<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) {}
 * };
 */

static const auto speedup = []() {
   std::ios::sync_with_stdio(false);
   std::cin.tie(nullptr);
   std::cout.tie(nullptr);
    return 0;
}();

class Solution {
public:
    int minCameraCover(TreeNode* root) {
        auto[f, s, t] = dfs(root);
        root->left = root->right = 0;
        return min(f, s);
    }

private:
    //first  -> camera in current node
    //second -> camera in prev node(this still covered)
    //third  -> camera does not cover this node
    tuple<int,int,int> dfs(TreeNode* root){

        if(root == 0){
            return {999999, 0, 0};
        }
        auto[lf,ls,lt] = dfs(root->left);
        auto[rf,rs,rt] = dfs(root->right);
        return {
            min({
                lt + rt, ls + rt, rs + lt, 
                ls + rs, lf + rt, rf + lt
            }) + 1,
            min({lf + rs, rf + ls, lf + rf}),
            ls + rs
        };
    }
};
16300