feat: add rust codes for array binary tree (#654)

* feat: add rust codes for array binary tree

* update tree_node.rs

* update: add implementation of vec_to_tree and tree_to_vec

* update tree_node.rs

* Update tree_node.rs

---------

Co-authored-by: Yudong Jin <krahets@163.com>

codes/rust/Cargo.toml

@@ -154,6 +154,11 @@ path = "chapter_stack_and_queue/array_stack.rs"
 name = "array_queue"
 path = "chapter_stack_and_queue/array_queue.rs"
 
+# Run Command: cargo run --bin array_binary_tree
+[[bin]]
+name = "array_binary_tree"
+path = "chapter_tree/array_binary_tree.rs"
+
 # Run Command: cargo run --bin avl_tree
 [[bin]]
 name = "avl_tree"

codes/rust/chapter_tree/array_binary_tree.rs

@@ -0,0 +1,199 @@
+/*
+ * File: array_binary_tree.rs
+ * Created Time: 2023-07-25
+ * Author: night-cruise (2586447362@qq.com)
+ */
+
+include!("../include/include.rs");
+
+/* 数组表示下的二叉树类 */
+struct ArrayBinaryTree {
+    tree: Vec<Option<i32>>,
+}
+
+impl ArrayBinaryTree {
+    /* 构造方法 */
+    fn new(arr: Vec<Option<i32>>) -> Self {
+        Self { tree: arr }
+    }
+
+    /* 节点数量 */
+    fn size(&self) -> i32 {
+        self.tree.len() as i32
+    }
+
+    /* 获取索引为 i 节点的值 */
+    fn val(&self, i: i32) -> Option<i32> {
+        // 若索引越界，则返回 None ，代表空位
+        if i < 0 || i >= self.size() {
+            None
+        } else {
+            self.tree[i as usize]
+        }
+    }
+
+    /* 获取索引为 i 节点的左子节点的索引 */
+    fn left(&self, i: i32) -> i32 {
+        2 * i + 1
+    }
+
+    /* 获取索引为 i 节点的右子节点的索引 */
+    fn right(&self, i: i32) -> i32 {
+        2 * i + 2
+    }
+
+    /* 获取索引为 i 节点的父节点的索引 */
+    fn parent(&self, i: i32) -> i32 {
+        (i - 1) / 2
+    }
+
+    /* 层序遍历 */
+    fn level_order(&self) -> Vec<i32> {
+        let mut res = vec![];
+        // 直接遍历数组
+        for i in 0..self.size() {
+            if let Some(val) = self.val(i) {
+                res.push(val)
+            }
+        }
+        res
+    }
+
+    /* 深度优先遍历 */
+    fn dfs(&self, i: i32, order: &str, res: &mut Vec<i32>) {
+        if self.val(i).is_none() {
+            return;
+        }
+        let val = self.val(i).unwrap();
+        // 前序遍历
+        if order == "pre" {
+            res.push(val);
+        }
+        self.dfs(self.left(i), order, res);
+        // 中序遍历
+        if order == "in" {
+            res.push(val);
+        }
+        self.dfs(self.right(i), order, res);
+        // 后序遍历
+        if order == "post" {
+            res.push(val);
+        }
+    }
+
+    /* 前序遍历 */
+    fn pre_order(&self) -> Vec<i32> {
+        let mut res = vec![];
+        self.dfs(0, "pre", &mut res);
+        res
+    }
+
+    /* 中序遍历 */
+    fn in_order(&self) -> Vec<i32> {
+        let mut res = vec![];
+        self.dfs(0, "in", &mut res);
+        res
+    }
+
+    /* 后序遍历 */
+    fn post_order(&self) -> Vec<i32> {
+        let mut res = vec![];
+        self.dfs(0, "post", &mut res);
+        res
+    }
+}
+
+/* Driver Code */
+fn main() {
+    // 初始化二叉树
+    // 这里借助了一个从数组直接生成二叉树的函数
+    let arr = vec![
+        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),
+    ];
+
+    let root = tree_node::vec_to_tree(arr.clone()).unwrap();
+    println!("\n初始化二叉树\n");
+    println!("二叉树的数组表示：");
+    println!(
+        "[{}]",
+        arr.iter()
+            .map(|&val| if let Some(val) = val {
+                format!("{val}")
+            } else {
+                "null".to_string()
+            })
+            .collect::<Vec<String>>()
+            .join(", ")
+    );
+    println!("二叉树的链表表示：");
+    print_util::print_tree(&root);
+
+    // 数组表示下的二叉树类
+    let abt = ArrayBinaryTree::new(arr);
+
+    // 访问节点
+    let i = 1;
+    let l = abt.left(i);
+    let r = abt.right(i);
+    let p = abt.parent(i);
+    println!(
+        "\n当前节点的索引为 {} ，值为 {}",
+        i,
+        if let Some(val) = abt.val(i) {
+            format!("{val}")
+        } else {
+            "null".to_string()
+        }
+    );
+    println!(
+        "其左子节点的索引为 {} ，值为 {}",
+        l,
+        if let Some(val) = abt.val(l) {
+            format!("{val}")
+        } else {
+            "null".to_string()
+        }
+    );
+    println!(
+        "其右子节点的索引为 {} ，值为 {}",
+        r,
+        if let Some(val) = abt.val(r) {
+            format!("{val}")
+        } else {
+            "null".to_string()
+        }
+    );
+    println!(
+        "其父节点的索引为 {} ，值为 {}",
+        p,
+        if let Some(val) = abt.val(p) {
+            format!("{val}")
+        } else {
+            "null".to_string()
+        }
+    );
+
+    // 遍历树
+    let mut res = abt.level_order();
+    println!("\n层序遍历为：{:?}", res);
+    res = abt.pre_order();
+    println!("前序遍历为：{:?}", res);
+    res = abt.in_order();
+    println!("中序遍历为：{:?}", res);
+    res = abt.post_order();
+    println!("后序遍历为：{:?}", res);
+}

codes/rust/include/tree_node.rs

@@ -1,14 +1,13 @@
-/**
+/*
  * File: tree_node.rs
  * Created Time: 2023-02-27
- * Author: xBLACKICEx (xBLACKICE@outlook.com)
+ * Author: xBLACKICEx (xBLACKICE@outlook.com), night-cruise (2586447362@qq.com)
  */
 
 use std::cell::RefCell;
-use std::collections::VecDeque;
 use std::rc::Rc;
 
-#[allow(dead_code)]
+/* 二叉树节点类型 */
 #[derive(Debug)]
 pub struct TreeNode {
     pub val: i32,
@@ -19,6 +18,7 @@ pub struct TreeNode {
 }
 
 impl TreeNode {
+    /* 构造方法 */
     pub fn new(val: i32) -> Rc<RefCell<Self>> {
         Rc::new(RefCell::new(Self {
             val,
@@ -39,63 +39,55 @@ macro_rules! op_vec {
     };
 }
 
-/// This function takes a vector of integers and generates a binary tree from it in a level order traversal manner.
-/// The first element of the vector is used as the root node of the tree. Each node in the tree is represented by a `TreeNode` struct that has a value and pointers to its left and right children.
-///
-/// # Arguments
-///
-/// * `list` - A vector of integers to be used to generate the binary tree.
-///
-/// # Returns
-///
-/// An `Option<Rc<RefCell<TreeNode>>>` where the `Option` is `None` if the vector is empty, and `Some` containing the root node of the tree otherwise.
-///
-/// # Examples
-///
-/// ```
-/// use std::rc::Rc;
-/// use std::cell::RefCell;
-/// use std::collections::VecDeque;
-///
-/// let list = vec![1, 2, 3, 4, 5, 6, 7];
-/// let root = vec_to_tree(list).unwrap();
-///
-/// // The resulting tree looks like:
-/// //
-/// //        1
-/// //       / \
-/// //      2   3
-/// //     / \ / \
-/// //    4   56  7
-/// ```
-pub fn vec_to_tree(list: Vec<Option<i32>>) -> Option<Rc<RefCell<TreeNode>>> {
-    if list.is_empty() {
+// 序列化编码规则请参考：
+// https://www.hello-algo.com/chapter_tree/array_representation_of_tree/
+// 二叉树的数组表示：
+// [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]
+// 二叉树的链表表示：
+//             /——— 15
+//         /——— 7
+//     /——— 3
+//    |    \——— 6
+//    |        \——— 12
+// ——— 1
+//     \——— 2
+//        |    /——— 9
+//         \——— 4
+//             \——— 8
+
+/* 将列表反序列化为二叉树：递归 */
+fn vec_to_tree_dfs(arr: &[Option<i32>], i: usize) -> Option<Rc<RefCell<TreeNode>>> {
+    if i >= arr.len() || arr[i].is_none() {
         return None;
     }
-
-    let root = TreeNode::new(list[0].unwrap());
-    let mut que = VecDeque::new();
-    que.push_back(Rc::clone(&root));
-
-    let mut index = 0;
-    while let Some(node) = que.pop_front() {
-        index += 1;
-        if index >= list.len() {
-            break;
+    let root = TreeNode::new(arr[i].unwrap());
+    root.borrow_mut().left = vec_to_tree_dfs(arr, 2 * i + 1);
+    root.borrow_mut().right = vec_to_tree_dfs(arr, 2 * i + 2);
+    Some(root)
 }
-        if let Some(val) = list[index] {
-            node.borrow_mut().left = Some(TreeNode::new(val));
-            que.push_back(Rc::clone(&node.borrow().left.as_ref().unwrap()));
+
+/* 将列表反序列化为二叉树 */
+pub fn vec_to_tree(arr: Vec<Option<i32>>) -> Option<Rc<RefCell<TreeNode>>> {
+    vec_to_tree_dfs(&arr, 0)
 }
 
-        index += 1;
-        if index >= list.len() {
-            break;
+/* 将二叉树序列化为列表：递归 */
+fn tree_to_vec_dfs(root: Option<Rc<RefCell<TreeNode>>>, i: usize, res: &mut Vec<Option<i32>>) {
+    if root.is_none() {
+        return;
     }    
-        if let Some(val) = list[index] {
-            node.borrow_mut().right = Some(TreeNode::new(val));
-            que.push_back(Rc::clone(&node.borrow().right.as_ref().unwrap()));
+    let root = root.unwrap();
+    while i >= res.len() {
+        res.push(None);
     }
+    res[i] = Some(root.borrow().val);
+    tree_to_vec_dfs(root.borrow().left.clone(), 2 * i + 1, res);
+    tree_to_vec_dfs(root.borrow().right.clone(), 2 * i + 2, res);
 }
-    Some(root)
+
+/* 将二叉树序列化为列表 */
+pub fn tree_to_vec(root: Option<Rc<RefCell<TreeNode>>>) -> Vec<Option<i32>> {
+    let mut res = vec![];
+    tree_to_vec_dfs(root, 0, &mut res);
+    res
 }