easyDSA

How do you check if a binary tree is symmetric?

Q: How do you check if a binary tree is symmetric?

**Intuition.** A tree is symmetric if its left and right subtrees are **mirror images**. Two trees mirror each other when their roots are equal and, crucially, the *outer* children match and the *inner* children match: left.left ↔ right.right and left.right ↔ right.left . mirror: compare left.left↔right.right, left.right↔right.left <line x1

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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

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