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
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
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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