<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 {
public:
    void dfs(map<int, vector<int>>& adj, int node, map<int, int>& visited, vector<int>& topo) {
        visited[node] = 1;
        for(int neighbor : adj[node]) {
            if(visited[neighbor] == 0) {
                dfs(adj, neighbor, visited, topo);
            }
        }
        topo.push_back(node);
    }

    bool isPrintable(vector<vector<int>>& targetGrid) {
        map<int, vector<int>> boundingBox;
        int m = targetGrid.size(), n = targetGrid[0].size();
        
        // Find bounding box for each color
        for(int i = 0; i < m; i++) {
            for(int j = 0; j < n; j++) {
                int color = targetGrid[i][j];
                if(boundingBox.find(color) == boundingBox.end()) {
                    boundingBox[color] = {i, j, i, j};
                } else {
                    boundingBox[color][0] = min(boundingBox[color][0], i);
                    boundingBox[color][1] = min(boundingBox[color][1], j);
                    boundingBox[color][2] = max(boundingBox[color][2], i);
                    boundingBox[color][3] = max(boundingBox[color][3], j);
                }
            }
        }
        
        // Create adjacency list based on color dependencies
        map<int, vector<int>> adj;
        for(auto& [color, box] : boundingBox) {
            int x1 = box[0], y1 = box[1], x2 = box[2], y2 = box[3];
            for(int i = x1; i <= x2; i++) {
                for(int j = y1; j <= y2; j++) {
                    if(targetGrid[i][j] != color) {
                        adj[targetGrid[i][j]].push_back(color);
                    }
                }
            }
        }

        // Perform topological sort
        vector<int> topo;
        map<int, int> visited;
        for(auto& [color, _] : boundingBox) {
            if(visited[color] == 0) {
                dfs(adj, color, visited, topo);
            }
        }

        // Check if topological sort is valid (no cycles)
        if(topo.size() != boundingBox.size()) {
            return false;
        }

        // Simulate printing process
        vector<vector<int>> simulatedGrid(m, vector<int>(n, -1));
        for(int color : topo) {
            auto& box = boundingBox[color];
            for(int i = box[0]; i <= box[2]; i++) {
                for(int j = box[1]; j <= box[3]; j++) {
                    simulatedGrid[i][j] = color;
                }
            }
        }

        // Validate if the simulated grid matches the input
        for(int i = 0; i < m; i++) {
            for(int j = 0; j < n; j++) {
                if(simulatedGrid[i][j] != targetGrid[i][j]) {
                    return false;
                }
            }
        }

        return true;
    }
};
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