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Rotate Matrix Elements

Last Updated : 15 May, 2024
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Given a matrix, clockwise rotate elements in it.

Examples:

Input
1 2 3
4 5 6
7 8 9

Output:
4 1 2
7 5 3
8 9 6

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

The idea is to use loops similar to the program for printing a matrix in spiral form. One by one rotate all rings of elements, starting from the outermost. To rotate a ring, we need to do following.

  1. Move elements of top row. 
  2. Move elements of last column. 
  3. Move elements of bottom row. 
  4. Move elements of first column. 

Repeat above steps for inner ring while there is an inner ring.

Below is the implementation of above idea. Thanks to Gaurav Ahirwar for suggesting below solution. 

C++
// C++ program to rotate a matrix 

#include <bits/stdc++.h> 
#define R 4 
#define C 4 
using namespace std; 

// A function to rotate a matrix mat[][] of size R x C. 
// Initially, m = R and n = C 
void rotatematrix(int m, int n, int mat[R][C]) 
{ 
    int row = 0, col = 0; 
    int prev, curr; 

    /* 
    row - Starting row index 
    m - ending row index 
    col - starting column index 
    n - ending column index 
    i - iterator 
    */
    while (row < m && col < n) 
    { 

        if (row + 1 == m || col + 1 == n) 
            break; 

        // Store the first element of next row, this 
        // element will replace first element of current 
        // row 
        prev = mat[row + 1][col]; 

        /* Move elements of first row from the remaining rows */
        for (int i = col; i < n; i++) 
        { 
            curr = mat[row][i]; 
            mat[row][i] = prev; 
            prev = curr; 
        } 
        row++; 

        /* Move elements of last column from the remaining columns */
        for (int i = row; i < m; i++) 
        { 
            curr = mat[i][n-1]; 
            mat[i][n-1] = prev; 
            prev = curr; 
        } 
        n--; 

        /* Move elements of last row from the remaining rows */
        if (row < m) 
        { 
            for (int i = n-1; i >= col; i--) 
            { 
                curr = mat[m-1][i]; 
                mat[m-1][i] = prev; 
                prev = curr; 
            } 
        } 
        m--; 

        /* Move elements of first column from the remaining rows */
        if (col < n) 
        { 
            for (int i = m-1; i >= row; i--) 
            { 
                curr = mat[i][col]; 
                mat[i][col] = prev; 
                prev = curr; 
            } 
        } 
        col++; 
    } 

    // Print rotated matrix 
    for (int i=0; i<R; i++) 
    { 
        for (int j=0; j<C; j++) 
        cout << mat[i][j] << " "; 
        cout << endl; 
    } 
} 

/* Driver program to test above functions */
int main() 
{ 
    // Test Case 1 
    int a[R][C] = { {1, 2, 3, 4}, 
        {5, 6, 7, 8}, 
        {9, 10, 11, 12}, 
        {13, 14, 15, 16} }; 

    // Test Case 2 
    /* int a[R][C] = {{1, 2, 3}, 
                    {4, 5, 6}, 
                    {7, 8, 9} 
                    }; 
    */ rotatematrix(R, C, a); 
    return 0; 
} 
Java
// Java program to rotate a matrix
import java.lang.*;
import java.util.*;

class GFG
{
    static int R = 4;
    static int C = 4;

    // A function to rotate a matrix 
    // mat[][] of size R x C.
    // Initially, m = R and n = C
    static void rotatematrix(int m,
                    int n, int mat[][])
    {
        int row = 0, col = 0;
        int prev, curr;

        /*
        row - Starting row index
        m - ending row index
        col - starting column index
        n - ending column index
        i - iterator
        */
        while (row < m && col < n)
        {
    
            if (row + 1 == m || col + 1 == n)
                break;
    
            // Store the first element of next
            // row, this element will replace 
            // first element of current row
            prev = mat[row + 1][col];
    
            // Move elements of first row 
            // from the remaining rows 
            for (int i = col; i < n; i++)
            {
                curr = mat[row][i];
                mat[row][i] = prev;
                prev = curr;
            }
            row++;
    
            // Move elements of last column
            // from the remaining columns 
            for (int i = row; i < m; i++)
            {
                curr = mat[i][n-1];
                mat[i][n-1] = prev;
                prev = curr;
            }
            n--;
    
            // Move elements of last row 
            // from the remaining rows 
            if (row < m)
            {
                for (int i = n-1; i >= col; i--)
                {
                    curr = mat[m-1][i];
                    mat[m-1][i] = prev;
                    prev = curr;
                }
            }
            m--;
    
            // Move elements of first column
            // from the remaining rows 
            if (col < n)
            {
                for (int i = m-1; i >= row; i--)
                {
                    curr = mat[i][col];
                    mat[i][col] = prev;
                    prev = curr;
                }
            }
            col++;
        }

            // Print rotated matrix
            for (int i = 0; i < R; i++)
            {
                for (int j = 0; j < C; j++)
                System.out.print( mat[i][j] + " ");
                System.out.print("\n");
            }
    }

/* Driver program to test above functions */
    public static void main(String[] args) 
    {
    // Test Case 1
    int a[][] = { {1, 2, 3, 4},
                  {5, 6, 7, 8},
                {9, 10, 11, 12},
                {13, 14, 15, 16} };

    // Test Case 2
    /* int a[][] = new int {{1, 2, 3},
                            {4, 5, 6},
                            {7, 8, 9}
                        };*/
    rotatematrix(R, C, a);
    
    }
}

// This code is contributed by Sahil_Bansall
Python
# Python program to rotate a matrix

# Function to rotate a matrix
def rotateMatrix(mat):

    if not len(mat):
        return
    
    """
        top : starting row index
        bottom : ending row index
        left : starting column index
        right : ending column index
    """

    top = 0
    bottom = len(mat)-1

    left = 0
    right = len(mat[0])-1

    while left < right and top < bottom:

        # Store the first element of next row,
        # this element will replace first element of
        # current row
        prev = mat[top+1][left]

        # Move elements of top row one step right
        for i in range(left, right+1):
            curr = mat[top][i]
            mat[top][i] = prev
            prev = curr

        top += 1

        # Move elements of rightmost column one step downwards
        for i in range(top, bottom+1):
            curr = mat[i][right]
            mat[i][right] = prev
            prev = curr

        right -= 1

        # Move elements of bottom row one step left
        for i in range(right, left-1, -1):
            curr = mat[bottom][i]
            mat[bottom][i] = prev
            prev = curr

        bottom -= 1

        # Move elements of leftmost column one step upwards
        for i in range(bottom, top-1, -1):
            curr = mat[i][left]
            mat[i][left] = prev
            prev = curr

        left += 1

    return mat

# Utility Function
def printMatrix(mat):
    for row in mat:
        print row


# Test case 1
matrix =[ 
            [1,  2,  3,  4 ],
            [5,  6,  7,  8 ],
            [9,  10, 11, 12 ],
            [13, 14, 15, 16 ]  
        ]
# Test case 2
"""
matrix =[
            [1, 2, 3],
            [4, 5, 6],
            [7, 8, 9]
        ]
"""

matrix = rotateMatrix(matrix)
# Print modified matrix
printMatrix(matrix)
C#
// C# program to rotate a matrix
using System;

class GFG {
    
    static int R = 4;
    static int C = 4;

    // A function to rotate a matrix 
    // mat[][] of size R x C.
    // Initially, m = R and n = C
    static void rotatematrix(int m,
                        int n, int [,]mat)
    {
        int row = 0, col = 0;
        int prev, curr;

        /*
        row - Starting row index
        m - ending row index
        col - starting column index
        n - ending column index
        i - iterator
        */
        while (row < m && col < n)
        {
    
            if (row + 1 == m || col + 1 == n)
                break;
    
            // Store the first element of next
            // row, this element will replace 
            // first element of current row
            prev = mat[row + 1, col];
    
            // Move elements of first row 
            // from the remaining rows 
            for (int i = col; i < n; i++)
            {
                curr = mat[row,i];
                mat[row, i] = prev;
                prev = curr;
            }
            row++;
    
            // Move elements of last column
            // from the remaining columns 
            for (int i = row; i < m; i++)
            {
                curr = mat[i,n-1];
                mat[i, n-1] = prev;
                prev = curr;
            }
            n--;
    
            // Move elements of last row 
            // from the remaining rows 
            if (row < m)
            {
                for (int i = n-1; i >= col; i--)
                {
                    curr = mat[m-1,i];
                    mat[m-1,i] = prev;
                    prev = curr;
                }
            }
            m--;
    
            // Move elements of first column
            // from the remaining rows 
            if (col < n)
            {
                for (int i = m-1; i >= row; i--)
                {
                    curr = mat[i,col];
                    mat[i,col] = prev;
                    prev = curr;
                }
            }
            col++;
        }

            // Print rotated matrix
            for (int i = 0; i < R; i++)
            {
                for (int j = 0; j < C; j++)
                Console.Write( mat[i,j] + " ");
                Console.Write("\n");
            }
    }

    /* Driver program to test above functions */
    public static void Main() 
    {
        // Test Case 1
        int [,]a = { {1, 2, 3, 4},
                    {5, 6, 7, 8},
                    {9, 10, 11, 12},
                    {13, 14, 15, 16} };
    
        // Test Case 2
        /* int a[][] = new int {{1, 2, 3},
                                {4, 5, 6},
                                {7, 8, 9}
                            };*/
        rotatematrix(R, C, a);
        
    }
}

// This code is contributed by nitin mittal.
Javascript
<script>

// Javascript program to rotate a matrix    

let R = 4;
let C = 4;

// A function to rotate a matrix 
// mat[][] of size R x C.
// Initially, m = R and n = C
function rotatematrix(m, n, mat)
{
    let row = 0, col = 0;
    let prev, curr;
    
    /*
    row - Starting row index
    m - ending row index
    col - starting column index
    n - ending column index
    i - iterator
    */
    while (row < m && col < n)
    {
        if (row + 1 == m || col + 1 == n)
            break;
  
        // Store the first element of next
        // row, this element will replace 
        // first element of current row
        prev = mat[row + 1][col];
  
        // Move elements of first row 
        // from the remaining rows 
        for(let i = col; i < n; i++)
        {
            curr = mat[row][i];
            mat[row][i] = prev;
            prev = curr;
        }
        row++;
  
        // Move elements of last column
        // from the remaining columns 
        for(let i = row; i < m; i++)
        {
            curr = mat[i][n - 1];
            mat[i][n - 1] = prev;
            prev = curr;
        }
        n--;
  
        // Move elements of last row 
        // from the remaining rows 
        if (row < m)
        {
            for(let i = n - 1; i >= col; i--)
            {
                curr = mat[m - 1][i];
                mat[m - 1][i] = prev;
                prev = curr;
            }
        }
        m--;
  
        // Move elements of first column
        // from the remaining rows 
        if (col < n)
        {
            for(let i = m - 1; i >= row; i--)
            {
                curr = mat[i][col];
                mat[i][col] = prev;
                prev = curr;
            }
        }
        col++;
    }

    // Print rotated matrix
    for(let i = 0; i < R; i++)
    {
        for(let j = 0; j < C; j++)
            document.write( mat[i][j] + " ");
            
        document.write("<br>");
    }
}

// Driver code

// Test Case 1
let a = [ [ 1, 2, 3, 4 ],
          [ 5, 6, 7, 8 ],
          [ 9, 10, 11, 12 ],
          [ 13, 14, 15, 16 ] ];
          
rotatematrix(R, C, a);

// This code is contributed by avanitrachhadiya2155

</script>
PHP
<?php
// PHP program to rotate a matrix
$R = 4;
$C = 4;

// A function to rotate a matrix 
// mat[][] of size R x C. Initially,
// m = R and n = C
function rotatematrix($m, $n, $mat)
{
    global $R, $C;
    $row = 0;
    $col = 0;
    $prev = 0;
    $curr = 0;

    /*
    row - Starting row index
    m - ending row index
    col - starting column index
    n - ending column index
    i - iterator
    */
    while ($row < $m && $col < $n)
    {

        if ($row + 1 == $m || 
            $col + 1 == $n)
            break;

        // Store the first element 
        // of next row, this element 
        // will replace first element 
        // of current row
        $prev = $mat[$row + 1][$col];

        /* Move elements of first row 
           from the remaining rows */
        for ($i = $col; $i < $n; $i++)
        {
            $curr = $mat[$row][$i];
            $mat[$row][$i] = $prev;
            $prev = $curr;
        }
        $row++;

        /* Move elements of last column
           from the remaining columns */
        for ($i = $row; $i < $m; $i++)
        {
            $curr = $mat[$i][$n - 1];
            $mat[$i][$n - 1] = $prev;
            $prev = $curr;
        }
        $n--;

        /* Move elements of last row
           from the remaining rows */
        if ($row < $m)
        {
            for ($i = $n - 1;
                 $i >= $col; $i--)
            {
                $curr = $mat[$m - 1][$i];
                $mat[$m - 1][$i] = $prev;
                $prev = $curr;
            }
        }
        $m--;

        /* Move elements of first column
           from the remaining rows */
        if ($col < $n)
        {
            for ($i = $m - 1; 
                 $i >= $row; $i--)
            {
                $curr = $mat[$i][$col];
                $mat[$i][$col] = $prev;
                $prev = $curr;
            }
        }
        $col++;
    }

    // Print rotated matrix
    for ($i = 0; $i < $R; $i++)
    {
        for ($j = 0; $j < $C; $j++)
        echo $mat[$i][$j] . " ";
        echo "\n";
    }
}

// Driver code

// Test Case 1
$a = array(array(1, 2, 3, 4),
           array(5, 6, 7, 8),
           array(9, 10, 11, 12),
           array(13, 14, 15, 16));

// Test Case 2
/* int $a = array(array(1, 2, 3),
                  array(4, 5, 6),
                  array(7, 8, 9));
*/ rotatematrix($R, $C, $a);
    return 0;
    
// This code is contributed
// by ChitraNayal
?>

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

Complexity Analysis:

  • Time Complexity: O(m*n) where m is the number of rows & n is the number of columns.
  • Auxiliary Space: O(1). 

Example: (Rotate anticlockwise – By using vectors in c++)

C++
#include <iostream>
#include <vector>

using namespace std;

// Function to rotate the matrix in a clockwise direction
void rotateMatrix(vector<vector<int>> &matrix) {
    int n = matrix.size();

    // Transpose the matrix
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            swap(matrix[i][j], matrix[j][i]);
        }
    }

    // Reverse the columns
    for (int i = 0; i < n; i++) {
        for (int j = 0, k = n - 1; j < k; j++, k--) {
            swap(matrix[j][i], matrix[k][i]);
        }
    }
}

// Function to print the matrix
void printMatrix(vector<vector<int>> &matrix) {
    for (int i = 0; i < matrix.size(); i++) {
        for (int j = 0; j < matrix[i].size(); j++) {
            cout << matrix[i][j] << " ";
        }
        cout << endl;
    }
}

int main() {
    vector<vector<int>> matrix = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    cout << "Original matrix:" << endl;
    printMatrix(matrix);
    rotateMatrix(matrix);
    cout << "Rotated matrix:" << endl;
    printMatrix(matrix);
    return 0;
}
Java
import java.util.ArrayList;
import java.util.List;

public class Main {

    // Function to rotate the matrix in a clockwise
    // direction
    public static void
    rotateMatrix(List<List<Integer> > matrix)
    {
        int n = matrix.size();

        // Transpose the matrix
        for (int i = 0; i < n; i++) {
            for (int j = i; j < n; j++) {
                int temp = matrix.get(i).get(j);
                matrix.get(i).set(j, matrix.get(j).get(i));
                matrix.get(j).set(i, temp);
            }
        }

        // Reverse the columns
        for (int i = 0; i < n; i++) {
            for (int j = 0, k = n - 1; j < k; j++, k--) {
                int temp = matrix.get(j).get(i);
                matrix.get(j).set(i, matrix.get(k).get(i));
                matrix.get(k).set(i, temp);
            }
        }
    }

    // Function to print the matrix
    public static void
    printMatrix(List<List<Integer> > matrix)
    {
        for (int i = 0; i < matrix.size(); i++) {
            for (int j = 0; j < matrix.get(i).size(); j++) {
                System.out.print(matrix.get(i).get(j)
                                 + " ");
            }
            System.out.println();
        }
    }

    public static void main(String[] args)
    {
        List<List<Integer> > matrix = new ArrayList<>();
        matrix.add(new ArrayList<Integer>() {
            {
                add(1);
                add(2);
                add(3);
            }
        });
        matrix.add(new ArrayList<Integer>() {
            {
                add(4);
                add(5);
                add(6);
            }
        });
        matrix.add(new ArrayList<Integer>() {
            {
                add(7);
                add(8);
                add(9);
            }
        });
        System.out.println("Original matrix:");
        printMatrix(matrix);
        rotateMatrix(matrix);
        System.out.println("Rotated matrix:");
        printMatrix(matrix);
    }
}
Python
def rotate_matrix(matrix):
    n = len(matrix)
    
    # Transpose the matrix
    for i in range(n):
        for j in range(i, n):
            matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
    
    # Reverse the columns
    for i in range(n):
        for j, k in zip(range(n//2), range(n-1, n//2-1, -1)):
            matrix[j][i], matrix[k][i] = matrix[k][i], matrix[j][i]

def print_matrix(matrix):
    for row in matrix:
        print(' '.join(str(elem) for elem in row))

matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
print("Original matrix:")
print_matrix(matrix)
rotate_matrix(matrix)
print("Rotated matrix:")
print_matrix(matrix)
C#
using System;
using System.Collections.Generic;

class Program {
// Function to rotate the matrix in a clockwise
// direction
public static void RotateMatrix(List<List<int>> matrix) {
int n = matrix.Count;
     // Transpose the matrix
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            int temp = matrix[i][j];
            matrix[i][j] = matrix[j][i];
            matrix[j][i] = temp;
        }
    }

    // Reverse the columns
    for (int i = 0; i < n; i++) {
        for (int j = 0, k = n - 1; j < k; j++, k--) {
            int temp = matrix[j][i];
            matrix[j][i] = matrix[k][i];
            matrix[k][i] = temp;
        }
    }
}

// Function to print the matrix
public static void PrintMatrix(List<List<int>> matrix) {
    for (int i = 0; i < matrix.Count; i++) {
        for (int j = 0; j < matrix[i].Count; j++) {
            Console.Write(matrix[i][j] + " ");
        }
        Console.WriteLine();
    }
}

static void Main(string[] args) {
    List<List<int>> matrix = new List<List<int>>();
    matrix.Add(new List<int>() { 1, 2, 3 });
    matrix.Add(new List<int>() { 4, 5, 6 });
    matrix.Add(new List<int>() { 7, 8, 9 });

    Console.WriteLine("Original matrix:");
    PrintMatrix(matrix);
    RotateMatrix(matrix);
    Console.WriteLine("Rotated matrix:");
    PrintMatrix(matrix);
}
}
Javascript
function rotateMatrix(grid) {
  const n = grid.length;

  // Transpose the matrix
  for (let i = 0; i < n; i++) {
    for (let j = i; j < n; j++) {
      [grid[i][j], matrix[j][i]] = [grid[j][i], grid[i][j]];
    }
  }

  // Reverse the columns
  for (let i = 0; i < n; i++) {
    for (let j = 0, k = n - 1; j < k; j++, k--) {
      [grid[j][i], matrix[k][i]] = [grid[k][i], matrix[j][i]];
    }
  }
}

function printMatrix(matrix) {
  for (let i = 0; i < grid.length; i++) {
    let row = "";
    for (let j = 0; j < grid[i].length; j++) {
      row += grid[i][j] + " ";
    }
    console.log(row);
  }
}

let matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]];
console.log("Original matrix:");
printMatrix(matrix);
rotateMatrix(matrix);
console.log("Rotated matrix:");
printMatrix(matrix);

Output
Original matrix:
1 2 3 
4 5 6 
7 8 9 
Rotated matrix:
3 6 9 
2 5 8 
1 4 7 

Complexity Analysis:

Time Complexity:
The time complexity of the given implementation is O(n^2), where n is the size of the matrix. This is because we need to traverse through all the elements of the matrix twice (once for transposing and once for reversing the columns). Therefore, the time complexity of this algorithm is quadratic.

Auxiliary Space:
The auxiliary space complexity of this implementation is O(1), which means that the amount of extra memory required for the algorithm is constant and does not depend on the input size. In this implementation, we are modifying the matrix in-place without using any additional data structure. Therefore, the space required for this algorithm is constant.

Read More about Matrix Rotation.



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