_124.java

package com.fishercoder.solutions;

import com.fishercoder.common.classes.TreeNode;

import java.util.HashMap;
import java.util.Map;

/**
 * 124. Binary Tree Maximum Path Sum

 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.
 */
public class _124 {

  public static class Solution1 {
    int max = Integer.MIN_VALUE;

    public int maxPathSum(TreeNode root) {
      dfs(root);
      return max;
    }

    private int dfs(TreeNode root) {
      if (root == null) {
        return 0;
      }

      int left = Math.max(dfs(root.left), 0);
      int right = Math.max(dfs(root.right), 0);

      max = Math.max(max, root.val + left + right);

      return root.val + Math.max(left, right);
    }
  }

  public static class Solution2 {
    /**
     * This one uses a map to cache, but surprisingly, it's 10% slower than all submissions compared
     * with solution1
     */
    int max = Integer.MIN_VALUE;

    public int maxPathSum(TreeNode root) {
      Map<TreeNode, Integer> map = new HashMap<>();
      dfs(root, map);
      return max;
    }

    private int dfs(TreeNode root, Map<TreeNode, Integer> map) {
      if (root == null) {
        return 0;
      }
      if (map.containsKey(root)) {
        return map.get(root);
      }
      int left = Math.max(0, dfs(root.left, map));
      int right = Math.max(0, dfs(root.right, map));
      max = Math.max(max, root.val + left + right);
      int pathSum = root.val + Math.max(left, right);
      map.put(root, pathSum);
      return pathSum;
    }
  }
}