<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:
    def orderOfLargestPlusSign(self, n: int, mines: List[List[int]]) -> int:
        map_mines = [[1 for _ in range(n)] for _ in range(n)]
        dp = [[{"->":0, "<-":0, "^": 0, "v": 0} for _ in range(n)] for _ in range(n)]

        for mine in mines :
            map_mines[mine[0]][mine[1]] = 0

        for r in range(n):
            for c in range(n):

                #left up
                if map_mines[r][c] == 1:
                    #up
                    if r == 0:
                        dp[r][c]["^"] = 1
                    else:
                        dp[r][c]["^"] = 1 + dp[r-1][c]["^"]
                    
                    #left
                    if c == 0:
                        dp[r][c]["<-"] = 1
                    else:
                        dp[r][c]["<-"] = 1 + dp[r][c-1]["<-"]
                

                #right down
                r_r = n - 1 - r
                c_r = n - 1 - c
                if map_mines[r_r][c_r] == 1:
                    # down
                    if r_r == n-1:
                        dp[r_r][c_r]["v"] = 1 
                    else:
                        dp[r_r][c_r]["v"] = 1 + dp[r_r+1][c_r]["v"]

                    # right
                    if c_r == n-1:
                        dp[r_r][c_r]["->"] = 1 
                    else:
                        dp[r_r][c_r]["->"] = 1 + dp[r_r][c_r+1]["->"]

        res = 0
        for r in range(n):
            for c in range(n):
                res = max(res, min(dp[r][c]["->"], min(dp[r][c]["<-"], min(dp[r][c]["^"], dp[r][c]["v"]))))

        return res
        
75076