101. Symmetric Tree - Explanation

Problem Link



# 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(left, right):
            if not left and not right:
                return True
            if not left or not right:
                return False
            return (
                left.val == right.val and
                dfs(left.left, right.right) and
                dfs(left.right, right.left)
            )
        return dfs(root.left, root.right)

Time & Space Complexity

  • Time complexity: O(n)O(n)
  • Space complexity: O(n)O(n) for recursion stack.

2. Iterative DFS

# 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:
        if not root:
            return True

        stack = [(root.left, root.right)]
        while stack:
            left, right = stack.pop()
            if not left and not right:
                continue
            if not left or not right or left.val != right.val:
                return False
            stack.append((left.left, right.right))
            stack.append((left.right, right.left))
        return True

Time & Space Complexity

  • Time complexity: O(n)O(n)
  • Space complexity: O(n)O(n)

# 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:
        if not root:
            return True

        queue = deque([(root.left, root.right)])
        while queue:
            for _ in range(len(queue)):
                left, right = queue.popleft()
                if not left and not right:
                    continue
                if not left or not right or left.val != right.val:
                    return False
                queue.append((left.left, right.right))
                queue.append((left.right, right.left))

        return True

Time & Space Complexity

  • Time complexity: O(n)O(n)
  • Space complexity: O(n)O(n)