<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) {}
 * };
 */// flag matlab ki vo vha par h ya ni
 // Flag yaani parent covered h ya nhi
 // Flagy yaani root khud
class Solution {
public:
    vector<vector<int>>dp;
    int idx = 0;
    void assign(TreeNode* root)
    {
        if(root == NULL) return;
        root->val = idx;
        idx++;
        assign(root->left);
        assign(root->right);
    }
    int solve(bool flag,bool flagy,TreeNode* root)
    {
        if(root == NULL) return 0;
        
        if(flag == true && flagy == false)
        {
            if(dp[0][root->val] != -1) return dp[0][root->val];
            int ans = INT_MAX;
            if(root->right == NULL && root->left == NULL) return 1; // if this is only left out
            ans = min(ans,1 + solve(true,true,root->left) + solve(true,true,root->right)); // putting camera at root
            if(root->left != NULL) // arranging itself from left one
            {
                ans = min(ans , solve(false,true,root->left) + solve(true,false,root->right));
            }
            if(root->right != NULL) // arranging itself from right
            {
                ans = min(ans , solve(false,true,root->right) + solve(true,false,root->left));
            }
            return dp[0][root->val] = ans;
        }
        if(flag == true && flagy == true)
        {
            if(dp[1][root->val] != -1) return dp[1][root->val];
            int ans = INT_MAX;
            if(root->right == NULL && root->left == NULL) return 0; // No need to put camera on it as flagy is true
            ans = min(ans,1 + solve(true,true,root->left) + solve(true,true,root->right)); // putting camera on itself
            ans = min(ans,solve(true,false,root->left) + solve(true,false,root->right)); // Passing to the children
            return dp[1][root->val] = ans;
        }
        if(flag == false)
        {
            if(dp[2][root->val] != -1) return dp[2][root->val];
            return dp[2][root->val] = 1 + solve(true,true,root->left) + solve(true,true,root->right);
        }
        return 0;
    }
    int minCameraCover(TreeNode* root) {
        // cout<<int(true);
        assign(root);
        dp.clear();
        dp.resize(3,vector<int>(idx+1,-1));
        return solve(true,false,root);
    }
};
20600