mediumDSA

How do you compute the diameter of a binary tree?

Q: How do you compute the diameter of a binary tree?

**Intuition.** The diameter is the longest path between any two nodes (counted in edges). At any node, the longest path *through* it is leftHeight + rightHeight . So compute heights bottom-up and, at every node, update a global best with that sum — one pass, O(n). longest path through a node = leftHeight + rightHeight <line x1="340" y1="116" x2="390" y2="160" stroke="#22c55

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Explain tree diameter.

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Height + global best

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

def diameter_of_binary_tree(root):
    best = 0
    def height(node):
        nonlocal best
        if not node:
            return 0
        lh = height(node.left)
        rh = height(node.right)
        best = max(best, lh + rh)        # path through this node
        return 1 + max(lh, rh)
    height(root)
    return best


# --- demo ---  longest path 4->2->1->3->5 = 4 edges
root = TreeNode(1, TreeNode(2, TreeNode(4), None), TreeNode(3, None, TreeNode(5)))
print(diameter_of_binary_tree(root))   # 4

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