<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:
int UNVISITED = 0, VISITING = 1, VISITED = 2;

    bool dfs(int node, unordered_map<int, int>& states, unordered_map<int, unordered_set<int>>& graph) {
        if (states[node] == VISITED)
            return false;
        if (states[node] == VISITING) //cycle found
            return true;

        states[node] = VISITING;

        for (auto& neighbour : graph[node]) {
            if (dfs(neighbour, states, graph))
                return true;
        }

        states[node] = VISITED;
        return false;
    }

    bool isCyclic(unordered_map<int, unordered_set<int>>& graph) {
        unordered_map<int, int> states;
        for (auto& x : graph)
            states[x.first] = UNVISITED;

        for (auto& x : graph) {
            if (states[x.first] == UNVISITED and dfs(x.first, states, graph)) {
                return true;
            }
        }

        return false;
    }

    bool isPrintable(vector<vector<int>>& targetGrid) {
        unordered_map<int, int> minRow, maxRow, minCol, maxCol;

        for (auto& row : targetGrid)
            for (int color : row)
                minRow[color] = INT_MAX, maxRow[color] = INT_MIN, minCol[color] = INT_MAX, maxCol[color] = INT_MIN;


        for (int i = 0; i < targetGrid.size(); i++) {
            for (int j = 0; j < targetGrid[0].size(); j++) {
                int color = targetGrid[i][j];
                minRow[color] = min(minRow[color], i), maxRow[color] = max(maxRow[color], i), minCol[color] =
                    min(minCol[color], j), maxCol[color] = max(maxCol[color], j);
            }
        }

        unordered_map<int, unordered_set<int>> graph(minRow.size());

        for (auto& x : minRow) {
            int color = x.first;
            for (int i = minRow[color]; i <= maxRow[color]; i++) {
                for (int j = minCol[color]; j <= maxCol[color]; j++) {
                    if (targetGrid[i][j] != color) {
                        graph[targetGrid[i][j]].insert(color);
                    }
                }
            }
        }

        return !isCyclic(graph);
    }
};
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