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/c/chapter_dynamic_programming/CMakeLists.txt

@@ -0,0 +1,8 @@
+add_executable(climbing_stairs_constraint_dp climbing_stairs_constraint_dp.c)
+add_executable(min_cost_climbing_stairs_dp min_cost_climbing_stairs_dp.c)
+add_executable(min_path_sum min_path_sum.c)
+add_executable(knapsack knapsack.c)
+add_executable(unbounded_knapsack unbounded_knapsack.c)
+add_executable(coin_change coin_change.c)
+add_executable(coin_change_ii coin_change_ii.c)
+add_executable(edit_distance edit_distance.c)

en/codes/c/chapter_dynamic_programming/climbing_stairs_backtrack.c

@@ -0,0 +1,47 @@
+/**
+ * File: climbing_stairs_backtrack.c
+ * Created Time: 2023-09-22
+ * Author: huawuque404 (huawuque404@163.com)
+ */
+
+#include "../utils/common.h"
+
+/* Backtracking */
+void backtrack(int *choices, int state, int n, int *res, int len) {
+    // When climbing to the n-th stair, add 1 to the solution count
+    if (state == n)
+        res[0]++;
+    // Traverse all choices
+    for (int i = 0; i < len; i++) {
+        int choice = choices[i];
+        // 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, len);
+        // Backtrack
+    }
+}
+
+/* Climbing stairs: Backtracking */
+int climbingStairsBacktrack(int n) {
+    int choices[2] = {1, 2}; // Can choose to climb up 1 or 2 stairs
+    int state = 0;           // Start climbing from the 0-th stair
+    int *res = (int *)malloc(sizeof(int));
+    *res = 0; // Use res[0] to record the solution count
+    int len = sizeof(choices) / sizeof(int);
+    backtrack(choices, state, n, res, len);
+    int result = *res;
+    free(res);
+    return result;
+}
+
+/* Driver Code */
+int main() {
+    int n = 9;
+
+    int res = climbingStairsBacktrack(n);
+    printf("Climbing %d stairs has %d solutions\n", n, res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/climbing_stairs_constraint_dp.c

@@ -0,0 +1,46 @@
+/**
+ * File: climbing_stairs_constraint_dp.c
+ * Created Time: 2023-10-02
+ * Author: Zuoxun (845242523@qq.com)
+ */
+
+#include "../utils/common.h"
+
+/* Climbing stairs with constraint: Dynamic programming */
+int climbingStairsConstraintDP(int n) {
+    if (n == 1 || n == 2) {
+        return 1;
+    }
+    // Initialize dp table, used to store solutions to subproblems
+    int **dp = malloc((n + 1) * sizeof(int *));
+    for (int i = 0; i <= n; i++) {
+        dp[i] = calloc(3, sizeof(int));
+    }
+    // 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 (int i = 3; i <= n; i++) {
+        dp[i][1] = dp[i - 1][2];
+        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];
+    }
+    int res = dp[n][1] + dp[n][2];
+    // Free memory
+    for (int i = 0; i <= n; i++) {
+        free(dp[i]);
+    }
+    free(dp);
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    int n = 9;
+
+    int res = climbingStairsConstraintDP(n);
+    printf("Climbing %d stairs has %d solutions\n", n, res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/climbing_stairs_dfs.c

@@ -0,0 +1,32 @@
+/**
+ * File: climbing_stairs_dfs.c
+ * Created Time: 2023-09-19
+ * Author: huawuque404 (huawuque404@163.com)
+ */
+
+#include "../utils/common.h"
+
+/* Search */
+int dfs(int i) {
+    // Known dp[1] and dp[2], return them
+    if (i == 1 || i == 2)
+        return i;
+    // dp[i] = dp[i-1] + dp[i-2]
+    int count = dfs(i - 1) + dfs(i - 2);
+    return count;
+}
+
+/* Climbing stairs: Search */
+int climbingStairsDFS(int n) {
+    return dfs(n);
+}
+
+/* Driver Code */
+int main() {
+    int n = 9;
+
+    int res = climbingStairsDFS(n);
+    printf("Climbing %d stairs has %d solutions\n", n, res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/climbing_stairs_dfs_mem.c

@@ -0,0 +1,44 @@
+/**
+ * File: climbing_stairs_dfs_mem.c
+ * Created Time: 2023-09-19
+ * Author: huawuque404 (huawuque404@163.com)
+ */
+
+#include "../utils/common.h"
+
+/* Memoization search */
+int dfs(int i, int *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]
+    int count = dfs(i - 1, mem) + dfs(i - 2, mem);
+    // Record dp[i]
+    mem[i] = count;
+    return count;
+}
+
+/* Climbing stairs: Memoization search */
+int climbingStairsDFSMem(int n) {
+    // mem[i] records the total number of solutions to climb to the i-th stair, -1 means no record
+    int *mem = (int *)malloc((n + 1) * sizeof(int));
+    for (int i = 0; i <= n; i++) {
+        mem[i] = -1;
+    }
+    int result = dfs(n, mem);
+    free(mem);
+    return result;
+}
+
+/* Driver Code */
+int main() {
+    int n = 9;
+
+    int res = climbingStairsDFSMem(n);
+    printf("Climbing %d stairs has %d solutions\n", n, res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/climbing_stairs_dp.c

@@ -0,0 +1,51 @@
+/**
+ * File: climbing_stairs_dp.c
+ * Created Time: 2023-09-19
+ * Author: huawuque404 (huawuque404@163.com)
+ */
+
+#include "../utils/common.h"
+
+/* Climbing stairs: Dynamic programming */
+int climbingStairsDP(int n) {
+    if (n == 1 || n == 2)
+        return n;
+    // Initialize dp table, used to store solutions to subproblems
+    int *dp = (int *)malloc((n + 1) * sizeof(int));
+    // 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 (int i = 3; i <= n; i++) {
+        dp[i] = dp[i - 1] + dp[i - 2];
+    }
+    int result = dp[n];
+    free(dp);
+    return result;
+}
+
+/* Climbing stairs: Space-optimized dynamic programming */
+int climbingStairsDPComp(int n) {
+    if (n == 1 || n == 2)
+        return n;
+    int a = 1, b = 2;
+    for (int i = 3; i <= n; i++) {
+        int tmp = b;
+        b = a + b;
+        a = tmp;
+    }
+    return b;
+}
+
+/* Driver Code */
+int main() {
+    int n = 9;
+
+    int res = climbingStairsDP(n);
+    printf("Climbing %d stairs has %d solutions\n", n, res);
+
+    res = climbingStairsDPComp(n);
+    printf("Climbing %d stairs has %d solutions\n", n, res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/coin_change.c

@@ -0,0 +1,92 @@
+/**
+ * File: coin_change.c
+ * Created Time: 2023-10-02
+ * Author: Zuoxun (845242523@qq.com)
+ */
+
+#include "../utils/common.h"
+
+/* Find minimum value */
+int myMin(int a, int b) {
+    return a < b ? a : b;
+}
+
+/* Coin change: Dynamic programming */
+int coinChangeDP(int coins[], int amt, int coinsSize) {
+    int n = coinsSize;
+    int MAX = amt + 1;
+    // Initialize dp table
+    int **dp = malloc((n + 1) * sizeof(int *));
+    for (int i = 0; i <= n; i++) {
+        dp[i] = calloc(amt + 1, sizeof(int));
+    }
+    // State transition: first row and first column
+    for (int a = 1; a <= amt; a++) {
+        dp[0][a] = MAX;
+    }
+    // State transition: rest of the rows and columns
+    for (int i = 1; i <= n; i++) {
+        for (int 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] = myMin(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);
+            }
+        }
+    }
+    int res = dp[n][amt] != MAX ? dp[n][amt] : -1;
+    // Free memory
+    for (int i = 0; i <= n; i++) {
+        free(dp[i]);
+    }
+    free(dp);
+    return res;
+}
+
+/* Coin change: Space-optimized dynamic programming */
+int coinChangeDPComp(int coins[], int amt, int coinsSize) {
+    int n = coinsSize;
+    int MAX = amt + 1;
+    // Initialize dp table
+    int *dp = malloc((amt + 1) * sizeof(int));
+    for (int j = 1; j <= amt; j++) {
+        dp[j] = MAX;
+    } 
+    dp[0] = 0;
+
+    // State transition
+    for (int i = 1; i <= n; i++) {
+        for (int 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] = myMin(dp[a], dp[a - coins[i - 1]] + 1);
+            }
+        }
+    }
+    int res = dp[amt] != MAX ? dp[amt] : -1;
+    // Free memory
+    free(dp);
+    return res;
+}
+
+/* Driver code */
+int main() {
+    int coins[] = {1, 2, 5};
+    int coinsSize = sizeof(coins) / sizeof(coins[0]);
+    int amt = 4;
+
+    // Dynamic programming
+    int res = coinChangeDP(coins, amt, coinsSize);
+    printf("Minimum number of coins needed to make target amount is %d\n", res);
+
+    // Space-optimized dynamic programming
+    res = coinChangeDPComp(coins, amt, coinsSize);
+    printf("Minimum number of coins needed to make target amount is %d\n", res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/coin_change_ii.c

@@ -0,0 +1,81 @@
+/**
+ * File: coin_change_ii.c
+ * Created Time: 2023-10-02
+ * Author: Zuoxun (845242523@qq.com)
+ */
+
+#include "../utils/common.h"
+
+/* Coin change II: Dynamic programming */
+int coinChangeIIDP(int coins[], int amt, int coinsSize) {
+    int n = coinsSize;
+    // Initialize dp table
+    int **dp = malloc((n + 1) * sizeof(int *));
+    for (int i = 0; i <= n; i++) {
+        dp[i] = calloc(amt + 1, sizeof(int));
+    }
+    // Initialize first column
+    for (int i = 0; i <= n; i++) {
+        dp[i][0] = 1;
+    }
+    // State transition
+    for (int i = 1; i <= n; i++) {
+        for (int 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]];
+            }
+        }
+    }
+    int res = dp[n][amt];
+    // Free memory
+    for (int i = 0; i <= n; i++) {
+        free(dp[i]);
+    }
+    free(dp);
+    return res;
+}
+
+/* Coin change II: Space-optimized dynamic programming */
+int coinChangeIIDPComp(int coins[], int amt, int coinsSize) {
+    int n = coinsSize;
+    // Initialize dp table
+    int *dp = calloc(amt + 1, sizeof(int));
+    dp[0] = 1;
+    // State transition
+    for (int i = 1; i <= n; i++) {
+        for (int 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]];
+            }
+        }
+    }
+    int res = dp[amt];
+    // Free memory
+    free(dp);
+    return res;
+}
+
+/* Driver code */
+int main() {
+    int coins[] = {1, 2, 5};
+    int coinsSize = sizeof(coins) / sizeof(coins[0]);
+    int amt = 5;
+
+    // Dynamic programming
+    int res = coinChangeIIDP(coins, amt, coinsSize);
+    printf("Number of coin combinations to make target amount is %d\n", res);
+
+    // Space-optimized dynamic programming
+    res = coinChangeIIDPComp(coins, amt, coinsSize);
+    printf("Number of coin combinations to make target amount is %d\n", res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/edit_distance.c

@@ -0,0 +1,159 @@
+/**
+ * File: edit_distance.c
+ * Created Time: 2023-10-02
+ * Author: Zuoxun (845242523@qq.com)
+ */
+
+#include "../utils/common.h"
+
+/* Find minimum value */
+int myMin(int a, int b) {
+    return a < b ? a : b;
+}
+
+/* Edit distance: Brute-force search */
+int editDistanceDFS(char *s, char *t, int i, int 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[i - 1] == t[j - 1])
+        return editDistanceDFS(s, t, i - 1, j - 1);
+    // Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+    int insert = editDistanceDFS(s, t, i, j - 1);
+    int del = editDistanceDFS(s, t, i - 1, j);
+    int replace = editDistanceDFS(s, t, i - 1, j - 1);
+    // Return minimum edit steps
+    return myMin(myMin(insert, del), replace) + 1;
+}
+
+/* Edit distance: Memoization search */
+int editDistanceDFSMem(char *s, char *t, int memCols, int **mem, int i, int 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[i - 1] == t[j - 1])
+        return editDistanceDFSMem(s, t, memCols, mem, i - 1, j - 1);
+    // Minimum edit steps = minimum edit steps of insert, delete, replace + 1
+    int insert = editDistanceDFSMem(s, t, memCols, mem, i, j - 1);
+    int del = editDistanceDFSMem(s, t, memCols, mem, i - 1, j);
+    int replace = editDistanceDFSMem(s, t, memCols, mem, i - 1, j - 1);
+    // Record and return minimum edit steps
+    mem[i][j] = myMin(myMin(insert, del), replace) + 1;
+    return mem[i][j];
+}
+
+/* Edit distance: Dynamic programming */
+int editDistanceDP(char *s, char *t, int n, int m) {
+    int **dp = malloc((n + 1) * sizeof(int *));
+    for (int i = 0; i <= n; i++) {
+        dp[i] = calloc(m + 1, sizeof(int));
+    }
+    // State transition: first row and first column
+    for (int i = 1; i <= n; i++) {
+        dp[i][0] = i;
+    }
+    for (int j = 1; j <= m; j++) {
+        dp[0][j] = j;
+    }
+    // State transition: rest of the rows and columns
+    for (int i = 1; i <= n; i++) {
+        for (int 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] = myMin(myMin(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;
+            }
+        }
+    }
+    int res = dp[n][m];
+    // Free memory
+    for (int i = 0; i <= n; i++) {
+        free(dp[i]);
+    }
+    return res;
+}
+
+/* Edit distance: Space-optimized dynamic programming */
+int editDistanceDPComp(char *s, char *t, int n, int m) {
+    int *dp = calloc(m + 1, sizeof(int));
+    // State transition: first row
+    for (int j = 1; j <= m; j++) {
+        dp[j] = j;
+    }
+    // State transition: rest of the rows
+    for (int i = 1; i <= n; i++) {
+        // State transition: first column
+        int leftup = dp[0]; // Temporarily store dp[i-1, j-1]
+        dp[0] = i;
+        // State transition: rest of the columns
+        for (int j = 1; j <= m; j++) {
+            int 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] = myMin(myMin(dp[j - 1], dp[j]), leftup) + 1;
+            }
+            leftup = temp; // Update for next round's dp[i-1, j-1]
+        }
+    }
+    int res = dp[m];
+    // Free memory
+    free(dp);
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    char *s = "bag";
+    char *t = "pack";
+    int n = strlen(s), m = strlen(t);
+
+    // Brute-force search
+    int res = editDistanceDFS(s, t, n, m);
+    printf("Changing %s to %s requires a minimum of %d edits\n", s, t, res);
+
+    // Memoization search
+    int **mem = malloc((n + 1) * sizeof(int *));
+    for (int i = 0; i <= n; i++) {
+        mem[i] = malloc((m + 1) * sizeof(int));
+        memset(mem[i], -1, (m + 1) * sizeof(int));
+    }
+    res = editDistanceDFSMem(s, t, m + 1, mem, n, m);
+    printf("Changing %s to %s requires a minimum of %d edits\n", s, t, res);
+    // Free memory
+    for (int i = 0; i <= n; i++) {
+        free(mem[i]);
+    }
+    free(mem);
+
+    // Dynamic programming
+    res = editDistanceDP(s, t, n, m);
+    printf("Changing %s to %s requires a minimum of %d edits\n", s, t, res);
+
+    // Space-optimized dynamic programming
+    res = editDistanceDPComp(s, t, n, m);
+    printf("Changing %s to %s requires a minimum of %d edits\n", s, t, res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/knapsack.c

@@ -0,0 +1,137 @@
+/**
+ * File: knapsack.c
+ * Created Time: 2023-10-02
+ * Author: Zuoxun (845242523@qq.com)
+ */
+
+#include "../utils/common.h"
+
+/* Find maximum value */
+int myMax(int a, int b) {
+    return a > b ? a : b;
+}
+
+/* 0-1 knapsack: Brute-force search */
+int knapsackDFS(int wgt[], int val[], int i, int 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
+    int no = knapsackDFS(wgt, val, i - 1, c);
+    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];
+    // Return the larger value of the two options
+    return myMax(no, yes);
+}
+
+/* 0-1 knapsack: Memoization search */
+int knapsackDFSMem(int wgt[], int val[], int memCols, int **mem, int i, int 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, memCols, mem, i - 1, c);
+    }
+    // Calculate the maximum value of not putting in and putting in item i
+    int no = knapsackDFSMem(wgt, val, memCols, mem, i - 1, c);
+    int yes = knapsackDFSMem(wgt, val, memCols, mem, i - 1, c - wgt[i - 1]) + val[i - 1];
+    // Record and return the larger value of the two options
+    mem[i][c] = myMax(no, yes);
+    return mem[i][c];
+}
+
+/* 0-1 knapsack: Dynamic programming */
+int knapsackDP(int wgt[], int val[], int cap, int wgtSize) {
+    int n = wgtSize;
+    // Initialize dp table
+    int **dp = malloc((n + 1) * sizeof(int *));
+    for (int i = 0; i <= n; i++) {
+        dp[i] = calloc(cap + 1, sizeof(int));
+    }
+    // State transition
+    for (int i = 1; i <= n; i++) {
+        for (int 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] = myMax(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);
+            }
+        }
+    }
+    int res = dp[n][cap];
+    // Free memory
+    for (int i = 0; i <= n; i++) {
+        free(dp[i]);
+    }
+    return res;
+}
+
+/* 0-1 knapsack: Space-optimized dynamic programming */
+int knapsackDPComp(int wgt[], int val[], int cap, int wgtSize) {
+    int n = wgtSize;
+    // Initialize dp table
+    int *dp = calloc(cap + 1, sizeof(int));
+    // State transition
+    for (int i = 1; i <= n; i++) {
+        // Traverse in reverse order
+        for (int c = cap; c >= 1; c--) {
+            if (wgt[i - 1] <= c) {
+                // The larger value between not selecting and selecting item i
+                dp[c] = myMax(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
+            }
+        }
+    }
+    int res = dp[cap];
+    // Free memory
+    free(dp);
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    int wgt[] = {10, 20, 30, 40, 50};
+    int val[] = {50, 120, 150, 210, 240};
+    int cap = 50;
+    int n = sizeof(wgt) / sizeof(wgt[0]);
+    int wgtSize = n;
+
+    // Brute-force search
+    int res = knapsackDFS(wgt, val, n, cap);
+    printf("Maximum item value not exceeding knapsack capacity is %d\n", res);
+
+    // Memoization search
+    int **mem = malloc((n + 1) * sizeof(int *));
+    for (int i = 0; i <= n; i++) {
+        mem[i] = malloc((cap + 1) * sizeof(int));
+        memset(mem[i], -1, (cap + 1) * sizeof(int));
+    }
+    res = knapsackDFSMem(wgt, val, cap + 1, mem, n, cap);
+    printf("Maximum item value not exceeding knapsack capacity is %d\n", res);
+    // Free memory
+    for (int i = 0; i <= n; i++) {
+        free(mem[i]);
+    }
+    free(mem);
+
+    // Dynamic programming
+    res = knapsackDP(wgt, val, cap, wgtSize);
+    printf("Maximum item value not exceeding knapsack capacity is %d\n", res);
+
+    // Space-optimized dynamic programming
+    res = knapsackDPComp(wgt, val, cap, wgtSize);
+    printf("Maximum item value not exceeding knapsack capacity is %d\n", res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/min_cost_climbing_stairs_dp.c

@@ -0,0 +1,62 @@
+/**
+ * File: min_cost_climbing_stairs_dp.c
+ * Created Time: 2023-10-02
+ * Author: Zuoxun (845242523@qq.com)
+ */
+
+#include "../utils/common.h"
+
+/* Find minimum value */
+int myMin(int a, int b) {
+    return a < b ? a : b;
+}
+
+/* Minimum cost climbing stairs: Dynamic programming */
+int minCostClimbingStairsDP(int cost[], int costSize) {
+    int n = costSize - 1;
+    if (n == 1 || n == 2)
+        return cost[n];
+    // Initialize dp table, used to store solutions to subproblems
+    int *dp = calloc(n + 1, sizeof(int));
+    // 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 (int i = 3; i <= n; i++) {
+        dp[i] = myMin(dp[i - 1], dp[i - 2]) + cost[i];
+    }
+    int res = dp[n];
+    // Free memory
+    free(dp);
+    return res;
+}
+
+/* Minimum cost climbing stairs: Space-optimized dynamic programming */
+int minCostClimbingStairsDPComp(int cost[], int costSize) {
+    int n = costSize - 1;
+    if (n == 1 || n == 2)
+        return cost[n];
+    int a = cost[1], b = cost[2];
+    for (int i = 3; i <= n; i++) {
+        int tmp = b;
+        b = myMin(a, tmp) + cost[i];
+        a = tmp;
+    }
+    return b;
+}
+
+/* Driver Code */
+int main() {
+    int cost[] = {0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1};
+    int costSize = sizeof(cost) / sizeof(cost[0]);
+    printf("Input stair cost list is:");
+    printArray(cost, costSize);
+
+    int res = minCostClimbingStairsDP(cost, costSize);
+    printf("Minimum cost to climb stairs is %d\n", res);
+
+    res = minCostClimbingStairsDPComp(cost, costSize);
+    printf("Minimum cost to climb stairs is %d\n", res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/min_path_sum.c

@@ -0,0 +1,134 @@
+/**
+ * File: min_path_sum.c
+ * Created Time: 2023-10-02
+ * Author: Zuoxun (845242523@qq.com)
+ */
+
+#include "../utils/common.h"
+
+// Assume max matrix rows and columns is 100
+#define MAX_SIZE 100
+
+/* Find minimum value */
+int myMin(int a, int b) {
+    return a < b ? a : b;
+}
+
+/* Minimum path sum: Brute-force search */
+int minPathSumDFS(int grid[MAX_SIZE][MAX_SIZE], int i, int 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 INT_MAX;
+    }
+    // Calculate the minimum path cost from top-left to (i-1, j) and (i, j-1)
+    int up = minPathSumDFS(grid, i - 1, j);
+    int left = minPathSumDFS(grid, i, j - 1);
+    // Return the minimum path cost from top-left to (i, j)
+    return myMin(left, up) != INT_MAX ? myMin(left, up) + grid[i][j] : INT_MAX;
+}
+
+/* Minimum path sum: Memoization search */
+int minPathSumDFSMem(int grid[MAX_SIZE][MAX_SIZE], int mem[MAX_SIZE][MAX_SIZE], int i, int 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 INT_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
+    int up = minPathSumDFSMem(grid, mem, i - 1, j);
+    int left = minPathSumDFSMem(grid, mem, i, j - 1);
+    // Record and return the minimum path cost from top-left to (i, j)
+    mem[i][j] = myMin(left, up) != INT_MAX ? myMin(left, up) + grid[i][j] : INT_MAX;
+    return mem[i][j];
+}
+
+/* Minimum path sum: Dynamic programming */
+int minPathSumDP(int grid[MAX_SIZE][MAX_SIZE], int n, int m) {
+    // Initialize dp table
+    int **dp = malloc(n * sizeof(int *));
+    for (int i = 0; i < n; i++) {
+        dp[i] = calloc(m, sizeof(int));
+    }
+    dp[0][0] = grid[0][0];
+    // State transition: first row
+    for (int j = 1; j < m; j++) {
+        dp[0][j] = dp[0][j - 1] + grid[0][j];
+    }
+    // State transition: first column
+    for (int i = 1; i < n; i++) {
+        dp[i][0] = dp[i - 1][0] + grid[i][0];
+    }
+    // State transition: rest of the rows and columns
+    for (int i = 1; i < n; i++) {
+        for (int j = 1; j < m; j++) {
+            dp[i][j] = myMin(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];
+        }
+    }
+    int res = dp[n - 1][m - 1];
+    // Free memory
+    for (int i = 0; i < n; i++) {
+        free(dp[i]);
+    }
+    return res;
+}
+
+/* Minimum path sum: Space-optimized dynamic programming */
+int minPathSumDPComp(int grid[MAX_SIZE][MAX_SIZE], int n, int m) {
+    // Initialize dp table
+    int *dp = calloc(m, sizeof(int));
+    // State transition: first row
+    dp[0] = grid[0][0];
+    for (int j = 1; j < m; j++) {
+        dp[j] = dp[j - 1] + grid[0][j];
+    }
+    // State transition: rest of the rows
+    for (int i = 1; i < n; i++) {
+        // State transition: first column
+        dp[0] = dp[0] + grid[i][0];
+        // State transition: rest of the columns
+        for (int j = 1; j < m; j++) {
+            dp[j] = myMin(dp[j - 1], dp[j]) + grid[i][j];
+        }
+    }
+    int res = dp[m - 1];
+    // Free memory
+    free(dp);
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    int grid[MAX_SIZE][MAX_SIZE] = {{1, 3, 1, 5}, {2, 2, 4, 2}, {5, 3, 2, 1}, {4, 3, 5, 2}};
+    int n = 4, m = 4; // Matrix capacity is MAX_SIZE * MAX_SIZE, valid rows and columns are n * m
+
+    // Brute-force search
+    int res = minPathSumDFS(grid, n - 1, m - 1);
+    printf("Minimum path sum from top-left to bottom-right is %d\n", res);
+
+    // Memoization search
+    int mem[MAX_SIZE][MAX_SIZE];
+    memset(mem, -1, sizeof(mem));
+    res = minPathSumDFSMem(grid, mem, n - 1, m - 1);
+    printf("Minimum path sum from top-left to bottom-right is %d\n", res);
+
+    // Dynamic programming
+    res = minPathSumDP(grid, n, m);
+    printf("Minimum path sum from top-left to bottom-right is %d\n", res);
+
+    // Space-optimized dynamic programming
+    res = minPathSumDPComp(grid, n, m);
+    printf("Minimum path sum from top-left to bottom-right is %d\n", res);
+
+    return 0;
+}

en/codes/c/chapter_dynamic_programming/unbounded_knapsack.c

@@ -0,0 +1,81 @@
+/**
+ * File: unbounded_knapsack.c
+ * Created Time: 2023-10-02
+ * Author: Zuoxun (845242523@qq.com)
+ */
+
+#include "../utils/common.h"
+
+/* Find maximum value */
+int myMax(int a, int b) {
+    return a > b ? a : b;
+}
+
+/* Unbounded knapsack: Dynamic programming */
+int unboundedKnapsackDP(int wgt[], int val[], int cap, int wgtSize) {
+    int n = wgtSize;
+    // Initialize dp table
+    int **dp = malloc((n + 1) * sizeof(int *));
+    for (int i = 0; i <= n; i++) {
+        dp[i] = calloc(cap + 1, sizeof(int));
+    }
+    // State transition
+    for (int i = 1; i <= n; i++) {
+        for (int 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] = myMax(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);
+            }
+        }
+    }
+    int res = dp[n][cap];
+    // Free memory
+    for (int i = 0; i <= n; i++) {
+        free(dp[i]);
+    }
+    return res;
+}
+
+/* Unbounded knapsack: Space-optimized dynamic programming */
+int unboundedKnapsackDPComp(int wgt[], int val[], int cap, int wgtSize) {
+    int n = wgtSize;
+    // Initialize dp table
+    int *dp = calloc(cap + 1, sizeof(int));
+    // State transition
+    for (int i = 1; i <= n; i++) {
+        for (int 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] = myMax(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
+            }
+        }
+    }
+    int res = dp[cap];
+    // Free memory
+    free(dp);
+    return res;
+}
+
+/* Driver code */
+int main() {
+    int wgt[] = {1, 2, 3};
+    int val[] = {5, 11, 15};
+    int wgtSize = sizeof(wgt) / sizeof(wgt[0]);
+    int cap = 4;
+
+    // Dynamic programming
+    int res = unboundedKnapsackDP(wgt, val, cap, wgtSize);
+    printf("Maximum item value not exceeding knapsack capacity is %d\n", res);
+
+    // Space-optimized dynamic programming
+    res = unboundedKnapsackDPComp(wgt, val, cap, wgtSize);
+    printf("Maximum item value not exceeding knapsack capacity is %d\n", res);
+
+    return 0;
+}