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$ curl repovive.com/roadmaps/data-structures/binary-trees/diameter-solution

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$ curl repovive.com/roadmaps/data-structures/binary-trees/diameter-solution

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Diameter Solution - Binary Trees | Data Structures | Repovive

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Data Structures19 sections · 729 units49h total

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Diameter Solution

Track max during DFS

The diameter through a node is leftHeight + rightHeight. Track the maximum across all nodes:

def diameterOfBinaryTree(root):
    diameter = 0

    def height(node):
        nonlocal diameter
        if node == null:
            return 0
        leftH = height(node.left)
        rightH = height(node.right)
        diameter = max(diameter, leftH + rightH)
        return 1 + max(leftH, rightH)

    height(root)
    return diameter

Notice: compute height recursively, but track the maximum diameter as a side effect. The diameter at each node is the sum of its children's heights.

Time: $O(n)$ . Space: $O(h)$ .