<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>

class Solution {
public:
    unordered_map<TreeNode *, vector<int>> mp;
    int recur(TreeNode *root, bool skip, bool hasCover) {
        if (root == nullptr) return 0;
        if (root->left == nullptr && root->right == nullptr) return (!skip || !hasCover);

        if (mp.find(root) == mp.end()) mp[root] = {-1, -1, -1};
        if (mp[root][skip+hasCover] != -1) return mp[root][skip+hasCover];

        int pick = 1 + recur(root->left, true, true) + recur(root->right, true, true);
        int notPick = INT_MAX;
        if (skip) {
            if (root->left) notPick = min(notPick, recur(root->left, hasCover, false) + recur(root->right, true, false));
            if (root->right) notPick = min(notPick, recur(root->left, true, false) + recur(root->right, hasCover, false));
        }
        return mp[root][skip+hasCover] = min(pick, notPick);
    }

    int minCameraCover(TreeNode *root) {
        return recur(root, true, false);
    }
};
24100