<p>You are given an <code>m x n</code> grid <code>grid</code> where:</p>

<ul>
	<li><code>&#39;.&#39;</code> is an empty cell.</li>
	<li><code>&#39;#&#39;</code> is a wall.</li>
	<li><code>&#39;@&#39;</code> is the starting point.</li>
	<li>Lowercase letters represent keys.</li>
	<li>Uppercase letters represent locks.</li>
</ul>

<p>You start at the starting point and one move consists of walking one space in one of the four cardinal directions. You cannot walk outside the grid, or walk into a wall.</p>

<p>If you walk over a key, you can pick it up and you cannot walk over a lock unless you have its corresponding key.</p>

<p>For some <code><font face="monospace">1 &lt;= k &lt;= 6</font></code>, there is exactly one lowercase and one uppercase letter of the first <code>k</code> letters of the English alphabet in the grid. This means that there is exactly one key for each lock, and one lock for each key; and also that the letters used to represent the keys and locks were chosen in the same order as the English alphabet.</p>

<p>Return <em>the lowest number of moves to acquire all keys</em>. If it is impossible, return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-keys2.jpg" style="width: 404px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [&quot;@.a..&quot;,&quot;###.#&quot;,&quot;b.A.B&quot;]
<strong>Output:</strong> 8
<strong>Explanation:</strong> Note that the goal is to obtain all the keys not to open all the locks.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-key2.jpg" style="width: 404px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [&quot;@..aA&quot;,&quot;..B#.&quot;,&quot;....b&quot;]
<strong>Output:</strong> 6
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-keys3.jpg" style="width: 244px; height: 85px;" />
<pre>
<strong>Input:</strong> grid = [&quot;@Aa&quot;]
<strong>Output:</strong> -1
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either an English letter, <code>&#39;.&#39;</code>, <code>&#39;#&#39;</code>, or <code>&#39;@&#39;</code>.&nbsp;</li>
	<li>There is exactly one&nbsp;<code>&#39;@&#39;</code>&nbsp;in the grid.</li>
	<li>The number of keys in the grid is in the range <code>[1, 6]</code>.</li>
	<li>Each key in the grid is <strong>unique</strong>.</li>
	<li>Each key in the grid has a matching lock.</li>
</ul>

class Solution {
public:
    vector<int>dir_x = {0,0,1,-1};
    vector<int>dir_y = {1,-1,0,0};
    bool isLock(vector<string>& grid, int x, int y){

        if(grid[x][y] == '.' || grid[x][y] == '#'){
            return false;
        }
        if(grid[x][y] - 'A' >= 0 && grid[x][y] - 'A' <= 5){
            return true;
        }

        return false;

    }
    bool isKey(vector<string>& grid, int x, int y){

        if(grid[x][y] == '.' || grid[x][y] == '#'){
            return false;
        }
        if(grid[x][y] - 'a' >= 0 && grid[x][y] - 'a' <= 5){
            return true;
        }

        return false;

    }
    bool validate(int x, int y, vector<string>& grid, int keys){

        if(grid[x][y] == '#'){
            return false;
        }

        if(isLock(grid,x,y)){
            int lock = grid[x][y] - 'A';
            if( (keys & (1<<lock)) != 0){
                return true;
            }
            return false;
        }

        return true;

    }
    bool isGood(int x, int y, vector<string>& grid, int keys){

        if(x<0 || y<0 || x>=grid.size() || y>=grid[0].size()){
            return 0;
        }
        if(grid[x][y] == '#'){
            return 0;
        }
        if(isLock(grid, x, y)){
            int lock = grid[x][y] - 'A';
            if( (keys & (1<<lock)) != 0){
                return true;
            }
            return false;
        }

        return true;

    }
    int shortestPathAllKeys(vector<string>& grid) {
        
        int ans = 0;
        set<vector<int>>vis;
        set<char>keys;
        int noOfKeys = 0;

        queue<vector<int>>q;

        for(int i=0;i<grid.size();i++){
            for(int j=0;j<grid[i].size();j++){
                if(grid[i][j] == '@'){
                    q.push({i,j,0});
                }
                else if(isLock(grid, i, j)){
                    noOfKeys++;
                }
            }
        }

        int req = (1<<(noOfKeys)) - 1;
        // cout<<req<<endl;

        while(q.size()){

            int n = q.size();
            while(n--){

                vector<int> curr = q.front();
                q.pop();
                if(vis.find(curr) != vis.end()){
                    continue;
                }
                vis.insert(curr);
                int x = curr[0], y = curr[1], keys = curr[2];
                
                if(!validate(x, y, grid, keys)){
                    continue;
                }
                if(isKey(grid, x, y)){
                    int key = (grid[x][y]-'a');
                    keys |= (1<<key);
                }
                if(keys == req){
                    return ans;
                }

                for(int i=0;i<4;i++){
                    int new_x = x+dir_x[i], new_y = y+dir_y[i];
                    if(isGood(new_x, new_y, grid, keys)){
                        q.push({new_x, new_y, keys});
                    }
                }

            }

            ans++;

        }

        return -1;

    }
};
85020