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easyDSA

How do you check if a binary tree is symmetric?

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01

Understand the problem

Explain mirror checking.

treesrecursion
02

Attempt it yourself

Sketch your approach before reading the solution — that's what interviews test.

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03

Study the solution

Compare the tree against its mirror: recursively check that left.left matches right.right and left.right matches right.left, with values equal at each step. O(n) time. It can also be done iteratively with a queue of node pairs.

Solution ready — 2 min read

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04

Read the code

Recursive mirror check
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class TreeNode:
    def __init__(self, val, left=None, right=None):
        self.val, self.left, self.right = val, left, right

def is_symmetric(root):
    def mirror(a, b):
        if not a and not b:
            return True
        if not a or not b or a.val != b.val:
            return False
        return mirror(a.left, b.right) and mirror(a.right, b.left)
    return mirror(root.left, root.right) if root else True


# --- demo ---
sym = TreeNode(1, TreeNode(2, TreeNode(3), TreeNode(4)), TreeNode(2, TreeNode(4), TreeNode(3)))
asym = TreeNode(1, TreeNode(2, None, TreeNode(3)), TreeNode(2, None, TreeNode(3)))
print(is_symmetric(sym))    # True
print(is_symmetric(asym))   # False
05

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