<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 Node{
    public:
    int i;
    int j;
    int key;
    int dist;
};

class Solution {
public:
    int shortestPathAllKeys(vector<string>& grid) {
        int m=grid.size();
        int n=grid[0].size();
        int k=0;
        map<pair<pair<int,int>,int>,int> mp;  // i,j,key; 
        queue<Node> q;
        int sx=-1,sy=-1;

        for(int i=0;i<m;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]=='@'){
                    sx=i;
                    sy=j;
                }
                if(grid[i][j]>=97 && grid[i][j]<=122){
                    k++;
                }
            }
        }
        int d=INT_MAX;
        q.push({sx,sy,0,0});
        mp[{{0,0},0}]=1;

        while(!q.empty()){
            Node front=q.front();
            q.pop();

            int i=front.i;
            int j=front.j;
            int key_state=front.key;
            int dist=front.dist;
            if(grid[i][j]>=97 && grid[i][j]<=122){
                
                int index=grid[i][j]-'a';
                key_state=key_state|(1<<index);
            }
            //cout<<i<<" "<<j<<" "<<key_state<<" "<<k<<" "<<dist<<endl;
            if(key_state==pow(2,k)-1){
                return dist;
                
            }
            if(grid[i][j]>=65 && grid[i][j]<=90){
                int index=grid[i][j]-'A';
                if(((1<<index) & key_state)==0){
                    continue;
                }
            }
            if(i+1<m && grid[i+1][j]!='#' && mp[{{i+1,j},key_state}]==0){
                mp[{{i+1,j},key_state}]=1;
                q.push({i+1,j,key_state,dist+1});
            }
            if(j+1<n && grid[i][j+1]!='#' && mp[{{i,j+1},key_state}]==0){
                mp[{{i,j+1},key_state}]=1;
                q.push({i,j+1,key_state,dist+1});
            }
            if(i-1>=0 && grid[i-1][j]!='#' && mp[{{i-1,j},key_state}]==0){
                mp[{{i-1,j},key_state}]=1;
                q.push({i-1,j,key_state,dist+1});
            }
            if(j-1>=0 && grid[i][j-1]!='#' && mp[{{i,j-1},key_state}]==0){
                mp[{{i,j-1},key_state}]=1;
                q.push({i,j-1,key_state,dist+1});
            }
            


        }

       
        return -1;




    }
};
27581