Count Operations to Change All Cells to Same Color in Python

Suppose we have a two-dimensional matrix M. Now in each cell contains a value that represents its color, and adjacent cells (top, bottom, left, right) with the same color are to be grouped together. Now, consider an operation where we set all cells in one group to some color. Then finally find the minimum number of operations required so that every cell has the same color. And when the color is transformed, it cannot be set again.

So, if the input is like

Then the output will be 2, as We can fill the group with 2 as color into 1 and then fill 3 with 1.

To solve this, we will follow these steps−

• if matrix is empty, then

  • return 0

• Define a function dfs() . This will take i, j, matrix, val

• n := row count of matrix, m := col count of matrix

• if i < 0 or i > n - 1 or j < 0 or j > m - 1, then

  • return

• if matrix[i, j] is same as -1, then

  • return

• if matrix[i, j] is same as val, then

  • matrix[i, j] := -1

  • dfs(i, j + 1, matrix, val)

  • dfs(i + 1, j, matrix, val)

  • dfs(i, j - 1, matrix, val)

  • dfs(i - 1, j, matrix, val)

• otherwise,

  • return

• From the main method, do the following−

• n := row count of matrix, m := col count of matrix

• d := empty map

• for i in range 0 to n-1, do

  • for j in range 0 to m-1, do

  • val := matrix[i, j]

  • if val is not same as -1, then

  • d[val] := d[val] + 1

  • dfs(i, j, matrix, val)

• sort dictionary elements of f based on their values

• safe := last element of l

• res := 0

• for each key value pairs k and v of d, do

  • if k is not same as safe, then

  • res := res + v

• return res

Let us see the following implementation to get better understanding −

Example

 Live Demo

from collections import defaultdict
class Solution:
   def solve(self, matrix):
      if not matrix:
         return 0
      def dfs(i, j, matrix, val):
         n, m = len(matrix), len(matrix[0])
      if i < 0 or i > n - 1 or j < 0 or j > m - 1:
         return
      if matrix[i][j] == -1:
         return
      if matrix[i][j] == val:
         matrix[i][j] = -1
      dfs(i, j + 1, matrix, val)
      dfs(i + 1, j, matrix, val)
      dfs(i, j - 1, matrix, val)
      dfs(i - 1, j, matrix, val)
      else:
         return
      n, m = len(matrix), len(matrix[0])
      d = defaultdict(int)
   for i in range(n):
      for j in range(m):
         val = matrix[i][j]
   if val != -1:
      d[val] += 1
      dfs(i, j, matrix, val)
      l = sorted(d,key=lambda x: d[x])
      safe = l[-1]
      res = 0
   for k, v in d.items():
      if k != safe:
         res += v
   return res
ob = Solution()
matrix = [
   [2, 2, 2, 2],
   [1, 1, 1, 1],
   [2, 3, 2, 1]
]
print(ob.solve(matrix))

Input

matrix = [[2, 2, 2, 2],[1, 1, 1, 1],[2, 3, 2, 1]]

Output

2