C++ Program to Rotate Matrix Elements

Rotating matrix elements means shifting the elements of each layer or ring of a matrix in a clockwise direction. The rotation is performed layer by layer, starting from the outermost ring and moving toward the inner rings.

Each ring is rotated independently in a clockwise direction.
The matrix is modified in-place without using an additional matrix.

Examples:

Input:
1 2 3
4 5 6
7 8 9

Output:
4 1 2
7 5 3
8 9 6
The outer ring elements are rotated clockwise, while the center element remains unchanged.
For 4*4 matrix:
Input:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

Output:
5 1 2 3
9 10 6 4
13 11 7 8
14 15 16 12

Approach

The matrix can be viewed as a set of concentric rings. We rotate each ring one at a time, starting from the outermost ring.

Maintain four boundaries: row, col, m, and n.
row and col represent the starting row and column of the current ring.
m and n represent the ending row and column of the current ring.
Store the first element of the next row in a temporary variable.
Move the elements of the top row one position to the right.
Move the elements of the last column one position downward.
Move the elements of the bottom row one position to the left.
Move the elements of the first column one position upward.
Move the boundaries inward and repeat the process for the next ring.

C++

#include <iostream>
using namespace std;

const int MAX = 100;

// Rotates all rings of the matrix clockwise by one position
void rotateMatrix(int mat[][MAX], int rows, int cols)
{
    int top = 0;
    int left = 0;
    int bottom = rows;
    int right = cols;

    while (top < bottom && left < right) {

        // A ring must contain at least two rows
        // and two columns to be rotated.
        if (top + 1 == bottom ||
            left + 1 == right) {
            break;
        }

        // Store the first element of the
        // second row.
        int prev = mat[top + 1][left];

        // Move the top row one position right.
        for (int j = left; j < right; j++) {
            int curr = mat[top][j];
            mat[top][j] = prev;
            prev = curr;
        }
        top++;

        // Move the right column one position down.
        for (int i = top; i < bottom; i++) {
            int curr = mat[i][right - 1];
            mat[i][right - 1] = prev;
            prev = curr;
        }
        right--;

        // Move the bottom row one position left.
        if (top < bottom) {
            for (int j = right - 1; j >= left; j--) {
                int curr = mat[bottom - 1][j];
                mat[bottom - 1][j] = prev;
                prev = curr;
            }
        }
        bottom--;

        // Move the left column one position up.
        if (left < right) {
            for (int i = bottom - 1; i >= top; i--) {
                int curr = mat[i][left];
                mat[i][left] = prev;
                prev = curr;
            }
        }
        left++;
    }
}

int main()
{
    int mat[4][MAX] = {
        {1, 2, 3, 4},
        {5, 6, 7, 8},
        {9, 10, 11, 12},
        {13, 14, 15, 16}
    };

    int rows = 4;
    int cols = 4;

    rotateMatrix(mat, rows, cols);

    cout << "Matrix after clockwise rotation:\n";

    for (int i = 0; i < rows; i++) {
        for (int j = 0; j < cols; j++) {
            cout << mat[i][j] << " ";
        }
        cout << '\n';
    }

    return 0;
}

Output

Matrix after clockwise rotation:
5 1 2 3 
9 10 6 4 
13 11 7 8 
14 15 16 12

Explanation

top, bottom, left, and right define the current ring boundaries.
prev temporarily stores elements during rotation.
Four loops shift the top row, right column, bottom row, and left column.
The boundaries move inward to rotate the next ring.
The matrix is modified in-place, so no extra matrix is required.

C++ Program to Rotate Matrix Elements

Approach

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