Diameter of Binary Tree

April 11, 2020

Introduction

Given a binary tree, you need to compute the length of the diameter of the tree. The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.

Example: Given a binary tree 1 /
2 3 / \
4 5
Return 3, which is the length of the path [4,2,1,3] or [5,2,1,3].

Note: The length of path between two nodes is represented by the number of edges between them.

Solution

The simple recursion solution would be to compare on each node sum of heights and max diameter of childs.

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */
func diameterOfBinaryTree(root *TreeNode) int {
    if root == nil {
        return 0
    }
    h := height(root.Left) + height(root.Right)
    d := max(diameterOfBinaryTree(root.Left), diameterOfBinaryTree(root.Right))
    return max(h, d)
}

func max(a, b int) int {
    if a > b {
        return a
    }
    return b
}

func height(root *TreeNode) int {
    if root == nil {
        return 0
    }
    return 1 + max(height(root.Left), height(root.Right))
}

Faster solution would be to use DFS search in the tree.

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */
func diameterOfBinaryTree(root *TreeNode) int {
    maxSoFar := 0
    dfs(root, &maxSoFar)
    return maxSoFar
}

func dfs(node *TreeNode, maxSoFar *int) int {
    if node == nil {
        return -1
    }
    left := 1 + dfs(node.Left, maxSoFar)
    right := 1 + dfs(node.Right, maxSoFar)
    *maxSoFar = max(*maxSoFar, left + right)
    return max(left, right)
}

func max(a, b int) int {
    if a > b {
        return a
    }
    return b
}