Add Java and C++ code for the chapter of

divide and conquer.

codes/cpp/CMakeLists.txt

@@ -12,7 +12,8 @@ add_subdirectory(chapter_hashing)
 add_subdirectory(chapter_tree)
 add_subdirectory(chapter_heap)
 add_subdirectory(chapter_graph)
-add_subdirectory(chapter_sorting)
 add_subdirectory(chapter_searching)
+add_subdirectory(chapter_sorting)
+add_subdirectory(chapter_divide_and_conquer)
 add_subdirectory(chapter_backtracking)
 add_subdirectory(chapter_dynamic_programming)

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)

codes/cpp/chapter_divide_and_conquer/binary_search_recur.cpp

@@ -0,0 +1,46 @@
+/**
+ * File: binary_search_recur.cpp
+ * Created Time: 2023-07-17
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* 二分查找：问题 f(i, j) */
+int dfs(vector<int> &nums, int target, int i, int j) {
+    // 若区间为空，代表无目标元素，则返回 -1
+    if (i > j) {
+        return -1;
+    }
+    // 计算中点索引 m
+    int m = (i + j) / 2;
+    if (nums[m] < target) {
+        // 递归子问题 f(m+1, j)
+        return dfs(nums, target, m + 1, j);
+    } else if (nums[m] > target) {
+        // 递归子问题 f(i, m-1)
+        return dfs(nums, target, i, m - 1);
+    } else {
+        // 找到目标元素，返回其索引
+        return m;
+    }
+}
+
+/* 二分查找 */
+int binarySearch(vector<int> &nums, int target) {
+    int n = nums.size();
+    // 求解问题 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};
+
+    // 二分查找（双闭区间）
+    int index = binarySearch(nums, target);
+    cout << "目标元素 6 的索引 = " << index << endl;
+
+    return 0;
+}

codes/cpp/chapter_divide_and_conquer/build_tree.cpp

@@ -0,0 +1,51 @@
+/**
+ * File: build_tree.cpp
+ * Created Time: 2023-07-17
+ * Author: Krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* 构建二叉树：分治 */
+TreeNode *dfs(vector<int> &preorder, vector<int> &inorder, unordered_map<int, int> &hmap, int i, int l, int r) {
+    // 子树区间为空时终止
+    if (r - l < 0)
+        return NULL;
+    // 初始化根节点
+    TreeNode *root = new TreeNode(preorder[i]);
+    // 查询 m ，从而划分左右子树
+    int m = hmap[preorder[i]];
+    // 子问题：构建左子树
+    root->left = dfs(preorder, inorder, hmap, i + 1, l, m - 1);
+    // 子问题：构建右子树
+    root->right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r);
+    // 返回根节点
+    return root;
+}
+
+/* 构建二叉树 */
+TreeNode *buildTree(vector<int> &preorder, vector<int> &inorder) {
+    // 初始化哈希表，存储 inorder 元素到索引的映射
+    unordered_map<int, int> hmap;
+    for (int i = 0; i < inorder.size(); i++) {
+        hmap[inorder[i]] = i;
+    }
+    TreeNode *root = dfs(preorder, inorder, hmap, 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 << "前序遍历 = ";
+    printVector(preorder);
+    cout << "中序遍历 = ";
+    printVector(inorder);
+
+    TreeNode *root = buildTree(preorder, inorder);
+    cout << "构建的二叉树为：\n";
+    printTree(root);
+
+    return 0;
+}

codes/cpp/chapter_divide_and_conquer/hanota.cpp

@@ -0,0 +1,66 @@
+/**
+ * File: hanota.cpp
+ * Created Time: 2023-07-17
+ * Author: Krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* 移动一个圆盘 */
+void move(vector<int> &src, vector<int> &tar) {
+    // 从 src 顶部拿出一个圆盘
+    int pan = src.back();
+    src.pop_back();
+    // 将圆盘放入 tar 顶部
+    tar.push_back(pan);
+}
+
+/* 求解汉诺塔：问题 f(i) */
+void dfs(int i, vector<int> &src, vector<int> &buf, vector<int> &tar) {
+    // 若 src 只剩下一个圆盘，则直接将其移到 tar
+    if (i == 1) {
+        move(src, tar);
+        return;
+    }
+    // 子问题 f(i-1) ：将 src 顶部 i-1 个圆盘借助 tar 移到 buf
+    dfs(i - 1, src, tar, buf);
+    // 子问题 f(1) ：将 src 剩余一个圆盘移到 tar
+    move(src, tar);
+    // 子问题 f(i-1) ：将 buf 顶部 i-1 个圆盘借助 src 移到 tar
+    dfs(i - 1, buf, src, tar);
+}
+
+/* 求解汉诺塔 */
+void hanota(vector<int> &A, vector<int> &B, vector<int> &C) {
+    int n = A.size();
+    // 将 A 顶部 n 个圆盘借助 B 移到 C
+    dfs(n, A, B, C);
+}
+
+/* Driver Code */
+int main() {
+    // 列表尾部是柱子顶部
+    vector<int> A = {5, 4, 3, 2, 1};
+    vector<int> B = {};
+    vector<int> C = {};
+
+    cout << "初始状态下：\n";
+    cout << "A =";
+    printVector(A);
+    cout << "B =";
+    printVector(B);
+    cout << "C =";
+    printVector(C);
+
+    hanota(A, B, C);
+
+    cout << "圆盘移动完成后：\n";
+    cout << "A =";
+    printVector(A);
+    cout << "B =";
+    printVector(B);
+    cout << "C =";
+    printVector(C);
+
+    return 0;
+}