rust : add codes for chapter_divide_and_conquer (#621)

codes/rust/Cargo.toml

@@ -334,5 +334,20 @@ path = "chapter_backtracking/preorder_traversal_iii_compact.rs"
 name = "preorder_traversal_iii_template"
 path = "chapter_backtracking/preorder_traversal_iii_template.rs"
 
+# Run Command: cargo run --bin binary_search_recur
+[[bin]]
+name = "binary_search_recur"
+path = "chapter_divide_and_conquer/binary_search_recur.rs"
+
+# Run Command: cargo run --bin hanota
+[[bin]]
+name = "hanota"
+path = "chapter_divide_and_conquer/hanota.rs"
+
+# Run Command: cargo run --bin build_tree
+[[bin]]
+name = "build_tree"
+path = "chapter_divide_and_conquer/build_tree.rs"
+
 [dependencies]
 rand = "0.8.5"

codes/rust/chapter_divide_and_conquer/binary_search_recur.rs

@@ -0,0 +1,39 @@
+/*
+ * File: binary_search_recur.rs
+ * Created Time: 2023-07-15
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+/* 二分查找：问题 f(i, j) */
+fn dfs(nums: &[i32], target: i32, i: i32, j: i32) -> i32 {
+    // 若区间为空，代表无目标元素，则返回 -1
+    if i > j { return -1; }
+    let m: i32 = (i + j) / 2;
+    if nums[m as usize] < target {
+        // 递归子问题 f(m+1, j)
+        return dfs(nums, target, m + 1, j);
+    } else if nums[m as usize] > 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 */
+fn binary_search(nums: &[i32], target: i32) -> i32 {
+    let n = nums.len() as i32;
+    // 求解问题 f(0, n-1)
+    dfs(nums, target, 0, n - 1)
+}
+
+/* Driver Code */
+pub fn main() {
+    let target = 6;
+    let nums = [ 1, 3, 6, 8, 12, 15, 23, 26, 31, 35 ];
+
+    // 二分查找（双闭区间）
+    let index = binary_search(&nums, target);
+    println!("目标元素 6 的索引 = {index}");
+}

codes/rust/chapter_divide_and_conquer/build_tree.rs

@@ -0,0 +1,50 @@
+/*
+ * File: build_tree.rs
+ * Created Time: 2023-07-15
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+ use std::{cell::RefCell, rc::Rc};
+ use std::collections::HashMap;
+ include!("../include/include.rs");
+ use tree_node::TreeNode;
+ 
+/* 构建二叉树：分治 */
+fn dfs(preorder: &[i32], inorder: &[i32], hmap: &HashMap<i32, i32>, i: i32, l: i32, r: i32) -> Option<Rc<RefCell<TreeNode>>> {
+    // 子树区间为空时终止
+    if r - l < 0 { return None; }
+    // 初始化根节点
+    let root = TreeNode::new(preorder[i as usize]);
+    // 查询 m ，从而划分左右子树
+    let m = hmap.get(&preorder[i as usize]).unwrap();
+    // 子问题：构建左子树
+    root.borrow_mut().left = dfs(preorder, inorder, hmap, i + 1, l, m - 1);
+    // 子问题：构建右子树
+    root.borrow_mut().right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r);
+    // 返回根节点
+    Some(root)
+}
+
+/* 构建二叉树 */
+ fn build_tree(preorder: &[i32], inorder: &[i32]) -> Option<Rc<RefCell<TreeNode>>> {
+    // 初始化哈希表，存储 inorder 元素到索引的映射
+    let mut hmap: HashMap<i32, i32> = HashMap::new();
+    for i in 0..inorder.len() {
+        hmap.insert(inorder[i], i as i32);
+    }
+    let root = dfs(preorder, inorder, &hmap, 0, 0, inorder.len() as i32 - 1);
+    root
+}
+
+ /* Driver Code */
+ fn main() {
+    let preorder = [ 3, 9, 2, 1, 7 ];
+    let inorder = [ 9, 3, 1, 2, 7 ];
+    println!("中序遍历 = {:?}", preorder);
+    println!("前序遍历 = {:?}", inorder);
+
+    let root = build_tree(&preorder, &inorder);
+    println!("构建的二叉树为：");
+    print_util::print_tree(root.as_ref().unwrap());
+ }
+ 

codes/rust/chapter_divide_and_conquer/hanota.rs

@@ -0,0 +1,53 @@
+/*
+ * File: hanota.rs
+ * Created Time: 2023-07-15
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+/* 移动一个圆盘 */
+fn move_pan(src: &mut Vec<i32>, tar: &mut Vec<i32>) {
+    // 从 src 顶部拿出一个圆盘
+    let pan = src.remove(src.len() - 1);
+    // 将圆盘放入 tar 顶部
+    tar.push(pan);
+}
+
+/* 求解汉诺塔：问题 f(i) */
+fn dfs(i: i32, src: &mut Vec<i32>, buf: &mut Vec<i32>, tar: &mut Vec<i32>) {
+    // 若 src 只剩下一个圆盘，则直接将其移到 tar
+    if i == 1 {
+        move_pan(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_pan(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 */
+fn hanota(A: &mut Vec<i32>, B: &mut Vec<i32>, C: &mut Vec<i32>) {
+    let n = A.len() as i32;
+    // 将 A 顶部 n 个圆盘借助 B 移到 C
+    dfs(n, A, B, C);
+}
+
+/* Driver Code */
+pub fn main() {
+    let mut A = vec![5, 4, 3, 2, 1];
+    let mut B = Vec::new();
+    let mut C = Vec::new();
+    println!("初始状态下：");
+    println!("A = {:?}", A);
+    println!("B = {:?}", B);
+    println!("C = {:?}", C);
+
+    hanota(&mut A, &mut B, &mut C);
+
+    println!("圆盘移动完成后：");
+    println!("A = {:?}", A);
+    println!("B = {:?}", B);
+    println!("C = {:?}", C);
+}