<p>A <strong>path</strong> 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 <strong>at most once</strong>. Note that the path does not need to pass through the root.</p>

<p>The <strong>path sum</strong> of a path is the sum of the node&#39;s values in the path.</p>

<p>Given the <code>root</code> of a binary tree, return <em>the maximum <strong>path sum</strong> of any <strong>non-empty</strong> path</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/10/13/exx1.jpg" style="width: 322px; height: 182px;" />
<pre>
<strong>Input:</strong> root = [1,2,3]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The optimal path is 2 -&gt; 1 -&gt; 3 with a path sum of 2 + 1 + 3 = 6.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/10/13/exx2.jpg" />
<pre>
<strong>Input:</strong> root = [-10,9,20,null,null,15,7]
<strong>Output:</strong> 42
<strong>Explanation:</strong> The optimal path is 15 -&gt; 20 -&gt; 7 with a path sum of 15 + 20 + 7 = 42.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 3 * 10<sup>4</sup>]</code>.</li>
	<li><code>-1000 &lt;= Node.val &lt;= 1000</code></li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    void inorder(TreeNode* root, vector<int>& ans){
        if(root==NULL){
            return;
        }
        inorder(root->left, ans);
        ans.push_back(root->val);
        inorder(root->right, ans);
    }
    int maxpathSum(TreeNode* node, int& maxi){
        if(node==NULL){
            return 0;
        }
        int left = max(0,maxpathSum(node->left,maxi));
        int right = max(0,maxpathSum(node->right,maxi));

        maxi = max(maxi, left+right+node->val);
        return max(left,right)+node->val;
    }
    int maxPathSum(TreeNode* root) {
        if(root->left==NULL && root->right==NULL){
            return root->val;
        }
  
        // to encounter if all are negative
        vector<int> ans;
        inorder(root, ans);
        bool check = false;
        for(int i=0;i<ans.size();i++){
            if(ans[i]>0){
                check = true;
            }
        }
        sort(ans.begin(), ans.end());
        if(check==false){
            return ans[ans.size()-1];
        }

        int maxi = 0;
        maxpathSum(root, maxi);
        
        return maxi;

    }
};
27200