Check if matrix can be converted to another matrix by transposing square sub-matrices in Python

Suppose we have two N X M called mat1 and mat2. In an operation, we can transpose any square sub-matrix in mat1. We have to check whether we can get mat2 from mat1 or not by performing given operation.

So, if the input is like

then the output will be True, because if we get transpose of top right sub-matrix of size 2x2 of mat1, we will get mat2.

To solve this, we will follow these steps −

• row := row count of matrices
• column := column count of matrices
• for i in range 0 to row - 1, do
  • temp1 := a new list, temp2 := a new list
  • r := i, col := 0
  • while r >= 0 and col < column, do
    • insert mat1[r, col] into temp1
    • insert mat2[r, col] into temp2
    • r := r - 1, col := col + 1
  • sort the list temp1 and temp2
  • for i in range 0 to size of temp1 - 1, do
    • if temp1[i] is not same as temp2[i], then
      • return False
• for j in range 1 to column - 1, do
  • temp1 := a new list, temp2 := a new list
  • r := row - 1, col := j
  • while r >= 0 and col < column, do
    • insert mat1[r, col] into temp1
    • insert mat2[r, col] into temp2
    • r := r - 1, col := col + 1
  • sort the list temp1 and temp2
  • for i in range 0 to size of temp1 - 1, do
    • if temp1[i] is not same as temp2[i], then
      • return False
• return True

Example

Let us see the following implementation to get better understanding −

def solve(mat1, mat2):
   row = len(mat1)
   column = len(mat1[0])
   for i in range(row):
      temp1 = []
      temp2 = []
      r = i
      col = 0
      while r >= 0 and col < column:
         temp1.append(mat1[r][col])
         temp2.append(mat2[r][col])
         r -= 1
         col += 1
      temp1.sort()
      temp2.sort()
      for i in range(len(temp1)):
         if temp1[i] != temp2[i]:
            return False
   for j in range(1, column):
      temp1 = []
      temp2 = []
      r = row - 1
      col = j
      while r >= 0 and col < column:
         temp1.append(mat1[r][col])
         temp2.append(mat2[r][col])
         r -= 1
         col += 1
      temp1.sort()
      temp2.sort()
      for i in range(len(temp1)):
         if temp1[i] != temp2[i]:
            return False
   return True
mat1 = [
      [5, 6, 7],
      [1, 2, 3],
      [6, 8, 9]]
mat2 = [
      [5, 6, 2],
      [1, 7, 3],
      [6, 8, 9]]
print(solve(mat1, mat2))

Input

[
   [5, 6, 7],
   [1, 2, 3],
   [6, 8, 9]],
[
   [5, 6, 2],
   [1, 7, 3],
   [6, 8, 9]]

Output

True