    static func main() {
+        let n = 9
+
+        let res = climbingStairsDFS(n: n)
+        print("Climbing \(n) stairs has \(res) solutions")
+    }
+}

en/codes/swift/chapter_dynamic_programming/climbing_stairs_dfs_mem.swift

@@ -0,0 +1,40 @@
+/**
+ * File: climbing_stairs_dfs_mem.swift
+ * Created Time: 2023-07-15
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* Memoization search */
+func dfs(i: Int, mem: inout [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]
+    let count = dfs(i: i - 1, mem: &mem) + dfs(i: i - 2, mem: &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
+    var mem = Array(repeating: -1, count: n + 1)
+    return dfs(i: n, mem: &mem)
+}
+
+@main
+enum ClimbingStairsDFSMem {
+    /* Driver Code */
+    static func main() {
+        let n = 9
+
+        let res = climbingStairsDFSMem(n: n)
+        print("Climbing \(n) stairs has \(res) solutions")
+    }
+}

en/codes/swift/chapter_dynamic_programming/climbing_stairs_dp.swift

@@ -0,0 +1,49 @@
+/**
+ * File: climbing_stairs_dp.swift
+ * Created Time: 2023-07-15
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* 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
+    var dp = Array(repeating: 0, count: 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 */
+func climbingStairsDPComp(n: Int) -> Int {
+    if n == 1 || n == 2 {
+        return n
+    }
+    var a = 1
+    var b = 2
+    for _ in 3 ... n {
+        (a, b) = (b, a + b)
+    }
+    return b
+}
+
+@main
+enum ClimbingStairsDP {
+    /* Driver Code */
+    static func main() {
+        let n = 9
+
+        var res = climbingStairsDP(n: n)
+        print("Climbing \(n) stairs has \(res) solutions")
+
+        res = climbingStairsDPComp(n: n)
+        print("Climbing \(n) stairs has \(res) solutions")
+    }
+}

en/codes/swift/chapter_dynamic_programming/coin_change.swift

@@ -0,0 +1,69 @@
+/**
+ * File: coin_change.swift
+ * Created Time: 2023-07-15
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* Coin change: Dynamic programming */
+func coinChangeDP(coins: [Int], amt: Int) -> Int {
+    let n = coins.count
+    let MAX = amt + 1
+    // Initialize dp table
+    var dp = Array(repeating: Array(repeating: 0, count: amt + 1), count: n + 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 dp[n][amt] != MAX ? dp[n][amt] : -1
+}
+
+/* Coin change: Space-optimized dynamic programming */
+func coinChangeDPComp(coins: [Int], amt: Int) -> Int {
+    let n = coins.count
+    let MAX = amt + 1
+    // Initialize dp table
+    var dp = Array(repeating: MAX, count: amt + 1)
+    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 dp[amt] != MAX ? dp[amt] : -1
+}
+
+@main
+enum CoinChange {
+    /* Driver Code */
+    static func main() {
+        let coins = [1, 2, 5]
+        let amt = 4
+
+        // Dynamic programming
+        var res = coinChangeDP(coins: coins, amt: amt)
+        print("Minimum coins needed to make target amount is \(res)")
+
+        // Space-optimized dynamic programming
+        res = coinChangeDPComp(coins: coins, amt: amt)
+        print("Minimum coins needed to make target amount is \(res)")
+    }
+}

en/codes/swift/chapter_dynamic_programming/coin_change_ii.swift

@@ -0,0 +1,67 @@
+/**
+ * File: coin_change_ii.swift
+ * Created Time: 2023-07-16
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* Coin change II: Dynamic programming */
+func coinChangeIIDP(coins: [Int], amt: Int) -> Int {
+    let n = coins.count
+    // Initialize dp table
+    var dp = Array(repeating: Array(repeating: 0, count: amt + 1), count: n + 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 */
+func coinChangeIIDPComp(coins: [Int], amt: Int) -> Int {
+    let n = coins.count
+    // Initialize dp table
+    var dp = Array(repeating: 0, count: 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]
+}
+
+@main
+enum CoinChangeII {
+    /* Driver Code */
+    static func main() {
+        let coins = [1, 2, 5]
+        let amt = 5
+
+        // Dynamic programming
+        var res = coinChangeIIDP(coins: coins, amt: amt)
+        print("Number of coin combinations to make target amount is \(res)")
+
+        // Space-optimized dynamic programming
+        res = coinChangeIIDPComp(coins: coins, amt: amt)
+        print("Number of coin combinations to make target amount is \(res)")
+    }
+}

en/codes/swift/chapter_dynamic_programming/edit_distance.swift

@@ -0,0 +1,147 @@
+/**
+ * File: edit_distance.swift
+ * Created Time: 2023-07-16
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* 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.utf8CString[i - 1] == t.utf8CString[j - 1] {
+        return editDistanceDFS(s: s, t: t, i: i - 1, j: j - 1)
+    }
+    // Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+    let insert = editDistanceDFS(s: s, t: t, i: i, j: j - 1)
+    let delete = editDistanceDFS(s: s, t: t, i: i - 1, j: j)
+    let replace = editDistanceDFS(s: s, t: t, i: i - 1, j: j - 1)
+    // Return minimum edit steps
+    return min(min(insert, delete), replace) + 1
+}
+
+/* Edit distance: Memoization search */
+func editDistanceDFSMem(s: String, t: String, mem: inout [[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.utf8CString[i - 1] == t.utf8CString[j - 1] {
+        return editDistanceDFS(s: s, t: t, i: i - 1, j: j - 1)
+    }
+    // Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+    let insert = editDistanceDFS(s: s, t: t, i: i, j: j - 1)
+    let delete = editDistanceDFS(s: s, t: t, i: i - 1, j: j)
+    let replace = editDistanceDFS(s: s, t: t, i: i - 1, j: 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 */
+func editDistanceDP(s: String, t: String) -> Int {
+    let n = s.utf8CString.count
+    let m = t.utf8CString.count
+    var dp = Array(repeating: Array(repeating: 0, count: m + 1), count: n + 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.utf8CString[i - 1] == t.utf8CString[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 */
+func editDistanceDPComp(s: String, t: String) -> Int {
+    let n = s.utf8CString.count
+    let m = t.utf8CString.count
+    var dp = Array(repeating: 0, count: 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 {
+            let temp = dp[j]
+            if s.utf8CString[i - 1] == t.utf8CString[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]
+}
+
+@main
+enum EditDistance {
+    /* Driver Code */
+    static func main() {
+        let s = "bag"
+        let t = "pack"
+        let n = s.utf8CString.count
+        let m = t.utf8CString.count
+
+        // Brute-force search
+        var res = editDistanceDFS(s: s, t: t, i: n, j: m)
+        print("Changing \(s) to \(t) requires minimum \(res) edits")
+
+        // Memoization search
+        var mem = Array(repeating: Array(repeating: -1, count: m + 1), count: n + 1)
+        res = editDistanceDFSMem(s: s, t: t, mem: &mem, i: n, j: m)
+        print("Changing \(s) to \(t) requires minimum \(res) edits")
+
+        // Dynamic programming
+        res = editDistanceDP(s: s, t: t)
+        print("Changing \(s) to \(t) requires minimum \(res) edits")
+
+        // Space-optimized dynamic programming
+        res = editDistanceDPComp(s: s, t: t)
+        print("Changing \(s) to \(t) requires minimum \(res) edits")
+    }
+}

en/codes/swift/chapter_dynamic_programming/knapsack.swift

@@ -0,0 +1,110 @@
+/**
+ * File: knapsack.swift
+ * Created Time: 2023-07-15
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* 0-1 knapsack: Brute-force search */
+func knapsackDFS(wgt: [Int], val: [Int], 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: wgt, val: val, i: i - 1, c: c)
+    }
+    // Calculate the maximum value of not putting in and putting in item i
+    let no = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c)
+    let yes = knapsackDFS(wgt: wgt, val: val, i: i - 1, c: c - wgt[i - 1]) + val[i - 1]
+    // Return the larger value of the two options
+    return max(no, yes)
+}
+
+/* 0-1 knapsack: Memoization search */
+func knapsackDFSMem(wgt: [Int], val: [Int], mem: inout [[Int]], 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: wgt, val: val, mem: &mem, i: i - 1, c: c)
+    }
+    // Calculate the maximum value of not putting in and putting in item i
+    let no = knapsackDFSMem(wgt: wgt, val: val, mem: &mem, i: i - 1, c: c)
+    let yes = knapsackDFSMem(wgt: wgt, val: val, mem: &mem, i: i - 1, c: 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 */
+func knapsackDP(wgt: [Int], val: [Int], cap: Int) -> Int {
+    let n = wgt.count
+    // Initialize dp table
+    var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 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 */
+func knapsackDPComp(wgt: [Int], val: [Int], cap: Int) -> Int {
+    let n = wgt.count
+    // Initialize dp table
+    var dp = Array(repeating: 0, count: cap + 1)
+    // State transition
+    for i in 1 ... n {
+        // Traverse in reverse order
+        for c in (1 ... cap).reversed() {
+            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]
+}
+
+@main
+enum Knapsack {
+    /* Driver Code */
+    static func main() {
+        let wgt = [10, 20, 30, 40, 50]
+        let val = [50, 120, 150, 210, 240]
+        let cap = 50
+        let n = wgt.count
+
+        // Brute-force search
+        var res = knapsackDFS(wgt: wgt, val: val, i: n, c: cap)
+        print("Maximum item value not exceeding knapsack capacity is \(res)")
+
+        // Memoization search
+        var mem = Array(repeating: Array(repeating: -1, count: cap + 1), count: n + 1)
+        res = knapsackDFSMem(wgt: wgt, val: val, mem: &mem, i: n, c: cap)
+        print("Maximum item value not exceeding knapsack capacity is \(res)")
+
+        // Dynamic programming
+        res = knapsackDP(wgt: wgt, val: val, cap: cap)
+        print("Maximum item value not exceeding knapsack capacity is \(res)")
+
+        // Space-optimized dynamic programming
+        res = knapsackDPComp(wgt: wgt, val: val, cap: cap)
+        print("Maximum item value not exceeding knapsack capacity is \(res)")
+    }
+}

en/codes/swift/chapter_dynamic_programming/min_cost_climbing_stairs_dp.swift

@@ -0,0 +1,51 @@
+/**
+ * File: min_cost_climbing_stairs_dp.swift
+ * Created Time: 2023-07-15
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* Minimum cost climbing stairs: Dynamic programming */
+func minCostClimbingStairsDP(cost: [Int]) -> Int {
+    let n = cost.count - 1
+    if n == 1 || n == 2 {
+        return cost[n]
+    }
+    // Initialize dp table, used to store solutions to subproblems
+    var dp = Array(repeating: 0, count: 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 */
+func minCostClimbingStairsDPComp(cost: [Int]) -> Int {
+    let n = cost.count - 1
+    if n == 1 || n == 2 {
+        return cost[n]
+    }
+    var (a, b) = (cost[1], cost[2])
+    for i in 3 ... n {
+        (a, b) = (b, min(a, b) + cost[i])
+    }
+    return b
+}
+
+@main
+enum MinCostClimbingStairsDP {
+    /* Driver Code */
+    static func main() {
+        let cost = [0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1]
+        print("Input stair cost list is \(cost)")
+
+        var res = minCostClimbingStairsDP(cost: cost)
+        print("Minimum cost to climb stairs is \(res)")
+
+        res = minCostClimbingStairsDPComp(cost: cost)
+        print("Minimum cost to climb stairs is \(res)")
+    }
+}

en/codes/swift/chapter_dynamic_programming/min_path_sum.swift

@@ -0,0 +1,123 @@
+/**
+ * File: min_path_sum.swift
+ * Created Time: 2023-07-15
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* Minimum path sum: Brute-force search */
+func minPathSumDFS(grid: [[Int]], 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 .max
+    }
+    // Calculate the minimum path cost from top-left to (i-1, j) and (i, j-1)
+    let up = minPathSumDFS(grid: grid, i: i - 1, j: j)
+    let left = minPathSumDFS(grid: grid, i: i, j: 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 */
+func minPathSumDFSMem(grid: [[Int]], mem: inout [[Int]], 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 .max
+    }
+    // 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
+    let up = minPathSumDFSMem(grid: grid, mem: &mem, i: i - 1, j: j)
+    let left = minPathSumDFSMem(grid: grid, mem: &mem, i: i, j: 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 */
+func minPathSumDP(grid: [[Int]]) -> Int {
+    let n = grid.count
+    let m = grid[0].count
+    // Initialize dp table
+    var dp = Array(repeating: Array(repeating: 0, count: m), count: n)
+    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 */
+func minPathSumDPComp(grid: [[Int]]) -> Int {
+    let n = grid.count
+    let m = grid[0].count
+    // Initialize dp table
+    var dp = Array(repeating: 0, count: 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]
+}
+
+@main
+enum MinPathSum {
+    /* Driver Code */
+    static func main() {
+        let grid = [
+            [1, 3, 1, 5],
+            [2, 2, 4, 2],
+            [5, 3, 2, 1],
+            [4, 3, 5, 2],
+        ]
+        let n = grid.count
+        let m = grid[0].count
+
+        // Brute-force search
+        var res = minPathSumDFS(grid: grid, i: n - 1, j: m - 1)
+        print("Minimum path sum from top-left to bottom-right is \(res)")
+
+        // Memoization search
+        var mem = Array(repeating: Array(repeating: -1, count: m), count: n)
+        res = minPathSumDFSMem(grid: grid, mem: &mem, i: n - 1, j: m - 1)
+        print("Minimum path sum from top-left to bottom-right is \(res)")
+
+        // Dynamic programming
+        res = minPathSumDP(grid: grid)
+        print("Minimum path sum from top-left to bottom-right is \(res)")
+
+        // Space-optimized dynamic programming
+        res = minPathSumDPComp(grid: grid)
+        print("Minimum path sum from top-left to bottom-right is \(res)")
+    }
+}

en/codes/swift/chapter_dynamic_programming/unbounded_knapsack.swift

@@ -0,0 +1,63 @@
+/**
+ * File: unbounded_knapsack.swift
+ * Created Time: 2023-07-15
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+/* Unbounded knapsack: Dynamic programming */
+func unboundedKnapsackDP(wgt: [Int], val: [Int], cap: Int) -> Int {
+    let n = wgt.count
+    // Initialize dp table
+    var dp = Array(repeating: Array(repeating: 0, count: cap + 1), count: n + 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 */
+func unboundedKnapsackDPComp(wgt: [Int], val: [Int], cap: Int) -> Int {
+    let n = wgt.count
+    // Initialize dp table
+    var dp = Array(repeating: 0, count: 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]
+}
+
+@main
+enum UnboundedKnapsack {
+    /* Driver Code */
+    static func main() {
+        let wgt = [1, 2, 3]
+        let val = [5, 11, 15]
+        let cap = 4
+
+        // Dynamic programming
+        var res = unboundedKnapsackDP(wgt: wgt, val: val, cap: cap)
+        print("Maximum item value not exceeding knapsack capacity is \(res)")
+
+        // Space-optimized dynamic programming
+        res = unboundedKnapsackDPComp(wgt: wgt, val: val, cap: cap)
+        print("Maximum item value not exceeding knapsack capacity is \(res)")
+    }
+}