Given a square matrix mat[][] of dimension N and an integer K, the task is to rotate the matrix by 90 degrees K times without changing the position of the diagonal elements.
Examples:
Input: mat[][] = {{1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}, {11, 12, 13, 14, 15}, {16, 17, 18, 19, 20}, {21, 22, 23, 24, 25}}, K = 1
Output:
 1 16 11 6 5 Â
 22 7 12 9 2
 23 18 13 8 3
 24 17 14 19 4
 21 20 15 10 25Input: mat[][] = {{10, 11}, {12, 13}}, K = 2
Output:
10 11
12 13
Approach: The given problem can be solved by using the idea discussed in this article and the fact that the matrix restores after performing clockwise rotation 4 times. Follow the below steps to solve the given problem:
- Update the value of K as K % 4.
- Iterate until K is a positive and perform the following steps:
- Traverse the matrix, for i over the range [0, N / 2) and j over the range[0, N – i – 1) and perform the following steps:
- If the value of i != j and (i + j) != (N – 1), then perform the following steps:
- Store the value of mat[i][j] in a temporary variable temp.
- Update the value of mat[i][j] as mat[N – 1 – j][i].
- Update the value of mat[N – 1 – j][i] as mat[N – 1 -i][N – 1 – j].
- Update the value of mat[N – 1  – i][N – 1 – j] as mat[j][N – 1 – i].
- Update the value of mat[j][N – 1 – i] as temp.
- After completing the above steps, print the updated matrix obtained.
Below is the implementation of the above approach:
Python3
# Python3 program for the above approach   # Function to print the matrix def printMat(mat):         # Iterate over the rows     for i in range(len(mat)):           # Iterate over the columns         for j in range(len(mat[0])):               # Print the value             print(mat[i][j], end = " ")                       print()   # Function to perform the swapping of # matrix elements in clockwise manner def performSwap(mat, i, j):         N = len(mat)       # Stores the last row     ei = N - 1 - i       # Stores the last column     ej = N - 1 - j       # Perform the swaps     temp = mat[i][j]     mat[i][j] = mat[ej][i]     mat[ej][i] = mat[ei][ej]     mat[ei][ej] = mat[j][ei]     mat[j][ei] = temp   # Function to rotate non - diagonal # elements of the matrix K times in # clockwise direction def rotate(mat, N, K):       # Update K to K % 4     K = K % 4      # Iterate until K is positive     while (K > 0):           # Iterate each up to N/2-th row         for i in range(int(N / 2)):               # Iterate each column             # from i to N - i - 1             for j in range(i, N - i - 1):                   # Check if the element                 # at i, j is not a                 # diagonal element                 if (i != j and (i + j) != N - 1):                       # Perform the swapping                     performSwap(mat, i, j)                               K -= 1                          # Print the matrix     printMat(mat)   # Driver Code K = 5mat = [ [ 1, 2, 3, 4 ],         [ 6, 7, 8, 9 ],         [ 11, 12, 13, 14 ],         [ 16, 17, 18, 19 ] ] N = len(mat)   rotate(mat, N, K)   # This code is contributed by Dharanendra L V. |
1 11 6 4 17 7 8 2 18 12 13 3 16 14 9 19
Â
Time Complexity: O(N2)
Auxiliary Space: O(1)
Please refer complete article on Rotate all Matrix elements except the diagonal K times by 90 degrees in clockwise direction for more details!
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