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

en/codes/cpp/chapter_divide_and_conquer/CMakeLists.txt

@@ -0,0 +1,3 @@
+add_executable(binary_search_recur binary_search_recur.cpp)
+add_executable(build_tree build_tree.cpp)
+add_executable(hanota hanota.cpp)

en/codes/cpp/chapter_divide_and_conquer/binary_search_recur.cpp

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+/**
+ * File: binary_search_recur.cpp
+ * Created Time: 2023-07-17
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Binary search: problem f(i, j) */
+int dfs(vector<int> &nums, int target, int i, int j) {
+    // If the interval is empty, indicating no target element, return -1
+    if (i > j) {
+        return -1;
+    }
+    // Calculate midpoint index m
+    int m = (i + j) / 2;
+    if (nums[m] < target) {
+        // Recursive subproblem f(m+1, j)
+        return dfs(nums, target, m + 1, j);
+    } else if (nums[m] > target) {
+        // Recursive subproblem f(i, m-1)
+        return dfs(nums, target, i, m - 1);
+    } else {
+        // Found the target element, thus return its index
+        return m;
+    }
+}
+
+/* Binary search */
+int binarySearch(vector<int> &nums, int target) {
+    int n = nums.size();
+    // Solve problem f(0, n-1)
+    return dfs(nums, target, 0, n - 1);
+}
+
+/* Driver Code */
+int main() {
+    int target = 6;
+    vector<int> nums = {1, 3, 6, 8, 12, 15, 23, 26, 31, 35};
+
+    // Binary search (double closed interval)
+    int index = binarySearch(nums, target);
+    cout << "Index of target element 6 =" << index << endl;
+
+    return 0;
+}

en/codes/cpp/chapter_divide_and_conquer/build_tree.cpp

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+/**
+ * File: build_tree.cpp
+ * Created Time: 2023-07-17
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Build binary tree: Divide and conquer */
+TreeNode *dfs(vector<int> &preorder, unordered_map<int, int> &inorderMap, int i, int l, int r) {
+    // Terminate when subtree interval is empty
+    if (r - l < 0)
+        return NULL;
+    // Initialize root node
+    TreeNode *root = new TreeNode(preorder[i]);
+    // Query m to divide left and right subtrees
+    int m = inorderMap[preorder[i]];
+    // Subproblem: build left subtree
+    root->left = dfs(preorder, inorderMap, i + 1, l, m - 1);
+    // Subproblem: build right subtree
+    root->right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);
+    // Return root node
+    return root;
+}
+
+/* Build binary tree */
+TreeNode *buildTree(vector<int> &preorder, vector<int> &inorder) {
+    // Initialize hash table, storing in-order elements to indices mapping
+    unordered_map<int, int> inorderMap;
+    for (int i = 0; i < inorder.size(); i++) {
+        inorderMap[inorder[i]] = i;
+    }
+    TreeNode *root = dfs(preorder, inorderMap, 0, 0, inorder.size() - 1);
+    return root;
+}
+
+/* Driver Code */
+int main() {
+    vector<int> preorder = {3, 9, 2, 1, 7};
+    vector<int> inorder = {9, 3, 1, 2, 7};
+    cout << "Pre-order traversal = ";
+    printVector(preorder);
+    cout << "In-order traversal = ";
+    printVector(inorder);
+
+    TreeNode *root = buildTree(preorder, inorder);
+    cout << "The constructed binary tree is:\n";
+    printTree(root);
+
+    return 0;
+}

en/codes/cpp/chapter_divide_and_conquer/hanota.cpp

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+/**
+ * File: hanota.cpp
+ * Created Time: 2023-07-17
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Move a disc */
+void move(vector<int> &src, vector<int> &tar) {
+    // Take out a disc from the top of src
+    int pan = src.back();
+    src.pop_back();
+    // Place the disc on top of tar
+    tar.push_back(pan);
+}
+
+/* Solve the Tower of Hanoi problem f(i) */
+void dfs(int i, vector<int> &src, vector<int> &buf, vector<int> &tar) {
+    // If only one disc remains on src, move it to tar
+    if (i == 1) {
+        move(src, tar);
+        return;
+    }
+    // Subproblem f(i-1): move the top i-1 discs from src with the help of tar to buf
+    dfs(i - 1, src, tar, buf);
+    // Subproblem f(1): move the remaining one disc from src to tar
+    move(src, tar);
+    // Subproblem f(i-1): move the top i-1 discs from buf with the help of src to tar
+    dfs(i - 1, buf, src, tar);
+}
+
+/* Solve the Tower of Hanoi problem */
+void solveHanota(vector<int> &A, vector<int> &B, vector<int> &C) {
+    int n = A.size();
+    // Move the top n discs from A with the help of B to C
+    dfs(n, A, B, C);
+}
+
+/* Driver Code */
+int main() {
+    // The tail of the list is the top of the pillar
+    vector<int> A = {5, 4, 3, 2, 1};
+    vector<int> B = {};
+    vector<int> C = {};
+
+    cout << "Initial state:\n";
+    cout << "A =";
+    printVector(A);
+    cout << "B =";
+    printVector(B);
+    cout << "C =";
+    printVector(C);
+
+    solveHanota(A, B, C);
+
+    cout << "After disk movement:\n";
+    cout << "A =";
+    printVector(A);
+    cout << "B =";
+    printVector(B);
+    cout << "C =";
+    printVector(C);
+
+    return 0;
+}