226. Invert Binary Tree
Problem Description
Given the root of a binary tree, invert the tree, and return its root.
Example 1:
Input: root = [4,2,7,1,3,6,9]
Output: [4,7,2,9,6,3,1]
Example 2:
Input: root = [2,1,3]
Output: [2,3,1]
Example 3:
Input: root = []
Output: []
Constraints:
- The number of nodes in the tree is in the range
[0, 100] -100 <= Node.val <= 100
Solution
Python Solution
# 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 invertTree(self, root: Optional[TreeNode]) -> Optional[TreeNode]:
# Base case: if root is None, return None
if not root:
return None
# Swap the left and right children
root.left, root.right = root.right, root.left
# Recursively invert the left and right subtrees
self.invertTree(root.left)
self.invertTree(root.right)
return root
Time Complexity: O(n)
Where n is the number of nodes in the tree. We visit each node exactly once.
Space Complexity: O(h)
Where h is the height of the tree, used by the recursion stack.
Java Solution
/**
* 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 TreeNode invertTree(TreeNode root) {
// Base case: if root is null, return null
if (root == null) {
return null;
}
// Swap the left and right children
TreeNode temp = root.left;
root.left = root.right;
root.right = temp;
// Recursively invert the left and right subtrees
invertTree(root.left);
invertTree(root.right);
return root;
}
}
Time Complexity: O(n)
Where n is the number of nodes in the tree. We visit each node exactly once.
Space Complexity: O(h)
Where h is the height of the tree, used by the recursion stack.
C++ Solution
/**
* 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:
TreeNode* invertTree(TreeNode* root) {
// Base case: if root is nullptr, return nullptr
if (!root) {
return nullptr;
}
// Swap the left and right children
TreeNode* temp = root->left;
root->left = root->right;
root->right = temp;
// Recursively invert the left and right subtrees
invertTree(root->left);
invertTree(root->right);
return root;
}
};
Time Complexity: O(n)
Where n is the number of nodes in the tree. We visit each node exactly once.
Space Complexity: O(h)
Where h is the height of the tree, used by the recursion stack.
JavaScript Solution
/**
* 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 {TreeNode}
*/
var invertTree = function(root) {
// Base case: if root is null, return null
if (!root) {
return null;
}
// Swap the left and right children
const temp = root.left;
root.left = root.right;
root.right = temp;
// Recursively invert the left and right subtrees
invertTree(root.left);
invertTree(root.right);
return root;
};
Time Complexity: O(n)
Where n is the number of nodes in the tree. We visit each node exactly once.
Space Complexity: O(h)
Where h is the height of the tree, used by the recursion stack.
C# Solution
/**
* Definition for a binary tree node.
* public class TreeNode {
* public int val;
* public TreeNode left;
* public TreeNode right;
* public TreeNode(int val=0, TreeNode left=null, TreeNode right=null) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
public class Solution {
public TreeNode InvertTree(TreeNode root) {
// Base case: if root is null, return null
if (root == null) {
return null;
}
// Swap the left and right children
TreeNode temp = root.left;
root.left = root.right;
root.right = temp;
// Recursively invert the left and right subtrees
InvertTree(root.left);
InvertTree(root.right);
return root;
}
}
Time Complexity: O(n)
Where n is the number of nodes in the tree. We visit each node exactly once.
Space Complexity: O(h)
Where h is the height of the tree, used by the recursion stack.
Approach Explanation
The solution uses a recursive approach to invert the binary tree. Here's how it works:
- Base Case:
- If the root is null, return null
- This handles empty trees and leaf nodes
- For each node:
- Swap its left and right children
- Recursively invert the left subtree
- Recursively invert the right subtree
Alternative approaches:
- Iterative solution using a queue (level-order traversal)
- Iterative solution using a stack (depth-first traversal)
- Both alternatives have the same time and space complexity