Leetcode-124: Binary Tree Maximum Path Sum
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Given a binary tree, find the maximum path sum.
For this problem, a path is defined as any sequence of nodes from some starting node to any node in the tree along the parent-child connections. The path must contain at least one node and does not need to go through the root.
For example:
Given the below binary tree,
1 / \ 2 3
Return 6
.
求给定的一颗二叉树中,从某个叶节点到另一个叶节点之间的最大路径和,这条路径不一定需要经过根节点。
思路:二叉树中如果一条路径要连接两个叶节点,那么这条路径一定经过两个叶节点的共同祖先节点A,而且路径的一部分是A经过A的左子节点A.left到叶节点的路径,另一部分是A经过A的右子节点A.right到另一个叶节点的路径。那么该题可以重新描述为:找到树种的一个节点A,使得A.left到叶节点的最大路径和、A.right到叶节点的最大路径和与A.val三者之和最大。可以看到遍历顺序是left->right->root,此时需要用后序遍历(postorder traversal)。
/** * Definition for a binary tree node. * public class TreeNode { * int val; * TreeNode left; * TreeNode right; * TreeNode(int x) { val = x; } * } */class Solution { private int maxValue = Integer.MIN_VALUE; public int maxPathSum(TreeNode root) { if (root == null) return 0; postorder(root); return maxValue; } private int postorder(TreeNode h) { if (h == null) return 0; int left = Math.max(0, postorder(h.left)); int right = Math.max(0, postorder(h.right)); maxValue = Math.max(maxValue, left + right + h.val); return Math.max(left, right) + h.val; }}
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