543. Diameter of Binary Tree

https://leetcode.com/problems/diameter-of-binary-tree/

Problem

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

1. Recursive

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int diameterOfBinaryTree(TreeNode* root) {
        if (root == nullptr) return 0;
        int diameter = getHeight(root->left) + getHeight(root->right);
        return max(max(diameterOfBinaryTree(root->left), diameterOfBinaryTree(root->right)), diameter);
    }
    int getHeight(TreeNode* root) {
        if (root == nullptr) return 0;
        return max(getHeight(root->left), getHeight(root->right)) + 1;
    }
};

2. Optimized

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int diameterOfBinaryTree(TreeNode* root) {
        int height = 0;
        return diameterOfBinaryTree(root, height);
    }
    int diameterOfBinaryTree(TreeNode* root, int &height) {
        if (root == nullptr) {
            height = 0; return 0;
        }
        int left_height, right_height;
        int diameter_left = diameterOfBinaryTree(root->left, left_height);
        int diameter_right = diameterOfBinaryTree(root->right, right_height);
        height = max(left_height, right_height) + 1;
        return max(max(diameter_left, diameter_right), left_height + right_height);
        
    }
};

• #tree

• #dfs

• #important