<p>There is a strange printer with the following two special requirements:</p>

<ul>
	<li>On each turn, the printer will print a solid rectangular pattern of a single color on the grid. This will cover up the existing colors in the rectangle.</li>
	<li>Once the printer has used a color for the above operation, <strong>the same color cannot be used again</strong>.</li>
</ul>

<p>You are given a <code>m x n</code> matrix <code>targetGrid</code>, where <code>targetGrid[row][col]</code> is the color in the position <code>(row, col)</code> of the grid.</p>

<p>Return <code>true</code><em> if it is possible to print the matrix </em><code>targetGrid</code><em>,</em><em> otherwise, return </em><code>false</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/print1.jpg" style="width: 600px; height: 175px;" />
<pre>
<strong>Input:</strong> targetGrid = [[1,1,1,1],[1,2,2,1],[1,2,2,1],[1,1,1,1]]
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/print2.jpg" style="width: 600px; height: 367px;" />
<pre>
<strong>Input:</strong> targetGrid = [[1,1,1,1],[1,1,3,3],[1,1,3,4],[5,5,1,4]]
<strong>Output:</strong> true
</pre>

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

<pre>
<strong>Input:</strong> targetGrid = [[1,2,1],[2,1,2],[1,2,1]]
<strong>Output:</strong> false
<strong>Explanation:</strong> It is impossible to form targetGrid because it is not allowed to print the same color in different turns.
</pre>

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

<ul>
	<li><code>m == targetGrid.length</code></li>
	<li><code>n == targetGrid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 60</code></li>
	<li><code>1 &lt;= targetGrid[row][col] &lt;= 60</code></li>
</ul>

class Solution:
    def isPrintable(self, grid: List[List[int]]) -> bool:
        # tuple represent (x_min, x_max, y_min, y_max)
        spread_hm: Dict[int, List[int]] = {}

        num_rows = len(grid)
        num_cols = len(grid[0])
        for r in range(num_rows):
            for c in range(num_cols):
                if grid[r][c] not in spread_hm:
                    spread_hm[grid[r][c]] = [inf, -inf, inf, -inf]

                spread_hm[grid[r][c]][0] = min(spread_hm[grid[r][c]][0], c)
                spread_hm[grid[r][c]][1] = max(spread_hm[grid[r][c]][1], c)
                spread_hm[grid[r][c]][2] = min(spread_hm[grid[r][c]][2], r)
                spread_hm[grid[r][c]][3] = max(spread_hm[grid[r][c]][3], r)

        graph: Dict[int, Set[int]] = {color: set() for color in spread_hm}
        indegree: Dict[int, int] = {color: 0 for color in spread_hm}

        for color, (x_min, x_max, y_min, y_max) in spread_hm.items():
            for r in range(y_min, y_max + 1):
                for c in range(x_min, x_max + 1):
                    if grid[r][c] != color and grid[r][c] not in graph[color]:
                        graph[color].add(grid[r][c])
                        indegree[grid[r][c]] += 1

        def has_cycle() -> bool:
            queue = deque()
            visited = 0
            for color in graph:
                if indegree[color] == 0:
                    queue.appendleft(color)
                    visited += 1

            while queue:
                out = queue.pop()

                for nbr in graph[out]:
                    indegree[nbr] -= 1
                    if indegree[nbr] == 0:
                        queue.appendleft(nbr)
                        visited += 1

            return visited == len(graph)

        return has_cycle()

16900