This approach employs recursion to invert the binary tree. The basic idea is to traverse the tree and swap the left and right children of every node recursively. We recursively call the function on the left and right subtrees until we reach the base case, which is when the node is null.
Time Complexity: O(n) where n is the number of nodes in the tree, because each node is visited once.
Space Complexity: O(h) where h is the height of the tree, for the recursion stack.
1#include <stdio.h>
2#include <stdlib.h>
3
4struct TreeNode {
5 int val;
6 struct TreeNode *left;
7 struct TreeNode *right;
8};
9
10struct TreeNode* invertTree(struct TreeNode* root) {
11 if (root == NULL) return NULL;
12 struct TreeNode* left = invertTree(root->left);
13 struct TreeNode* right = invertTree(root->right);
14 root->left = right;
15 root->right = left;
16 return root;
17}This C solution defines a struct for the tree node, and then uses a recursive function invertTree that swaps the left and right children of each node starting from the root. The recursion continues until all nodes have been swapped.
The iterative approach involves using a queue or stack to traverse the tree level by level (or depth by depth) while inverting the child nodes by putting the left child in place of the right child and vice versa for each node. This is effectively a breadth-first traversal that swaps children iteratively.
Time Complexity: O(n) where n is the number of nodes in the tree.
Space Complexity: O(n) due to the queue data structure.
1from collections import deque
2
3class TreeNode:
4 def __init__(self, val=0, left=None, right=None):
5 self.val = val
6 self.left = left
7 self.right = right
8
9class Solution:
10 def invertTree(self, root: TreeNode) -> TreeNode:
11 if root is None:
12 return None
13 queue = deque([root])
14 while queue:
15 current = queue.popleft()
16 current.left, current.right = current.right, current.left
17 if current.left:
18 queue.append(current.left)
19 if current.right:
20 queue.append(current.right)
21 return rootIn this Python solution, the deque from the collections module is used to implement the queue-based iterative approach. Nodes are processed in a breadth-first manner and swapped in place.