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This approach uses a depth-first search (DFS) to calculate the diameter of the binary tree. The key idea is to determine the longest path passing through each node and update the maximum diameter accordingly.
By computing the height of the left and right subtrees at each node, we can obtain the potential diameter passing through that node as the sum of the heights plus one. We will keep track of the global diameter, updating it as necessary.
Time Complexity: O(N), where N is the number of nodes. Each node is visited once.
Space Complexity: O(H), where H is the height of the tree, representing the call stack size due to recursion.
1#include <stdio.h>
2#define max(a,b) ((a)>(b)?(a):(b))
3
4struct TreeNode {
5 int val;
6 struct TreeNode *left;
7 struct TreeNode *right;
8};
9
10int diameter = 0;
11
12int dfs(struct TreeNode* root) {
13 if (!root) return 0;
14 int left = dfs(root->left);
15 int right = dfs(root->right);
16 diameter = max(diameter, left + right);
17 return max(left, right) + 1;
18}
19
20int diameterOfBinaryTree(struct TreeNode* root) {
21 diameter = 0;
22 dfs(root);
23 return diameter;
24}The implementation involves a helper function dfs that traverses the tree recursively. For each node, it calculates the height of the left and right subtrees. The diameter is updated as the maximum of the current diameter and the sum of the heights of the left and right subtrees. The function diameterOfBinaryTree initializes the diameter and invokes the DFS.
This method enhances the recursive DFS approach by incorporating memoization for subtree height calculations, thereby eliminating redundant computations and improving performance, especially beneficial for trees with high duplication of node structures.
Time Complexity: Approaches O(N) due to controlled redundant calculations via memoization.
Space Complexity: O(N) for storing the heights in the memo array.
1
The JavaScript solution incorporates the Map for caching node heights in DFS, prioritizing optimized recursion by memoizing previously processed nodes' results.