<p>Given a 2D array of characters <code>grid</code> of size <code>m x n</code>, you need to find if there exists any cycle consisting of the <strong>same value</strong> in <code>grid</code>.</p>

<p>A cycle is a path of <strong>length 4 or more</strong> in the grid that starts and ends at the same cell. From a given cell, you can move to one of the cells adjacent to it - in one of the four directions (up, down, left, or right), if it has the <strong>same value</strong> of the current cell.</p>

<p>Also, you cannot move to the cell that you visited in your last move. For example, the cycle <code>(1, 1) -&gt; (1, 2) -&gt; (1, 1)</code> is invalid because from <code>(1, 2)</code> we visited <code>(1, 1)</code> which was the last visited cell.</p>

<p>Return <code>true</code> if any cycle of the same value exists in <code>grid</code>, otherwise, return <code>false</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/07/15/1.png" style="width: 231px; height: 152px;" /></strong></p>

<pre>
<strong>Input:</strong> grid = [[&quot;a&quot;,&quot;a&quot;,&quot;a&quot;,&quot;a&quot;],[&quot;a&quot;,&quot;b&quot;,&quot;b&quot;,&quot;a&quot;],[&quot;a&quot;,&quot;b&quot;,&quot;b&quot;,&quot;a&quot;],[&quot;a&quot;,&quot;a&quot;,&quot;a&quot;,&quot;a&quot;]]
<strong>Output:</strong> true
<strong>Explanation: </strong>There are two valid cycles shown in different colors in the image below:
<img alt="" src="https://assets.leetcode.com/uploads/2020/07/15/11.png" style="width: 225px; height: 163px;" />
</pre>

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

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/07/15/22.png" style="width: 236px; height: 154px;" /></strong></p>

<pre>
<strong>Input:</strong> grid = [[&quot;c&quot;,&quot;c&quot;,&quot;c&quot;,&quot;a&quot;],[&quot;c&quot;,&quot;d&quot;,&quot;c&quot;,&quot;c&quot;],[&quot;c&quot;,&quot;c&quot;,&quot;e&quot;,&quot;c&quot;],[&quot;f&quot;,&quot;c&quot;,&quot;c&quot;,&quot;c&quot;]]
<strong>Output:</strong> true
<strong>Explanation: </strong>There is only one valid cycle highlighted in the image below:
<img alt="" src="https://assets.leetcode.com/uploads/2020/07/15/2.png" style="width: 229px; height: 157px;" />
</pre>

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

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/07/15/3.png" style="width: 183px; height: 120px;" /></strong></p>

<pre>
<strong>Input:</strong> grid = [[&quot;a&quot;,&quot;b&quot;,&quot;b&quot;],[&quot;b&quot;,&quot;z&quot;,&quot;b&quot;],[&quot;b&quot;,&quot;b&quot;,&quot;a&quot;]]
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 500</code></li>
	<li><code>grid</code> consists only of lowercase English letters.</li>
</ul>

class Solution {
    using matrix = std::vector<std::vector<char>>;
    int rowCount, colCount;
    using cell = std::pair<int,int>;
    std::set<cell> visited;
    std::set<cell> path;

public:
    bool containsCycle(vector<vector<char>>& grid) {

        // init
        rowCount = grid.size();
        colCount = grid.at(0).size();    

        // check if we have any cycle
        for (int r = 0; r < rowCount; ++r) {
            for (int c = 0; c < colCount; ++c) {

                const cell parent = {-1,-1};
                const char value  = grid[r][c];
                const cell pos    = {r,c};
                if (visited.find(pos) == visited.end() 
                    && hasCycle(grid, pos, value, parent)) return true;
            }
        }

        // no cycle detected after traversing the whole graph
        return false;
    }

    bool isValid(matrix& grid, cell pos, char value) {
        auto [r,c] = pos;
        return
            r >= 0 && r < rowCount &&  // out of bounds
            c >= 0 && c < colCount &&  // out of bounds
            grid[r][c] == value;       // connected component
    }

    bool hasCycle(matrix& grid, cell pos, char value, cell parent) {
        
        visited.insert(pos);

        // check all neighbors
        auto [r,c] = pos;
        std::vector<cell> neighbors{{r+1,c}, {r-1,c}, {r,c+1}, {r,c-1}};
        for (cell nbr : neighbors) {
            if (!isValid(grid, nbr, value)) continue; // discard invalid nodes

            if (visited.find(nbr) == visited.end()) {
                if (hasCycle(grid, nbr, value, pos)) return true;
            } else if (nbr != parent) return true;
        }

        return false;
    }
};
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