feat(csharp): add csharp code for charper divide and conquer (#628)

codes/csharp/chapter_divide_and_conquer/binary_search_recur.cs

@@ -0,0 +1,46 @@
+/**
+* File: binary_search_recur.cs
+* Created Time: 2023-07-18
+* Author: hpstory (hpstory1024@163.com)
+*/
+
+namespace hello_algo.chapter_divide_and_conquer;
+
+public class binary_search_recur {
+    /* 二分查找：问题 f(i, j) */
+    public int dfs(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 */
+    public int binarySearch(int[] nums, int target) {
+        int n = nums.Length;
+        // 求解问题 f(0, n-1)
+        return dfs(nums, target, 0, n - 1);
+    }
+
+    [Test]
+    public void Test() {
+        int target = 6;
+        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);
+        Console.WriteLine("目标元素 6 的索引 = " + index);
+    }
+}

codes/csharp/chapter_divide_and_conquer/build_tree.cs

@@ -0,0 +1,49 @@
+/**
+* File: build_tree.cs
+* Created Time: 2023-07-18
+* Author: hpstory (hpstory1024@163.com)
+*/
+
+namespace hello_algo.chapter_divide_and_conquer;
+
+public class build_tree {
+    /* 构建二叉树：分治 */
+    public TreeNode dfs(int[] preorder, int[] inorder, Dictionary<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 */
+    public TreeNode buildTree(int[] preorder, int[] inorder) {
+        // 初始化哈希表，存储 inorder 元素到索引的映射
+        Dictionary<int, int> hmap = new Dictionary<int, int>();
+        for (int i = 0; i < inorder.Length; i++) {
+            hmap.TryAdd(inorder[i], i);
+        }
+        TreeNode root = dfs(preorder, inorder, hmap, 0, 0, inorder.Length - 1);
+        return root;
+    }
+
+    [Test]
+    public void Test() {
+        int[] preorder = { 3, 9, 2, 1, 7 };
+        int[] inorder = { 9, 3, 1, 2, 7 };
+        Console.WriteLine("前序遍历 = " + string.Join(", ", preorder));
+        Console.WriteLine("中序遍历 = " + string.Join(", ", inorder));
+
+        TreeNode root = buildTree(preorder, inorder);
+        Console.WriteLine("构建的二叉树为：");
+        PrintUtil.PrintTree(root);
+    }
+}

codes/csharp/chapter_divide_and_conquer/hanota.cs

@@ -0,0 +1,59 @@
+/**
+* File: hanota.cs
+* Created Time: 2023-07-18
+* Author: hpstory (hpstory1024@163.com)
+*/
+
+namespace hello_algo.chapter_divide_and_conquer;
+
+public class hanota {
+    /* 移动一个圆盘 */
+    public void move(List<int> src, List<int> tar) {
+        // 从 src 顶部拿出一个圆盘
+        int pan = src[^1];
+        src.RemoveAt(src.Count - 1);
+        // 将圆盘放入 tar 顶部
+        tar.Add(pan);
+    }
+
+    /* 求解汉诺塔：问题 f(i) */
+    public void dfs(int i, List<int> src, List<int> buf, List<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 */
+    public void solveHanota(List<int> A, List<int> B, List<int> C) {
+        int n = A.Count;
+        // 将 A 顶部 n 个圆盘借助 B 移到 C
+        dfs(n, A, B, C);
+    }
+
+    [Test]
+    public void Test() {
+        // 列表尾部是柱子顶部
+        List<int> A = new List<int> { 5, 4, 3, 2, 1 };
+        List<int> B = new List<int>();
+        List<int> C = new List<int>();
+        Console.WriteLine("初始状态下：");
+        Console.WriteLine("A = " + string.Join(", ", A));
+        Console.WriteLine("B = " + string.Join(", ", B));
+        Console.WriteLine("C = " + string.Join(", ", C));
+
+        solveHanota(A, B, C);
+
+        Console.WriteLine("圆盘移动完成后：");
+        Console.WriteLine("A = " + string.Join(", ", A));
+        Console.WriteLine("B = " + string.Join(", ", B));
+        Console.WriteLine("C = " + string.Join(", ", C));
+    }
+}

docs/chapter_divide_and_conquer/hanota_problem.md

@@ -153,7 +153,7 @@
 
     [class]{hanota}-[func]{dfs}
 
-    [class]{hanota}-[func]{hanota}
+    [class]{hanota}-[func]{solveHanota}
     ```
 
 === "Swift"