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en/codes/javascript/chapter_dynamic_programming/climbing_stairs_backtrack.js

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+/**
+ * File: climbing_stairs_backtrack.js
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* Backtracking */
+function backtrack(choices, state, n, res) {
+    // When climbing to the n-th stair, add 1 to the solution count
+    if (state === n) res.set(0, res.get(0) + 1);
+    // Traverse all choices
+    for (const choice of 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 */
+function climbingStairsBacktrack(n) {
+    const choices = [1, 2]; // Can choose to climb up 1 or 2 stairs
+    const state = 0; // Start climbing from the 0-th stair
+    const res = new Map();
+    res.set(0, 0); // Use res[0] to record the solution count
+    backtrack(choices, state, n, res);
+    return res.get(0);
+}
+
+/* Driver Code */
+const n = 9;
+const res = climbingStairsBacktrack(n);
+console.log(`Climbing ${n} stairs has ${res} solutions`);

en/codes/javascript/chapter_dynamic_programming/climbing_stairs_constraint_dp.js

@@ -0,0 +1,30 @@
+/**
+ * File: climbing_stairs_constraint_dp.js
+ * Created Time: 2023-08-23
+ * Author: Gaofer Chou (gaofer-chou@qq.com)
+ */
+
+/* Climbing stairs with constraint: Dynamic programming */
+function climbingStairsConstraintDP(n) {
+    if (n === 1 || n === 2) {
+        return 1;
+    }
+    // Initialize dp table, used to store solutions to subproblems
+    const dp = Array.from(new Array(n + 1), () => new Array(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 (let 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];
+}
+
+/* Driver Code */
+const n = 9;
+const res = climbingStairsConstraintDP(n);
+console.log(`Climbing ${n} stairs has ${res} solutions`);

en/codes/javascript/chapter_dynamic_programming/climbing_stairs_dfs.js

@@ -0,0 +1,24 @@
+/**
+ * File: climbing_stairs_dfs.js
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* Search */
+function dfs(i) {
+    // Known dp[1] and dp[2], return them
+    if (i === 1 || i === 2) return i;
+    // dp[i] = dp[i-1] + dp[i-2]
+    const count = dfs(i - 1) + dfs(i - 2);
+    return count;
+}
+
+/* Climbing stairs: Search */
+function climbingStairsDFS(n) {
+    return dfs(n);
+}
+
+/* Driver Code */
+const n = 9;
+const res = climbingStairsDFS(n);
+console.log(`Climbing ${n} stairs has ${res} solutions`);

en/codes/javascript/chapter_dynamic_programming/climbing_stairs_dfs_mem.js

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+/**
+ * File: climbing_stairs_dfs_mem.js
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* Memoization search */
+function dfs(i, mem) {
+    // 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]
+    const count = dfs(i - 1, mem) + dfs(i - 2, mem);
+    // Record dp[i]
+    mem[i] = count;
+    return count;
+}
+
+/* Climbing stairs: Memoization search */
+function climbingStairsDFSMem(n) {
+    // mem[i] records the total number of solutions to climb to the i-th stair, -1 means no record
+    const mem = new Array(n + 1).fill(-1);
+    return dfs(n, mem);
+}
+
+/* Driver Code */
+const n = 9;
+const res = climbingStairsDFSMem(n);
+console.log(`Climbing ${n} stairs has ${res} solutions`);

en/codes/javascript/chapter_dynamic_programming/climbing_stairs_dp.js

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+/**
+ * File: climbing_stairs_dp.js
+ * Created Time: 2023-07-26
+ * Author: yuan0221 (yl1452491917@gmail.com)
+ */
+
+/* Climbing stairs: Dynamic programming */
+function climbingStairsDP(n) {
+    if (n === 1 || n === 2) return n;
+    // Initialize dp table, used to store solutions to subproblems
+    const dp = new Array(n + 1).fill(-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 (let i = 3; i <= n; i++) {
+        dp[i] = dp[i - 1] + dp[i - 2];
+    }
+    return dp[n];
+}
+
+/* Climbing stairs: Space-optimized dynamic programming */
+function climbingStairsDPComp(n) {
+    if (n === 1 || n === 2) return n;
+    let a = 1,
+        b = 2;
+    for (let i = 3; i <= n; i++) {
+        const tmp = b;
+        b = a + b;
+        a = tmp;
+    }
+    return b;
+}
+
+/* Driver Code */
+const n = 9;
+let res = climbingStairsDP(n);
+console.log(`Climbing ${n} stairs has ${res} solutions`);
+res = climbingStairsDPComp(n);
+console.log(`Climbing ${n} stairs has ${res} solutions`);

en/codes/javascript/chapter_dynamic_programming/coin_change.js

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+/**
+ * File: coin_change.js
+ * Created Time: 2023-08-23
+ * Author: Gaofer Chou (gaofer-chou@qq.com)
+ */
+
+/* Coin change: Dynamic programming */
+function coinChangeDP(coins, amt) {
+    const n = coins.length;
+    const MAX = amt + 1;
+    // Initialize dp table
+    const dp = Array.from({ length: n + 1 }, () =>
+        Array.from({ length: amt + 1 }, () => 0)
+    );
+    // State transition: first row and first column
+    for (let a = 1; a <= amt; a++) {
+        dp[0][a] = MAX;
+    }
+    // State transition: rest of the rows and columns
+    for (let i = 1; i <= n; i++) {
+        for (let 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] = Math.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 */
+function coinChangeDPComp(coins, amt) {
+    const n = coins.length;
+    const MAX = amt + 1;
+    // Initialize dp table
+    const dp = Array.from({ length: amt + 1 }, () => MAX);
+    dp[0] = 0;
+    // State transition
+    for (let i = 1; i <= n; i++) {
+        for (let 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] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);
+            }
+        }
+    }
+    return dp[amt] !== MAX ? dp[amt] : -1;
+}
+
+/* Driver Code */
+const coins = [1, 2, 5];
+const amt = 4;
+
+// Dynamic programming
+let res = coinChangeDP(coins, amt);
+console.log(`Minimum coins needed to make target amount is ${res}`);
+
+// Space-optimized dynamic programming
+res = coinChangeDPComp(coins, amt);
+console.log(`Minimum coins needed to make target amount is ${res}`);

en/codes/javascript/chapter_dynamic_programming/coin_change_ii.js

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+/**
+ * File: coin_change_ii.js
+ * Created Time: 2023-08-23
+ * Author: Gaofer Chou (gaofer-chou@qq.com)
+ */
+
+/* Coin change II: Dynamic programming */
+function coinChangeIIDP(coins, amt) {
+    const n = coins.length;
+    // Initialize dp table
+    const dp = Array.from({ length: n + 1 }, () =>
+        Array.from({ length: amt + 1 }, () => 0)
+    );
+    // Initialize first column
+    for (let i = 0; i <= n; i++) {
+        dp[i][0] = 1;
+    }
+    // State transition
+    for (let i = 1; i <= n; i++) {
+        for (let 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 */
+function coinChangeIIDPComp(coins, amt) {
+    const n = coins.length;
+    // Initialize dp table
+    const dp = Array.from({ length: amt + 1 }, () => 0);
+    dp[0] = 1;
+    // State transition
+    for (let i = 1; i <= n; i++) {
+        for (let 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];
+}
+
+/* Driver Code */
+const coins = [1, 2, 5];
+const amt = 5;
+
+// Dynamic programming
+let res = coinChangeIIDP(coins, amt);
+console.log(`Number of coin combinations to make target amount is ${res}`);
+
+// Space-optimized dynamic programming
+res = coinChangeIIDPComp(coins, amt);
+console.log(`Number of coin combinations to make target amount is ${res}`);

en/codes/javascript/chapter_dynamic_programming/edit_distance.js

@@ -0,0 +1,135 @@
+/**
+ * File: edit_distance.js
+ * Created Time: 2023-08-23
+ * Author: Gaofer Chou (gaofer-chou@qq.com)
+ */
+
+/* Edit distance: Brute-force search */
+function editDistanceDFS(s, t, i, j) {
+    // 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.charAt(i - 1) === t.charAt(j - 1))
+        return editDistanceDFS(s, t, i - 1, j - 1);
+
+    // Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+    const insert = editDistanceDFS(s, t, i, j - 1);
+    const del = editDistanceDFS(s, t, i - 1, j);
+    const replace = editDistanceDFS(s, t, i - 1, j - 1);
+    // Return minimum edit steps
+    return Math.min(insert, del, replace) + 1;
+}
+
+/* Edit distance: Memoization search */
+function editDistanceDFSMem(s, t, mem, i, j) {
+    // 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.charAt(i - 1) === t.charAt(j - 1))
+        return editDistanceDFSMem(s, t, mem, i - 1, j - 1);
+
+    // Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+    const insert = editDistanceDFSMem(s, t, mem, i, j - 1);
+    const del = editDistanceDFSMem(s, t, mem, i - 1, j);
+    const replace = editDistanceDFSMem(s, t, mem, i - 1, j - 1);
+    // Record and return minimum edit steps
+    mem[i][j] = Math.min(insert, del, replace) + 1;
+    return mem[i][j];
+}
+
+/* Edit distance: Dynamic programming */
+function editDistanceDP(s, t) {
+    const n = s.length,
+        m = t.length;
+    const dp = Array.from({ length: n + 1 }, () => new Array(m + 1).fill(0));
+    // State transition: first row and first column
+    for (let i = 1; i <= n; i++) {
+        dp[i][0] = i;
+    }
+    for (let j = 1; j <= m; j++) {
+        dp[0][j] = j;
+    }
+    // State transition: rest of the rows and columns
+    for (let i = 1; i <= n; i++) {
+        for (let j = 1; j <= m; j++) {
+            if (s.charAt(i - 1) === t.charAt(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] =
+                    Math.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 */
+function editDistanceDPComp(s, t) {
+    const n = s.length,
+        m = t.length;
+    const dp = new Array(m + 1).fill(0);
+    // State transition: first row
+    for (let j = 1; j <= m; j++) {
+        dp[j] = j;
+    }
+    // State transition: rest of the rows
+    for (let i = 1; i <= n; i++) {
+        // State transition: first column
+        let leftup = dp[0]; // Temporarily store dp[i-1, j-1]
+        dp[0] = i;
+        // State transition: rest of the columns
+        for (let j = 1; j <= m; j++) {
+            const temp = dp[j];
+            if (s.charAt(i - 1) === t.charAt(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] = Math.min(dp[j - 1], dp[j], leftup) + 1;
+            }
+            leftup = temp; // Update for next round's dp[i-1, j-1]
+        }
+    }
+    return dp[m];
+}
+
+const s = 'bag';
+const t = 'pack';
+const n = s.length,
+    m = t.length;
+
+// Brute-force search
+let res = editDistanceDFS(s, t, n, m);
+console.log(`Changing ${s} to ${t} requires minimum ${res} edits`);
+
+// Memoization search
+const mem = Array.from(new Array(n + 1), () => new Array(m + 1).fill(-1));
+res = editDistanceDFSMem(s, t, mem, n, m);
+console.log(`Changing ${s} to ${t} requires minimum ${res} edits`);
+
+// Dynamic programming
+res = editDistanceDP(s, t);
+console.log(`Changing ${s} to ${t} requires minimum ${res} edits`);
+
+// Space-optimized dynamic programming
+res = editDistanceDPComp(s, t);
+console.log(`Changing ${s} to ${t} requires minimum ${res} edits`);

en/codes/javascript/chapter_dynamic_programming/knapsack.js

@@ -0,0 +1,113 @@
+/**
+ * File: knapsack.js
+ * Created Time: 2023-08-23
+ * Author: Gaofer Chou (gaofer-chou@qq.com)
+ */
+
+/* 0-1 knapsack: Brute-force search */
+function knapsackDFS(wgt, val, i, c) {
+    // 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
+    const no = knapsackDFS(wgt, val, i - 1, c);
+    const yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];
+    // Return the larger value of the two options
+    return Math.max(no, yes);
+}
+
+/* 0-1 knapsack: Memoization search */
+function knapsackDFSMem(wgt, val, mem, i, c) {
+    // 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
+    const no = knapsackDFSMem(wgt, val, mem, i - 1, c);
+    const 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] = Math.max(no, yes);
+    return mem[i][c];
+}
+
+/* 0-1 knapsack: Dynamic programming */
+function knapsackDP(wgt, val, cap) {
+    const n = wgt.length;
+    // Initialize dp table
+    const dp = Array(n + 1)
+        .fill(0)
+        .map(() => Array(cap + 1).fill(0));
+    // State transition
+    for (let i = 1; i <= n; i++) {
+        for (let 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] = Math.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 */
+function knapsackDPComp(wgt, val, cap) {
+    const n = wgt.length;
+    // Initialize dp table
+    const dp = Array(cap + 1).fill(0);
+    // State transition
+    for (let i = 1; i <= n; i++) {
+        // Traverse in reverse order
+        for (let c = cap; c >= 1; c--) {
+            if (wgt[i - 1] <= c) {
+                // The larger value between not selecting and selecting item i
+                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
+            }
+        }
+    }
+    return dp[cap];
+}
+
+/* Driver Code */
+const wgt = [10, 20, 30, 40, 50];
+const val = [50, 120, 150, 210, 240];
+const cap = 50;
+const n = wgt.length;
+
+// Brute-force search
+let res = knapsackDFS(wgt, val, n, cap);
+console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);
+
+// Memoization search
+const mem = Array.from({ length: n + 1 }, () =>
+    Array.from({ length: cap + 1 }, () => -1)
+);
+res = knapsackDFSMem(wgt, val, mem, n, cap);
+console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);
+
+// Dynamic programming
+res = knapsackDP(wgt, val, cap);
+console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);
+
+// Space-optimized dynamic programming
+res = knapsackDPComp(wgt, val, cap);
+console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);

en/codes/javascript/chapter_dynamic_programming/min_cost_climbing_stairs_dp.js

@@ -0,0 +1,49 @@
+/**
+ * File: min_cost_climbing_stairs_dp.js
+ * Created Time: 2023-08-23
+ * Author: Gaofer Chou (gaofer-chou@qq.com)
+ */
+
+/* Minimum cost climbing stairs: Dynamic programming */
+function minCostClimbingStairsDP(cost) {
+    const n = cost.length - 1;
+    if (n === 1 || n === 2) {
+        return cost[n];
+    }
+    // Initialize dp table, used to store solutions to subproblems
+    const dp = new Array(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 (let i = 3; i <= n; i++) {
+        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];
+    }
+    return dp[n];
+}
+
+/* Minimum cost climbing stairs: Space-optimized dynamic programming */
+function minCostClimbingStairsDPComp(cost) {
+    const n = cost.length - 1;
+    if (n === 1 || n === 2) {
+        return cost[n];
+    }
+    let a = cost[1],
+        b = cost[2];
+    for (let i = 3; i <= n; i++) {
+        const tmp = b;
+        b = Math.min(a, tmp) + cost[i];
+        a = tmp;
+    }
+    return b;
+}
+
+/* Driver Code */
+const cost = [0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1];
+console.log('Input stair cost list is:', cost);
+
+let res = minCostClimbingStairsDP(cost);
+console.log(`Minimum cost to climb stairs is: ${res}`);
+
+res = minCostClimbingStairsDPComp(cost);
+console.log(`Minimum cost to climb stairs is: ${res}`);

en/codes/javascript/chapter_dynamic_programming/min_path_sum.js

@@ -0,0 +1,121 @@
+/**
+ * File: min_path_sum.js
+ * Created Time: 2023-08-23
+ * Author: Gaofer Chou (gaofer-chou@qq.com)
+ */
+
+/* Minimum path sum: Brute-force search */
+function minPathSumDFS(grid, i, j) {
+    // 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 Infinity;
+    }
+    // Calculate the minimum path cost from top-left to (i-1, j) and (i, j-1)
+    const up = minPathSumDFS(grid, i - 1, j);
+    const left = minPathSumDFS(grid, i, j - 1);
+    // Return the minimum path cost from top-left to (i, j)
+    return Math.min(left, up) + grid[i][j];
+}
+
+/* Minimum path sum: Memoization search */
+function minPathSumDFSMem(grid, mem, i, j) {
+    // 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 Infinity;
+    }
+    // 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
+    const up = minPathSumDFSMem(grid, mem, i - 1, j);
+    const left = minPathSumDFSMem(grid, mem, i, j - 1);
+    // Record and return the minimum path cost from top-left to (i, j)
+    mem[i][j] = Math.min(left, up) + grid[i][j];
+    return mem[i][j];
+}
+
+/* Minimum path sum: Dynamic programming */
+function minPathSumDP(grid) {
+    const n = grid.length,
+        m = grid[0].length;
+    // Initialize dp table
+    const dp = Array.from({ length: n }, () =>
+        Array.from({ length: m }, () => 0)
+    );
+    dp[0][0] = grid[0][0];
+    // State transition: first row
+    for (let j = 1; j < m; j++) {
+        dp[0][j] = dp[0][j - 1] + grid[0][j];
+    }
+    // State transition: first column
+    for (let i = 1; i < n; i++) {
+        dp[i][0] = dp[i - 1][0] + grid[i][0];
+    }
+    // State transition: rest of the rows and columns
+    for (let i = 1; i < n; i++) {
+        for (let j = 1; j < m; j++) {
+            dp[i][j] = Math.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 */
+function minPathSumDPComp(grid) {
+    const n = grid.length,
+        m = grid[0].length;
+    // Initialize dp table
+    const dp = new Array(m);
+    // State transition: first row
+    dp[0] = grid[0][0];
+    for (let j = 1; j < m; j++) {
+        dp[j] = dp[j - 1] + grid[0][j];
+    }
+    // State transition: rest of the rows
+    for (let i = 1; i < n; i++) {
+        // State transition: first column
+        dp[0] = dp[0] + grid[i][0];
+        // State transition: rest of the columns
+        for (let j = 1; j < m; j++) {
+            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];
+        }
+    }
+    return dp[m - 1];
+}
+
+/* Driver Code */
+const grid = [
+    [1, 3, 1, 5],
+    [2, 2, 4, 2],
+    [5, 3, 2, 1],
+    [4, 3, 5, 2],
+];
+const n = grid.length,
+    m = grid[0].length;
+// Brute-force search
+let res = minPathSumDFS(grid, n - 1, m - 1);
+console.log(`Minimum path sum from top-left to bottom-right is ${res}`);
+
+// Memoization search
+const mem = Array.from({ length: n }, () =>
+    Array.from({ length: m }, () => -1)
+);
+res = minPathSumDFSMem(grid, mem, n - 1, m - 1);
+console.log(`Minimum path sum from top-left to bottom-right is ${res}`);
+
+// Dynamic programming
+res = minPathSumDP(grid);
+console.log(`Minimum path sum from top-left to bottom-right is ${res}`);
+
+// Space-optimized dynamic programming
+res = minPathSumDPComp(grid);
+console.log(`Minimum path sum from top-left to bottom-right is ${res}`);

en/codes/javascript/chapter_dynamic_programming/unbounded_knapsack.js

@@ -0,0 +1,63 @@
+/**
+ * File: unbounded_knapsack.js
+ * Created Time: 2023-08-23
+ * Author: Gaofer Chou (gaofer-chou@qq.com)
+ */
+
+/* Unbounded knapsack: Dynamic programming */
+function unboundedKnapsackDP(wgt, val, cap) {
+    const n = wgt.length;
+    // Initialize dp table
+    const dp = Array.from({ length: n + 1 }, () =>
+        Array.from({ length: cap + 1 }, () => 0)
+    );
+    // State transition
+    for (let i = 1; i <= n; i++) {
+        for (let 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] = Math.max(
+                    dp[i - 1][c],
+                    dp[i][c - wgt[i - 1]] + val[i - 1]
+                );
+            }
+        }
+    }
+    return dp[n][cap];
+}
+
+/* Unbounded knapsack: Space-optimized dynamic programming */
+function unboundedKnapsackDPComp(wgt, val, cap) {
+    const n = wgt.length;
+    // Initialize dp table
+    const dp = Array.from({ length: cap + 1 }, () => 0);
+    // State transition
+    for (let i = 1; i <= n; i++) {
+        for (let 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] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
+            }
+        }
+    }
+    return dp[cap];
+}
+
+/* Driver Code */
+const wgt = [1, 2, 3];
+const val = [5, 11, 15];
+const cap = 4;
+
+// Dynamic programming
+let res = unboundedKnapsackDP(wgt, val, cap);
+console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);
+
+// Space-optimized dynamic programming
+res = unboundedKnapsackDPComp(wgt, val, cap);
+console.log(`Maximum item value not exceeding knapsack capacity is ${res}`);