<p>Given the <code>root</code> of a binary tree and an integer <code>limit</code>, delete all <strong>insufficient nodes</strong> in the tree simultaneously, and return <em>the root of the resulting binary tree</em>.</p>

<p>A node is <strong>insufficient</strong> if every root to <strong>leaf</strong> path intersecting this node has a sum strictly less than <code>limit</code>.</p>

<p>A <strong>leaf</strong> is a node with no children.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/06/05/insufficient-11.png" style="width: 500px; height: 207px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,4,-99,-99,7,8,9,-99,-99,12,13,-99,14], limit = 1
<strong>Output:</strong> [1,2,3,4,null,null,7,8,9,null,14]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/06/05/insufficient-3.png" style="width: 400px; height: 274px;" />
<pre>
<strong>Input:</strong> root = [5,4,8,11,null,17,4,7,1,null,null,5,3], limit = 22
<strong>Output:</strong> [5,4,8,11,null,17,4,7,null,null,null,5]
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/06/11/screen-shot-2019-06-11-at-83301-pm.png" style="width: 250px; height: 199px;" />
<pre>
<strong>Input:</strong> root = [1,2,-3,-5,null,4,null], limit = -1
<strong>Output:</strong> [1,null,-3,4]
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 5000]</code>.</li>
	<li><code>-10<sup>5</sup> &lt;= Node.val &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= limit &lt;= 10<sup>9</sup></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 {
    bool dfs(TreeNode* root, int pathSum, int limit) {
        if(root == nullptr) {
            return false;
        }
        // leaf
        pathSum += root->val;
        if(root->left == nullptr && root->right == nullptr) {
            return pathSum >= limit;
        }

        bool lhs = dfs(root->left, pathSum, limit);
        if(!lhs && root->left) {
            delete root->left;
            root->left = nullptr;
        }

        bool rhs = dfs(root->right, pathSum, limit);
        if(!rhs && root->right) {
            delete root->right;
            root->right = nullptr;
        }
        return lhs || rhs;
    }
public:
    TreeNode* sufficientSubset(TreeNode* root, int limit) {
        if(!dfs(root, 0, limit)) {
            // delete root;
            return nullptr;
        }
        return root;
    }
};
//  limit = 4
//       5

35400