<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:
  def containsCycle(self, grid: List[List[str]]) -> bool:
    m,n = len(grid), len(grid[0])
    # i=0 j=0
    grid_connected = [[set()]]
    for j in range(1,n):
      grid_connected[0].append(set())
      # i=0
      if grid[0][j-1]==grid[0][j]:
        grid_connected[0][j].add(j-1)
        grid_connected[0][j-1].add(j)
    for i in range(1,m):
      grid_connected.append([set()])
      # j=0
      if grid[i-1][0]==grid[i][0]:
        grid_connected[i][0].add((i-1)*n)
        grid_connected[i-1][0].add(i*n)
      for j in range(1,n):
        grid_connected[i].append(set())
        # up
        if grid[i-1][j]==grid[i][j]:
          grid_connected[i][j].add((i-1)*n+j)
          grid_connected[i-1][j].add(i*n+j)
        # left
        if grid[i][j-1]==grid[i][j]:
          grid_connected[i][j].add(i*n+j-1)
          grid_connected[i][j-1].add(i*n+j)

    vals = dict()
    queue = set()
    for i in range(m):
      for j in range(n):
        legNum = len(grid_connected[i][j])
        if legNum>1:
          val = grid[i][j]
          if val in vals:
            vals[val]+=1
          else:
            vals[val]=1
        elif legNum==1:
          queue.add(i*n+j)

    while(queue):
      i,j = divmod(queue.pop(),n)

      next = set()
      for coord in grid_connected[i][j]:
        k,l = divmod(coord,n)
        legNum = len(grid_connected[k][l])
        if legNum == 2:
          next.add(coord)
        grid_connected[k][l].remove(i*n+j)

      val = grid[i][j]
      if grid[i][j] in vals:
        vals[val]-=len(next)
      queue.update(next)

    for n in vals.values():
      if n>0:return True
    
    return False
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