tags: leetcode hard Dynamic Programming Tree Depth-First Search Binary Tree

124. Binary Tree Maximum Path Sum

Description

A path in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence at most once. Note that the path does not need to pass through the root.

The path sum of a path is the sum of the node’s values in the path.

Given the root of a binary tree, return the maximum path sum of any non-empty path.

Examples

Example 1:

Input: root = [1,2,3]
Output: 6
Explanation: The optimal path is 2 -> 1 -> 3 with a path sum of 2 + 1 + 3 = 6.

Example 2:

Input: root = [-10,9,20,null,null,15,7]
Output: 42
Explanation: The optimal path is 15 -> 20 -> 7 with a path sum of 15 + 20 + 7 = 42.

Constraints:

• The number of nodes in the tree is in the range $[1, 3 * 10^4]$.
• $-1000 \leq Node.val \leq 1000$

Code

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     struct TreeNode *left;
 *     struct TreeNode *right;
 * };
 */
typedef struct TreeNode TNODE;
#define CASE_MIN -1001
#define MAX(x, y) ((x) > (y) ? (x) : (y))

// Find the depth from root to leaf
int DEPTH_MAX_SEARCH(TNODE* root, int* crossMax) {
    // If node is null, return CASE_MIN
    if (!root)
        return CASE_MIN;
    int left = DEPTH_MAX_SEARCH(root->left, crossMax);
    int right = DEPTH_MAX_SEARCH(root->right, crossMax);
    // No-child leaf return its value
    if (left == CASE_MIN && right == CASE_MIN)
        return root->val;
    int maxChild = MAX(left, right);
    // Avoid child having CASE_MIN, using maxChild as filter
    *crossMax = MAX(*crossMax, maxChild);
    *crossMax = MAX(*crossMax, root->val);
    *crossMax = MAX(*crossMax, (left + right + root->val));
    return MAX((maxChild + root->val), root->val);
}

int maxPathSum(struct TreeNode* root) {
    int crossMax = CASE_MIN;
    int depthMax = DEPTH_MAX_SEARCH(root, &crossMax);
    return MAX(crossMax, depthMax);
}

Complexity

Space	Time
$O(1)$	$O(N)$

Result

• Runtime : 18 ms, 95.54%
• Memory : 13.6 MB, 50.89%