未通过所有测试用例的二叉树的最大路径

Question

我正在尝试解决这个 Leetcode 问题：Binary Tree Maximum Path Sum. 我知道这个问题有很多 SO 答案。但我找不到与我的问题相关的任何内容。因此，在深入研究代码之前，我想简要介绍一下我是如何编写算法的。

If I am at a particular node, I considered the following cases.
 Case 1: The maximum path is somewhere inside the left subtree (not including the current node)
 Case 2: The maximum path is somewhere inside the right subtree (not including the current node)
 Case 3: The maximum path starts from the current node and ends somewhere in the left subtree
 Case 4: The maximum path starts from the current node and ends somewhere in the right subtree
 Case 5: The maximum path is the current node itself.
 Case 6: The maximum path starts somewhere in the left subtree, goes through the current node, and ends somewhere in the right subtree.

这里是代码：

var maxPathSum = function(root) {
    if (root.left === null && root.right === null) {
        return root.val;
    }
    
    // Case 1: Max sum is in the left subtree (not including the root)
    let leftPathSum = 0;
    if (root.left) {
        leftPathSum = maxPathSum(root.left);
    }
     // Case 2: Max sum is in the right subtree (not including the root)
    let rightPathSum = 0;
    if (root.right) {
        rightPathSum = maxPathSum(root.right);
    }
     
    
    // Case 3: root + leftPathSum
    let leftSumWithRoot = leftPathSum + root.val; 
    // Case 4: root + rightPathSum
    let rightSumWithRoot = rightPathSum + root.val; 
    
    let maxWithRoot = Math.max(leftSumWithRoot, rightSumWithRoot); 
    let maxWithoutRoot = Math.max(leftPathSum, rightPathSum); 
    
    let maxSoFar = Math.max(maxWithRoot, maxWithoutRoot); 
    
    // Case 5: Root with alone
    maxSoFar = Math.max(maxSoFar, root.val); 
    
    // Case 6: Max path goes through the root
    let maxThroughRoot = leftSumWithRoot + rightSumWithRoot - root.val;
    
    return Math.max(maxThroughRoot, maxSoFar);
    
};

我得到了一些测试用例通过，一些没有通过，尤其是那些具有负值的测试用例。我知道我的算法很可能有问题，但是有人可以帮我解决我的想法错误的方向。我看到了这个问题的不同解决方案。在某些解决方案中，他们将 ma​​xPathSum(node.left) 和 maxPathSum(node.right) 与 0 进行比较，问题与此有关吗？此外，在其他一些解决方案中，他们没有考虑左右子树内的 maxPathSum。我不应该这样做吗？如果有人让我知道我在哪里做错了，我将非常感激。提前致谢。

Answer 1

您的代码在此输入中失败：[-2,-1]

图表如下所示：

   -2
   /
 -1

所以，let maxWithoutRoot = Math.max(leftPathSum, rightPathSum); 将是 0。然后 maxSoFar 将是零，所以最终你的输出是 0。如果我组织你的代码：

var maxPathSum = function(root) {
    let res=root.val
    function dfs(node){
        if (node===null){
            return 0
        }
        let left=dfs(node.left)
        let right=dfs(node.right)
        // ignoring negatives. looking for max, so if left or right is negative, do not add it
        let leftMax=Math.max(left,0)
        let rightMax=Math.max(right,0)
        res=Math.max(node.val+leftMax+rightMax,res)
        return node.val+Math.max(leftMax,rightMax)
    }
    dfs(root)
    return res
};