feat: add rust docs (#815)

* feat: add rust docs

* Import std types for built_in_hash doc

docs/chapter_backtracking/backtracking_algorithm.md

@@ -532,7 +532,27 @@
 === "Rust"
 
     ```rust title=""
-
+    /* 回溯算法框架 */
+    fn backtrack(state: &mut State, choices: &Vec<Choice>, res: &mut Vec<State>) {
+        // 判断是否为解
+        if is_solution(state) {
+            // 记录解
+            record_solution(state, res);
+            // 停止继续搜索
+            return;
+        }
+        // 遍历所有选择
+        for choice in choices {
+            // 剪枝：判断选择是否合法
+            if is_valid(state, choice) {
+                // 尝试：做出选择，更新状态
+                make_choice(state, choice);
+                backtrack(state, choices, res);
+                // 回退：撤销选择，恢复到之前的状态
+                undo_choice(state, choice);
+            }
+        }
+    }
     ```
 
 === "C"

docs/chapter_data_structure/basic_data_types.md

@@ -135,7 +135,11 @@
 === "Rust"
 
     ```rust title=""
-
+    // 使用多种基本数据类型来初始化数组
+    let numbers: Vec<i32> = vec![0; 5];
+    let decimals: Vec<float> = vec![0.0, 5];
+    let characters: Vec<char> = vec!['0'; 5];
+    let bools: Vec<bool> = vec![false; 5];
     ```
 
 === "C"

docs/chapter_hashing/hash_algorithm.md

@@ -436,6 +436,45 @@ $$
 === "Rust"
 
     ```rust title="built_in_hash.rs"
+    use std::collections::hash_map::DefaultHasher;
+    use std::hash::{Hash, Hasher};
+    
+    let num = 3;
+    let mut num_hasher = DefaultHasher::new();
+    num.hash(&mut num_hasher);
+    let hash_num = num_hasher.finish();
+    // 整数 3 的哈希值为 568126464209439262
+
+    let bol = true;
+    let mut bol_hasher = DefaultHasher::new();
+    bol.hash(&mut bol_hasher);
+    let hash_bol = bol_hasher.finish();
+    // 布尔量 true 的哈希值为 4952851536318644461
+
+    let dec: f32 = 3.14159;
+    let mut dec_hasher = DefaultHasher::new();
+    dec.to_bits().hash(&mut dec_hasher);
+    let hash_dec = dec_hasher.finish();
+    println!("小数 {} 的哈希值为 {}", dec, hash_dec);
+    // 小数 3.14159 的哈希值为 2566941990314602357
+
+    let str = "Hello 算法";
+    let mut str_hasher = DefaultHasher::new();
+    str.hash(&mut str_hasher);
+    let hash_str = str_hasher.finish();
+    // 字符串 Hello 算法 的哈希值为 16092673739211250988
+
+    let arr = (&12836, &"小哈");
+    let mut tup_hasher = DefaultHasher::new();
+    arr.hash(&mut tup_hasher);
+    let hash_tup = tup_hasher.finish();
+    // 元组 (12836, "小哈") 的哈希值为 1885128010422702749
+
+    let node = ListNode::new(42);
+    let mut hasher = DefaultHasher::new();
+    node.borrow().val.hash(&mut hasher);
+    let hash = hasher.finish();
+    // 节点对象 RefCell { value: ListNode { val: 42, next: None } } 的哈希值为15387811073369036852
 
     ```
 

docs/chapter_heap/heap.md

@@ -296,7 +296,41 @@
 === "Rust"
 
     ```rust title="heap.rs"
+    use std::collections::BinaryHeap;
+    use std::cmp::Reverse;
 
+    /* 初始化堆 */
+    // 初始化小顶堆
+    let mut min_heap = BinaryHeap::<Reverse<i32>>::new();
+    // 初始化大顶堆
+    let mut max_heap = BinaryHeap::new();
+
+    /* 元素入堆 */
+    max_heap.push(1);
+    max_heap.push(3);
+    max_heap.push(2);
+    max_heap.push(5);
+    max_heap.push(4);
+    
+    /* 获取堆顶元素 */
+    let peek = max_heap.peek().unwrap();  // 5
+
+    /* 堆顶元素出堆 */
+    // 出堆元素会形成一个从大到小的序列
+    let peek = max_heap.pop().unwrap();   // 5
+    let peek = max_heap.pop().unwrap();   // 4
+    let peek = max_heap.pop().unwrap();   // 3
+    let peek = max_heap.pop().unwrap();   // 2
+    let peek = max_heap.pop().unwrap();   // 1
+
+    /* 获取堆大小 */
+    let size = max_heap.len();
+
+    /* 判断堆是否为空 */
+    let is_empty = max_heap.is_empty();
+
+    /* 输入列表并建堆 */
+    let min_heap = BinaryHeap::from(vec![Reverse(1), Reverse(3), Reverse(2), Reverse(5), Reverse(4)]);
     ```
 
 === "C"

docs/chapter_stack_and_queue/stack.md

@@ -278,20 +278,16 @@
     stack.push(4);
 
     /* 访问栈顶元素 */
-    if let Some(top) = stack.get(stack.len() - 1) {
+    let top = stack[stack.len() - 1];
-    } 
-    if let Some(top) = stack.last() {
-    }
 
     /* 元素出栈 */
-    if let Some(pop) = stack.pop() {
+    let pop = stack.pop().unwrap();
-    }
 
     /* 获取栈的长度 */
     let size = stack.len();
 
     /* 判断是否为空 */
-    let isEmpty = stack.is_empty();
+    let is_empty = stack.is_empty();
     ```
 
 === "C"

docs/chapter_tree/array_representation_of_tree.md

@@ -99,7 +99,9 @@
 === "Rust"
 
     ```rust title=""
-
+    /* 二叉树的数组表示 */
+    // 使用 None 来标记空位
+    let tree = [Some(1), Some(2), Some(3), Some(4), None, Some(6), Some(7), Some(8), Some(9), None, None, Some(12), None, None, Some(15)];
     ```
 
 === "C"

docs/chapter_tree/avl_tree.md

@@ -153,7 +153,28 @@ AVL 树既是二叉搜索树也是平衡二叉树，同时满足这两类二叉
 === "Rust"
 
     ```rust title=""
+    use std::rc::Rc;
+    use std::cell::RefCell;
 
+    /* AVL 树节点类型 */
+    struct TreeNode {
+        val: i32,                               // 节点值
+        height: i32,                            // 节点高度
+        left: Option<Rc<RefCell<TreeNode>>>,    // 左子节点
+        right: Option<Rc<RefCell<TreeNode>>>,   // 右子节点
+    }
+
+    impl TreeNode {
+        /* AVL 树节点构造方法 */
+        fn new(val: i32) -> Rc<RefCell<Self>> {
+            Rc::new(RefCell::new(Self {
+                val,
+                height: 0,
+                left: None,
+                right: None
+            }))
+        }
+    }
     ```
 
 === "C"

docs/chapter_tree/binary_tree.md

@@ -126,7 +126,26 @@
 === "Rust"
 
     ```rust title=""
+    use std::rc::Rc;
+    use std::cell::RefCell;
 
+    /* 二叉树节点类型 */
+    struct TreeNode {
+        val: i32,                               // 节点值
+        left: Option<Rc<RefCell<TreeNode>>>,    // 左子节点引用
+        right: Option<Rc<RefCell<TreeNode>>>,   // 右子节点引用
+    }
+
+    impl TreeNode {
+        /* 二叉树节点构造方法 */
+        fn new(val: i32) -> Rc<RefCell<Self>> {
+            Rc::new(RefCell::new(Self {
+                val,
+                left: None,
+                right: None
+            }))
+        }
+    }
     ```
 
 === "C"
@@ -346,7 +365,17 @@
 === "Rust"
 
     ```rust title="binary_tree.rs"
-
+    // 初始化节点
+    let n1 = TreeNode::new(1);
+    let n2 = TreeNode::new(2);
+    let n3 = TreeNode::new(3);
+    let n4 = TreeNode::new(4);
+    let n5 = TreeNode::new(5);
+    // 构建引用指向（即指针）
+    n1.borrow_mut().left = Some(n2.clone());
+    n1.borrow_mut().right = Some(n3);
+    n2.borrow_mut().left = Some(n4);
+    n2.borrow_mut().right = Some(n5);
     ```
 
 === "C"
@@ -487,7 +516,12 @@
 === "Rust"
 
     ```rust title="binary_tree.rs"
-
+    let p = TreeNode::new(0);
+    // 在 n1 -> n2 中间插入节点 P
+    n1.borrow_mut().left = Some(p.clone());
+    p.borrow_mut().left = Some(n2.clone());
+    // 删除节点 p
+    n1.borrow_mut().left = Some(n2);
     ```
 
 === "C"