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101. Symmetric Tree

Description

Given the root of a binary tree, check whether it is a mirror of itself (i.e., symmetric around its center).

 

Example 1:

Input: root = [1,2,2,3,4,4,3]
Output: true

Example 2:

Input: root = [1,2,2,null,3,null,3]
Output: false

 

Constraints:

  • The number of nodes in the tree is in the range [1, 1000].
  • -100 <= Node.val <= 100

 

Follow up: Could you solve it both recursively and iteratively?

Solutions

Solution 1: Recursion

We design a function $dfs(root1, root2)$ to determine whether two binary trees are symmetric. The answer is $dfs(root, root)$.

The logic of the function $dfs(root1, root2)$ is as follows:

  • If both $root1$ and $root2$ are null, then the two binary trees are symmetric, return true.
  • If only one of $root1$ and $root2$ is null, or if $root1.val \neq root2.val$, then the two binary trees are not symmetric, return false.
  • Otherwise, determine whether the left subtree of $root1$ is symmetric to the right subtree of $root2$, and whether the right subtree of $root1$ is symmetric to the left subtree of $root2$. Here we use recursion.

The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the number of nodes in the binary tree.

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# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def isSymmetric(self, root: Optional[TreeNode]) -> bool:
        def dfs(root1, root2):
            if root1 is None and root2 is None:
                return True
            if root1 is None or root2 is None or root1.val != root2.val:
                return False
            return dfs(root1.left, root2.right) and dfs(root1.right, root2.left)

        return dfs(root, root)

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/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public boolean isSymmetric(TreeNode root) {
        return dfs(root, root);
    }

    private boolean dfs(TreeNode root1, TreeNode root2) {
        if (root1 == null && root2 == null) {
            return true;
        }
        if (root1 == null || root2 == null || root1.val != root2.val) {
            return false;
        }
        return dfs(root1.left, root2.right) && dfs(root1.right, root2.left);
    }
}

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/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    bool isSymmetric(TreeNode* root) {
        function<bool(TreeNode*, TreeNode*)> dfs = [&](TreeNode* root1, TreeNode* root2) -> bool {
            if (!root1 && !root2) return true;
            if (!root1 || !root2 || root1->val != root2->val) return false;
            return dfs(root1->left, root2->right) && dfs(root1->right, root2->left);
        };
        return dfs(root, root);
    }
};

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/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */
func isSymmetric(root *TreeNode) bool {
    var dfs func(*TreeNode, *TreeNode) bool
    dfs = func(root1, root2 *TreeNode) bool {
        if root1 == nil && root2 == nil {
            return true
        }
        if root1 == nil || root2 == nil || root1.Val != root2.Val {
            return false
        }
        return dfs(root1.Left, root2.Right) && dfs(root1.Right, root2.Left)
    }
    return dfs(root, root)
}

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/**
 * Definition for a binary tree node.
 * class TreeNode {
 *     val: number
 *     left: TreeNode | null
 *     right: TreeNode | null
 *     constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
 *         this.val = (val===undefined ? 0 : val)
 *         this.left = (left===undefined ? null : left)
 *         this.right = (right===undefined ? null : right)
 *     }
 * }
 */

const dfs = (root1: TreeNode | null, root2: TreeNode | null) => {
    if (root1 == root2) {
        return true;
    }
    if (root1 == null || root2 == null || root1.val != root2.val) {
        return false;
    }
    return dfs(root1.left, root2.right) && dfs(root1.right, root2.left);
};

function isSymmetric(root: TreeNode | null): boolean {
    return dfs(root.left, root.right);
}

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// Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//     TreeNode {
//       val,
//       left: None,
//       right: None
//     }
//   }
// }
use std::cell::RefCell;
use std::rc::Rc;
impl Solution {
    fn dfs(root1: &Option<Rc<RefCell<TreeNode>>>, root2: &Option<Rc<RefCell<TreeNode>>>) -> bool {
        if root1.is_none() && root2.is_none() {
            return true;
        }
        if root1.is_none() || root2.is_none() {
            return false;
        }
        let node1 = root1.as_ref().unwrap().borrow();
        let node2 = root2.as_ref().unwrap().borrow();
        node1.val == node2.val
            && Self::dfs(&node1.left, &node2.right)
            && Self::dfs(&node1.right, &node2.left)
    }

    pub fn is_symmetric(root: Option<Rc<RefCell<TreeNode>>>) -> bool {
        let node = root.as_ref().unwrap().borrow();
        Self::dfs(&node.left, &node.right)
    }
}

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/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @return {boolean}
 */
var isSymmetric = function (root) {
    function dfs(root1, root2) {
        if (!root1 && !root2) return true;
        if (!root1 || !root2 || root1.val != root2.val) return false;
        return dfs(root1.left, root2.right) && dfs(root1.right, root2.left);
    }
    return dfs(root, root);
};

Solution 2

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// Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//     TreeNode {
//       val,
//       left: None,
//       right: None
//     }
//   }
// }
use std::cell::RefCell;
use std::collections::VecDeque;
use std::rc::Rc;
impl Solution {
    pub fn is_symmetric(root: Option<Rc<RefCell<TreeNode>>>) -> bool {
        let root = root.unwrap();
        let mut node = root.as_ref().borrow_mut();
        let mut queue = VecDeque::new();
        queue.push_back([node.left.take(), node.right.take()]);
        while let Some([root1, root2]) = queue.pop_front() {
            if root1.is_none() && root2.is_none() {
                continue;
            }
            if root1.is_none() || root2.is_none() {
                return false;
            }
            if let (Some(node1), Some(node2)) = (root1, root2) {
                let mut node1 = node1.as_ref().borrow_mut();
                let mut node2 = node2.as_ref().borrow_mut();
                if node1.val != node2.val {
                    return false;
                }
                queue.push_back([node1.left.take(), node2.right.take()]);
                queue.push_back([node1.right.take(), node2.left.take()]);
            }
        }
        true
    }
}

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