C++ Program to Rotate all Matrix elements except the diagonal K times by 90 degrees in clockwise direction

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 25

Input: 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:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to print the matrix
void print(vector<vector<int> >& mat)
{
    // Iterate over the rows
    for (int i = 0; i < mat.size(); i++) {

        // Iterate over the columns
        for (int j = 0; j < mat[0].size(); j++)

            // Print the value
            cout << setw(3) << mat[i][j];
        cout << "
";
    }
}

// Function to perform the swapping of
// matrix elements in clockwise manner
void performSwap(vector<vector<int> >& mat,
                 int i, int j)
{
    int N = mat.size();

    // Stores the last row
    int ei = N - 1 - i;

    // Stores the last column
    int ej = N - 1 - j;

    // Perform the swaps
    int 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
void rotate(vector<vector<int> >& mat,
            int N, int K)
{
    // Update K to K % 4
    K = K % 4;

    // Iterate until K is positive
    while (K--) {

        // Iterate each up to N/2-th row
        for (int i = 0; i < N / 2; i++) {

            // Iterate each column
            // from i to N - i - 1
            for (int j = i;
                 j < N - i - 1; j++) {

                // Check if the element
                // at i, j is not a
                // diagonal element
                if (i != j
                    && (i + j) != N - 1) {

                    // Perform the swapping
                    performSwap(mat, i, j);
                }
            }
        }
    }

    // Print the matrix
    print(mat);
}

// Driver Code
int main()
{
    int K = 5;
    vector<vector<int> > mat = {
        { 1, 2, 3, 4 },
        { 6, 7, 8, 9 },
        { 11, 12, 13, 14 },
        { 16, 17, 18, 19 },
    };
    int N = mat.size();
    rotate(mat, N, K);

    return 0;
}

Output:

  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!