<p>You are given an integer <code>n</code>. You have an <code>n x n</code> binary grid <code>grid</code> with all values initially <code>1</code>&#39;s except for some indices given in the array <code>mines</code>. The <code>i<sup>th</sup></code> element of the array <code>mines</code> is defined as <code>mines[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> where <code>grid[x<sub>i</sub>][y<sub>i</sub>] == 0</code>.</p>

<p>Return <em>the order of the largest <strong>axis-aligned</strong> plus sign of </em>1<em>&#39;s contained in </em><code>grid</code>. If there is none, return <code>0</code>.</p>

<p>An <strong>axis-aligned plus sign</strong> of <code>1</code>&#39;s of order <code>k</code> has some center <code>grid[r][c] == 1</code> along with four arms of length <code>k - 1</code> going up, down, left, and right, and made of <code>1</code>&#39;s. Note that there could be <code>0</code>&#39;s or <code>1</code>&#39;s beyond the arms of the plus sign, only the relevant area of the plus sign is checked for <code>1</code>&#39;s.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/13/plus1-grid.jpg" style="width: 404px; height: 405px;" />
<pre>
<strong>Input:</strong> n = 5, mines = [[4,2]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> In the above grid, the largest plus sign can only be of order 2. One of them is shown.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/13/plus2-grid.jpg" style="width: 84px; height: 85px;" />
<pre>
<strong>Input:</strong> n = 1, mines = [[0,0]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There is no plus sign, so return 0.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>1 &lt;= mines.length &lt;= 5000</code></li>
	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt; n</code></li>
	<li>All the pairs <code>(x<sub>i</sub>, y<sub>i</sub>)</code> are <strong>unique</strong>.</li>
</ul>

class Solution {
public:
    int orderOfLargestPlusSign(int n, vector<vector<int>>& mines) {
        vector<vector<int>> grid(n,vector<int>(n,1));
        for(auto it:mines){
            grid[it[0]][it[1]]=0;
        }
        int dp[n+2][n+2][4];
        memset(dp,0,sizeof(dp));
        for(int i=1;i<=n;i++){
            for(int j=1;j<=n;j++){
                if(grid[i-1][j-1]==1){
                    dp[i][j][0]=dp[i][j-1][0]+1;
                    dp[i][j][1]=dp[i-1][j][1]+1;
                }
            }
        }
        for(int i=n;i>=1;i--){
            for(int j=n;j>=1;j--){
                if(grid[i-1][j-1]==1){
                    dp[i][j][2]=dp[i][j+1][2]+1;
                    dp[i][j][3]=dp[i+1][j][3]+1;
                }
            }
        }
        
        int sum=-10000;
        for(int i=1;i<=n;i++){
            for(int j=1;j<=n;j++){
                if(grid[i-1][j-1]==1){
                    int mini=min({dp[i][j][0],dp[i][j][1],dp[i][j][2],dp[i][j][3]});
                    sum=max(sum,mini);
                }
            }
        }
        if(sum==-10000) return 0;
        return sum;
    }
};
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