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/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);
+}