<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:
    unordered_map<TreeNode*, vector<int>> dp;

    int minCameraCover(TreeNode* root) {
        return min(minCamera(root, 1, 1), minCamera(root, 0, 0));
    }

    int minCamera(TreeNode* root, int cam, int covered) {
        if (dp.find(root) != dp.end() && dp[root][(cam << 1) + covered] != -1)
            return dp[root][(cam << 1) + covered];

        if (dp.find(root) == dp.end())
            dp[root] = vector<int>(4, -1);

        if (!root->left && !root->right) {
            return dp[root][(cam << 1) + covered] = covered ? cam : 1;
        }

        if (!root->left || !root->right) {
            TreeNode* child = root->left ? root->left : root->right;
            if (covered)
                return dp[root][(cam << 1) + covered] = cam + min(minCamera(child, 0, cam), minCamera(child, 1, 1));
            return dp[root][(cam << 1) + covered] = cam + minCamera(child, 1, 1);
        }

        if (covered) {
            return dp[root][(cam << 1) + covered] = cam + 
                min(min(minCamera(root->left, 0, cam) + minCamera(root->right, 0, cam), 
                        minCamera(root->left, 1, 1) + minCamera(root->right, 0, cam)),
                    min(minCamera(root->left, 0, cam) + minCamera(root->right, 1, 1),
                        minCamera(root->left, 1, 1) + minCamera(root->right, 1, 1)));
        }

        return dp[root][(cam << 1) + covered] = cam + 
                min(minCamera(root->left, 1, 1) + minCamera(root->right, 0, cam),
                    min(minCamera(root->left, 0, cam) + minCamera(root->right, 1, 1),
                        minCamera(root->left, 1, 1) + minCamera(root->right, 1, 1)));
    }
};
27000