<p>There is a 2D <code>grid</code> of size <code>n x n</code> where each cell of this grid has a lamp that is initially <strong>turned off</strong>.</p>

<p>You are given a 2D array of lamp positions <code>lamps</code>, where <code>lamps[i] = [row<sub>i</sub>, col<sub>i</sub>]</code> indicates that the lamp at <code>grid[row<sub>i</sub>][col<sub>i</sub>]</code> is <strong>turned on</strong>. Even if the same lamp is listed more than once, it is turned on.</p>

<p>When a lamp is turned on, it <strong>illuminates its cell</strong> and <strong>all other cells</strong> in the same <strong>row, column, or diagonal</strong>.</p>

<p>You are also given another 2D array <code>queries</code>, where <code>queries[j] = [row<sub>j</sub>, col<sub>j</sub>]</code>. For the <code>j<sup>th</sup></code> query, determine whether <code>grid[row<sub>j</sub>][col<sub>j</sub>]</code> is illuminated or not. After answering the <code>j<sup>th</sup></code> query, <strong>turn off</strong> the lamp at <code>grid[row<sub>j</sub>][col<sub>j</sub>]</code> and its <strong>8 adjacent lamps</strong> if they exist. A lamp is adjacent if its cell shares either a side or corner with <code>grid[row<sub>j</sub>][col<sub>j</sub>]</code>.</p>

<p>Return <em>an array of integers </em><code>ans</code><em>,</em><em> where </em><code>ans[j]</code><em> should be </em><code>1</code><em> if the cell in the </em><code>j<sup>th</sup></code><em> query was illuminated, or </em><code>0</code><em> if the lamp was not.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/illu_1.jpg" style="width: 750px; height: 209px;" />
<pre>
<strong>Input:</strong> n = 5, lamps = [[0,0],[4,4]], queries = [[1,1],[1,0]]
<strong>Output:</strong> [1,0]
<strong>Explanation:</strong> We have the initial grid with all lamps turned off. In the above picture we see the grid after turning on the lamp at grid[0][0] then turning on the lamp at grid[4][4].
The 0<sup>th</sup>&nbsp;query asks if the lamp at grid[1][1] is illuminated or not (the blue square). It is illuminated, so set ans[0] = 1. Then, we turn off all lamps in the red square.
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/illu_step1.jpg" style="width: 500px; height: 218px;" />
The 1<sup>st</sup>&nbsp;query asks if the lamp at grid[1][0] is illuminated or not (the blue square). It is not illuminated, so set ans[1] = 0. Then, we turn off all lamps in the red rectangle.
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/illu_step2.jpg" style="width: 500px; height: 219px;" />
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 5, lamps = [[0,0],[4,4]], queries = [[1,1],[1,1]]
<strong>Output:</strong> [1,1]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 5, lamps = [[0,0],[0,4]], queries = [[0,4],[0,1],[1,4]]
<strong>Output:</strong> [1,1,0]
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>
	<li><code>0 &lt;= lamps.length &lt;= 20000</code></li>
	<li><code>0 &lt;= queries.length &lt;= 20000</code></li>
	<li><code>lamps[i].length == 2</code></li>
	<li><code>0 &lt;= row<sub>i</sub>, col<sub>i</sub> &lt; n</code></li>
	<li><code>queries[j].length == 2</code></li>
	<li><code>0 &lt;= row<sub>j</sub>, col<sub>j</sub> &lt; n</code></li>
</ul>

class Solution:
    
    def gridIllumination(self, n: int, lamps: List[List[int]], queries: List[List[int]]) -> List[int]:
        """
        IDEAS:
        - State is a 2D array of the board of 0's - when the light goes on, turn the 0 to one of the light
        - at the illumination fields to a list - row, col,lead_diag, other_diag
        - When checking a cell if illuminated - if either the row, col diags in the list then yes, otherwise no
        - When turning off a light, remove the row, col, diags from the list. 
        - Multiple entries of the same row/col/diag imply mutiple lamps are illuminating the squares - ie duplicates are ok

        """
        def turn_on_lamps(rows, cols, lead_diag, other_diag,state):
            for lamp in lamps:
                if tuple(lamp) in state: continue
                r, c = lamp[0], lamp[1]
                state[tuple(lamp)] = 1
                if r in rows: rows[r] += 1 
                else: rows[r] = 1
                if c in cols: cols[c] += 1 
                else: cols[c] = 1
                if r-c in lead_diag: lead_diag[r-c] += 1 
                else: lead_diag[r-c] = 1
                if r+c in other_diag: other_diag[r+c] += 1 
                else: other_diag[r+c] = 1

            return rows, cols, lead_diag, other_diag, state

        def run_queries(rows,cols,lead_diag, other_diag, state):
            for query in queries:
                #print(state)
                #print(rows,cols,lead_diag,other_diag)
                r, c = query[0], query[1]                
                if (r in rows and rows[r] > 0) \
                    or (c in cols and cols[c] > 0) \
                    or (r-c in lead_diag and lead_diag[r-c] > 0) \
                    or (r+c in other_diag and other_diag[r+c] > 0):
                    
                    ans.append(1)
                else:
                    ans.append(0)

                for r_delta in [-1,0,1]:
                    for c_delta in [-1,0,1]:
                        if not (0 <= r+r_delta < n and  0 <= c+c_delta < n): continue
                        if not (r+r_delta,c+c_delta) in state: continue
                        if state[(r+r_delta,c+c_delta)] == 0: #On if it is in State
                            continue
                        
                        state[(r+r_delta,c+c_delta)] = 0
                        rows[r+r_delta] -= 1
                        cols[c+c_delta] -= 1
                        lead_diag[(r+r_delta) - (c+c_delta)] -= 1
                        other_diag[(r+r_delta + c+c_delta)] -= 1

        empty_board = {}
        #lamps = set([tuple(lamp) for lamp in lamps])
        rows, cols, lead_diag, other_diag, state = turn_on_lamps({},{},{},{},empty_board)
        ans = []
        run_queries(rows,cols,lead_diag, other_diag, state)
        return ans
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