<p>You are given the <code>root</code> of a binary tree. We install cameras on the tree nodes where each camera at a node can monitor its parent, itself, and its immediate children.</p>

<p>Return <em>the minimum number of cameras needed to monitor all nodes of the tree</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/29/bst_cameras_01.png" style="width: 138px; height: 163px;" />
<pre>
<strong>Input:</strong> root = [0,0,null,0,0]
<strong>Output:</strong> 1
<strong>Explanation:</strong> One camera is enough to monitor all nodes if placed as shown.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/29/bst_cameras_02.png" style="width: 139px; height: 312px;" />
<pre>
<strong>Input:</strong> root = [0,0,null,0,null,0,null,null,0]
<strong>Output:</strong> 2
<strong>Explanation:</strong> At least two cameras are needed to monitor all nodes of the tree. The above image shows one of the valid configurations of camera placement.
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 1000]</code>.</li>
	<li><code>Node.val == 0</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:
    int minCameraCover(TreeNode* root) {
        vector<int> out = mincam_sub(root);
        return min(out[0],out[1]);
    }

    vector<int> mincam_sub(TreeNode* root){
        //return # of cams needed in subtree if this parent node is {not set, set}xthis node {not set, set}
        if(root==nullptr){
            return {-1};
        }
        vector<int> left_sub = mincam_sub(root->left);
        vector<int> right_sub = mincam_sub(root->right);
        vector<int> out;
        if(root->left){
            if(root->right){
                return {
                    min(left_sub[1]+min(right_sub[0],right_sub[1]),right_sub[1]+min(left_sub[0],left_sub[1])),
                    1+min(left_sub[2],left_sub[3])+min(right_sub[2],right_sub[3]),
                    min(left_sub[0],left_sub[1])+min(right_sub[0],right_sub[1]),
                    1+min(left_sub[2],left_sub[3])+min(right_sub[2],right_sub[3])
                };
            }
            else{
                return {
                    left_sub[1],
                    1+min(left_sub[2],left_sub[3]),
                    min(left_sub[0],left_sub[1]),
                    1+min(left_sub[2],left_sub[3])
                };
            }
        }
        else if(root->right){
            return {
                right_sub[1],
                1+min(right_sub[2],right_sub[3]),
                min(right_sub[0],right_sub[1]),
                1+min(right_sub[2],right_sub[3])
            };
        }
        else{
            return {20000,1,0,1};
        }
    }
};
27300