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Rotate a matrix clockwise by 90 degree without using any extra space | Set 3

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  • Difficulty Level : Medium
  • Last Updated : 28 Jun, 2022
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Given a rectangular matrix mat[][] with N rows and M columns, the task is to rotate the matrix by 90 degrees in a clockwise direction without using extra space.

Examples:

Input: mat[][] = {{1, 2, 3},  {4, 5, 6},   {7, 8, 9},  {10, 11, 12}}
Output: 10 7 4 1 
               11 8 5 2 
               12 9 6 3

Input: mat[][] = {{1, 2, 3, 4, 5, 6}, {7, 8, 9, 10, 11, 12}}
Output: 7 1 
              8 2 
              9 3 
             10 4 
             11 5 
             12 6

 

Note: The approach to rotate square matrix is already discussed as follows: 
 

Approach: The main idea is to perform an in-place rotation.

Follow the below steps to solve the given problem:

  1. Swap all the elements of the sub-matrix min(N, M) * min(N, M), along the main diagonal i.e from the upper top corner to the bottom right corner.
  2. If N is greater than M,
    • Push all the unswapped elements of each column i where (min(N, M) ≤ i) to the ith row.
    • Otherwise, push all the unswapped elements of each row i where (min(N, M) ≤ i) to the ith column.
  3. Reverse each row of the matrix
  4. Print the updated matrix of dimension M × N.

Procedure:

Let the given matrix be : 
1 2 3 
4 5 6 
7 8 9 
10 11 12
13 14 15
Swap all the elements of the sub-matrix min(N, M) * min(N, M) i.e 3 * 3 for this example
1 4 7
2 5 8
3 6 9
10 11 12
13 14 15

Since N > M, push all the unswapped elements of each column i (min(N, M) ≤ i) to the ith row
1 4 7 10 13
2 5 8 11 14
3 6 9 12 15

Reverse each column to get the final rotated matrix as:
13 10 7 4 1
14 11 8 5 2
15 12 9 6 3

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 mat
// with N rows and M columns
void print(vector<vector<int> > mat,
           int N, int M)
{
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            cout << mat[i][j] << " ";
        }
 
        cout << "\n";
    }
}
 
// Function to rotate the matrix
// by 90 degree clockwise
void rotate(vector<vector<int> > mat)
{
    // Number of rows
    int N = mat.size();
 
    // Number of columns
    int M = mat[0].size();
 
    // Swap all the elements along main diagonal
    // in the submatrix min(N, M) * min(N, M)
    for (int i = 0; i < min(N, M); i++) {
        for (int j = i; j < min(N, M); j++) {
 
            // Swap mat[i][j] and mat[j][i]
            swap(mat[i][j], mat[j][i]);
        }
    }
 
    // If N is greater than M
    if (N > M) {
 
        // Push all the unswapped elements
        // of ith column to ith row
        for (int i = 0; i < M; i++) {
            for (int j = min(N, M); j < N; j++) {
                mat[i].push_back(mat[j][i]);
            }
        }
    }
    else {
        // Resize mat to have M rows
        mat.resize(M, {});
 
        // Push all the unswapped elements
        // of ith column to ith row
        for (int i = min(N, M); i < M; i++) {
            for (int j = 0; j < N; j++) {
                mat[i].push_back(mat[j][i]);
            }
        }
    }
 
    // Reverse each row of the matrix
    for (int i = 0; i < M; i++) {
        reverse(mat[i].begin(), mat[i].end());
    }
 
    // Print the final matrix
    print(mat, M, N);
}
 
// Driver Code
int main()
{
    // Input
    vector<vector<int> > mat = { { 1, 2, 3 },
                                 { 4, 5, 6 },
                                 { 7, 8, 9 },
                                 { 10, 11, 12 } };
 
    // Function Call
    rotate(mat);
 
    return 0;
}

Java




/*package whatever //do not write package name here */
import java.io.*;
import java.util.*;
 
class GFG {
  // Java program for
  // the above approach
 
  // Function to print the matrix mat
  // with N rows and M columns
  static void print(ArrayList<ArrayList<Integer>> mat,int N, int M)
  {
    for (int i = 0; i < N; i++) {
      for (int j = 0; j < M; j++) {
        System.out.print(mat.get(i).get(j) + " ");
      }
 
      System.out.println();
    }
  }
 
  // Function to rotate the matrix
  // by 90 degree clockwise
  static void rotate(ArrayList<ArrayList<Integer>> mat)
  {
    // Number of rows
    int N = mat.size();
 
    // Number of columns
    int M = mat.get(0).size();
 
    // Swap all the elements along main diagonal
    // in the submatrix min(N, M) * min(N, M)
    for (int i = 0; i < Math.min(N, M); i++) {
      for (int j = i; j < Math.min(N, M); j++) {
 
        // Swap mat[i][j] and mat[j][i]
        int temp = mat.get(i).get(j);
        mat.get(i).set(j,mat.get(j).get(i));
        mat.get(j).set(i,temp);
      }
    }
 
    // If N is greater than M
    if (N > M) {
 
      // Push all the unswapped elements
      // of ith column to ith row
      for (int i = 0; i < M; i++) {
        for (int j = Math.min(N, M); j < N; j++) {
          mat.get(i).add(mat.get(j).get(i));
        }
      }
    }
    else {
      // Resize mat to have M rows
      mat = new ArrayList<>(M);
      for(int i=0;i<M;i++){
        mat.add(i , new ArrayList<>());
      }
 
      // Push all the unswapped elements
      // of ith column to ith row
      for (int i = Math.min(N, M); i < M; i++) {
        for (int j = 0; j < N; j++) {
          mat.get(i).add(mat.get(j).get(i));
        }
      }
    }
 
    // Reverse each row of the matrix
    for (int i = 0; i < M; i++) {
      Collections.reverse(mat.get(i));
    }
 
    // Print the final matrix
    print(mat, M, N);
  }
 
  /* Driver program to test above function*/
  public static void main(String args[])
  {
    // Input
    ArrayList<ArrayList<Integer>> mat = new ArrayList<>();
    mat.add(new ArrayList<Integer>(Arrays.asList(1,2,3)));
    mat.add(new ArrayList<Integer>(Arrays.asList(4,5,6)));
    mat.add(new ArrayList<Integer>(Arrays.asList(7,8,9)));
    mat.add(new ArrayList<Integer>(Arrays.asList(10,11,12)));
 
    // Function Call
    rotate(mat);
  }
}
 
// This code is contributed by shinjanpatra

Python3




# Python3 program for
# the above approach
 
# Function to print the matrix mat
# with N rows and M columns
def Print(mat, N, M):
 
    for i in range(N):
        for j in range(M):
            print(mat[i][j] , end = " ")
        print()
 
# Function to rotate the matrix
# by 90 degree clockwise
def rotate(mat):
 
    # Number of rows
    N = len(mat)
 
    # Number of columns
    M = len(mat[0])
 
    # Swap all the elements along main diagonal
    # in the submatrix min(N, M) * min(N, M)
    for i in range(min(N, M)):
        for j in range(i,min(N, M)):
 
            # Swap mat[i][j] and mat[j][i]
            mat[i][j], mat[j][i] = mat[j][i], mat[i][j]
 
    # If N is greater than M
    if (N > M):
 
        # Push all the unswapped elements
        # of ith column to ith row
        for i in range(M):
            for j in range(min(N, M),N):
                mat[i].append(mat[j][i])
             
    else:
        # Resize mat to have M rows
        mat = [[] for i in range(M)]
 
        # Push all the unswapped elements
        # of ith column to ith row
        for i in range(min(N, M),M):
            for j in range(N):
                mat[i].append(mat[j][i])
 
    # Reverse each row of the matrix
    for i in range(M):
        mat[i] = mat[i][::-1]
 
    # Print the final matrix
    Print(mat, M, N)
 
# Driver Code
 
# Input
mat = [ [ 1, 2, 3 ],
        [ 4, 5, 6 ],
        [ 7, 8, 9 ],
        [ 10, 11, 12 ] ]
 
# Function Call
rotate(mat)
 
# This code is contributed by shinjanpatra

Javascript




<script>
 
// JavaScript program for
// the above approach
 
// Function to print the matrix mat
// with N rows and M columns
function print(mat,N,M)
{
    for (let i = 0; i < N; i++) {
        for (let j = 0; j < M; j++) {
            document.write(mat[i][j] , " ");
        }
 
        document.write("</br>");
    }
}
 
// Function to rotate the matrix
// by 90 degree clockwise
function rotate(mat)
{
    // Number of rows
    let N = mat.length;
 
    // Number of columns
    let M = mat[0].length;
 
    // Swap all the elements along main diagonal
    // in the submatrix min(N, M) * min(N, M)
    for (let i = 0; i < Math.min(N, M); i++) {
        for (let j = i; j < Math.min(N, M); j++) {
 
            // Swap mat[i][j] and mat[j][i]
            let temp = mat[i][j];
            mat[i][j] = mat[j][i];
            mat[j][i] = temp;
        }
    }
 
    // If N is greater than M
    if (N > M) {
 
        // Push all the unswapped elements
        // of ith column to ith row
        for (let i = 0; i < M; i++) {
            for (let j = Math.min(N, M); j < N; j++) {
                mat[i].push(mat[j][i]);
            }
        }
    }
    else {
        // Resize mat to have M rows
        mat = new Array(M).fill(0).map(()=>[])
 
        // Push all the unswapped elements
        // of ith column to ith row
        for (let i = Math.min(N, M); i < M; i++) {
            for (let j = 0; j < N; j++) {
                mat[i].push(mat[j][i]);
            }
        }
    }
 
    // Reverse each row of the matrix
    for (let i = 0; i < M; i++) {
        mat[i] = mat[i].reverse();
    }
 
    // Print the final matrix
    print(mat, M, N);
}
 
// Driver Code
 
// Input
let mat = [ [ 1, 2, 3 ],
        [ 4, 5, 6 ],
        [ 7, 8, 9 ],
        [ 10, 11, 12 ] ];
 
// Function Call
rotate(mat);
 
// This code is contributed by shinjanpatra
 
</script>

Output

10 7 4 1 
11 8 5 2 
12 9 6 3 

Time Complexity: O(N * M)
Auxiliary Space: O(1)

 


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