Add the initial EN translation for C++ code (#1346)

en/codes/cpp/chapter_dynamic_programming/knapsack.cpp

@@ -0,0 +1,109 @@
+#include <algorithm>
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+/* 0-1 Knapsack: Brute force search */
+int knapsackDFS(vector<int> &wgt, vector<int> &val, int i, int c) {
+    // If all items have been chosen or the knapsack has no remaining capacity, return value 0
+    if (i == 0 || c == 0) {
+        return 0;
+    }
+    // If exceeding the knapsack capacity, can only choose not to put it in the knapsack
+    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 greater value of the two options
+    return max(no, yes);
+}
+
+/* 0-1 Knapsack: Memoized search */
+int knapsackDFSMem(vector<int> &wgt, vector<int> &val, vector<vector<int>> &mem, int i, int c) {
+    // If all items have been chosen or the knapsack has no remaining capacity, return value 0
+    if (i == 0 || c == 0) {
+        return 0;
+    }
+    // If there is a record, return it
+    if (mem[i][c] != -1) {
+        return mem[i][c];
+    }
+    // If exceeding the knapsack capacity, can only choose not to put it in the knapsack
+    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
+    int no = knapsackDFSMem(wgt, val, mem, i - 1, c);
+    int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];
+    // Record and return the greater value of the two options
+    mem[i][c] = max(no, yes);
+    return mem[i][c];
+}
+
+/* 0-1 Knapsack: Dynamic programming */
+int knapsackDP(vector<int> &wgt, vector<int> &val, int cap) {
+    int n = wgt.size();
+    // Initialize dp table
+    vector<vector<int>> dp(n + 1, vector<int>(cap + 1, 0));
+    // State transition
+    for (int i = 1; i <= n; i++) {
+        for (int c = 1; c <= cap; c++) {
+            if (wgt[i - 1] > c) {
+                // If exceeding the knapsack capacity, do not choose item i
+                dp[i][c] = dp[i - 1][c];
+            } else {
+                // The greater value between not choosing and choosing 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 */
+int knapsackDPComp(vector<int> &wgt, vector<int> &val, int cap) {
+    int n = wgt.size();
+    // Initialize dp table
+    vector<int> dp(cap + 1, 0);
+    // 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 greater value between not choosing and choosing item i
+                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
+            }
+        }
+    }
+    return dp[cap];
+}
+
+/* Driver Code */
+int main() {
+    vector<int> wgt = {10, 20, 30, 40, 50};
+    vector<int> val = {50, 120, 150, 210, 240};
+    int cap = 50;
+    int n = wgt.size();
+
+    // Brute force search
+    int res = knapsackDFS(wgt, val, n, cap);
+    cout << "The maximum value within the bag capacity is " << res << endl;
+
+    // Memoized search
+    vector<vector<int>> mem(n + 1, vector<int>(cap + 1, -1));
+    res = knapsackDFSMem(wgt, val, mem, n, cap);
+    cout << "The maximum value within the bag capacity is " << res << endl;
+
+    // Dynamic programming
+    res = knapsackDP(wgt, val, cap);
+    cout << "The maximum value within the bag capacity is " << res << endl;
+
+    // Space-optimized dynamic programming
+    res = knapsackDPComp(wgt, val, cap);
+    cout << "The maximum value within the bag capacity is " << res << endl;
+
+    return 0;
+}