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Rotate a Matrix by 180 degree

Given a square matrix the task is that we turn it by 180 degrees in anti-clockwise direction without using any extra space.
Examples :

Input :  1  2  3
         4  5  6
         7  8  9
Output : 9 8 7 
         6 5 4 
         3 2 1

Input :  1 2 3 4 
         5 6 7 8 
         9 0 1 2 
         3 4 5 6 
Output : 6 5 4 3 
         2 1 0 9 
         8 7 6 5 
         4 3 2 1

Method : 1 (Only prints rotated matrix)
The solution of this problem is that to rotate a matrix by 180 degree we can easily follow that step

Matrix =  a00 a01 a02
          a10 a11 a12
          a20 a21 a22

when we rotate it by 90 degree
then matrix is
Matrix = a02 a12 a22
         a01 a11 a21
         a00 a10 a20
  
when we rotate it by again 90 
degree then matrix is 
Matrix = a22 a21 a20
         a12 a11 a10
         a02 a01 a00 

From the above illustration we get that simply to rotate the matrix by 180 degree then we will have to print given matrix in reverse manner .

C++

// C++ program to rotate a matrix by 180 degrees
#include <bits/stdc++.h>
#define N 3
using namespace std;
  
// Function to Rotate the matrix by 180 degree
void rotateMatrix(int mat[][N])
{
    // Simply print from last cell to first cell.
    for (int i = N - 1; i >= 0; i--) {
        for (int j = N - 1; j >= 0; j--)
            printf("%d ", mat[i][j]);
  
        printf(" ");
    }
}
  
// Driven code
int main()
{
    int mat[N][N] = {
        { 1, 2, 3 },
        { 4, 5, 6 },
        { 7, 8, 9 }
    };
  
    rotateMatrix(mat);
    return 0;
}

Java

// Java program to rotate a
// matrix by 180 degrees
import java.util.*;
  
class GFG {
    static int N = 3;
  
    // Function to Rotate the
    // matrix by 180 degree
    static void rotateMatrix(int mat[][])
    {
  
        // Simply print from last
        // cell to first cell.
        for (int i = N - 1; i >= 0; i--) {
            for (int j = N - 1; j >= 0; j--)
                System.out.print(mat[i][j] + " ");
  
            System.out.println();
        }
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        int[][] mat = { { 1, 2, 3 },
                        { 4, 5, 6 },
                        { 7, 8, 9 } };
  
        rotateMatrix(mat);
    }
}
  
// This code is contributed by ChitraNayal

Python3

# Python3 program to 
# rotate a matrix by 
# 180 degrees
N = 3;
  
# Function to Rotate 
# the matrix by 180 degree
def rotateMatrix(mat):
      
    # Simply print from
    # last cell to first cell.
    i = N - 1
    while(i >= 0):
        j = N - 1;
        while(j >= 0):
            print(mat[i][j], end = " ");
            j = j - 1;
        print();
        i = i - 1;
  
# Driven code
mat = [[1, 2, 3],
       [ 4, 5, 6 ],
       [ 7, 8, 9 ]];
rotateMatrix(mat);
  
# This code is contributed 
# by mits

C#

// C# program to rotate a
// matrix by 180 degrees
using System;
  
class GFG {
    static int N = 3;
  
    // Function to Rotate the
    // matrix by 180 degree
    static void rotateMatrix(int[, ] mat)
    {
        // Simply print from last
        // cell to first cell.
        for (int i = N - 1; i >= 0; i--) {
            for (int j = N - 1; j >= 0; j--)
                Console.Write(mat[i, j] + " ");
  
            Console.WriteLine();
        }
    }
  
    // Driver Code
    static public void Main()
    {
        int[, ] mat = { { 1, 2, 3 },
                        { 4, 5, 6 },
                        { 7, 8, 9 } };
  
        rotateMatrix(mat);
    }
}
  
// This code is contributed by aj_36

PHP

<?php
// PHP program to rotate 
// a matrix by 180 degree
$N = 3;
  
// Function to Rotate the
// matrix by 180 degree
function rotateMatrix($mat)
{
    global $N;
      
    // Simply print from 
    // last cell to first cell.
    for ($i = $N - 1; $i >= 0; $i--) 
    {
        for ($j = $N - 1; $j >= 0; $j--) 
            echo $mat[$i][$j], " ";
          
    echo " ";
    }
}
  
// Driver Code
$mat = array(array(1, 2, 3),
             array(4, 5, 6),
             array(7, 8, 9));
  
rotateMatrix($mat);
  
// This code is contributed by ajit
?>


Output :

 9 8 7 
 6 5 4 
 3 2 1  

Time complexity : O(N*N)
Auxiliary Space : O(1)



 

Method : 2(In-place rotation)
There are four steps :
1- Find transpose of matrix.
2- Reverse columns of the transpose.
3- Find transpose of matrix.
4- Reverse columns of the transpose

Let the given matrix be
1  2  3  4
5  6  7  8
9  10 11 12
13 14 15 16

First we find transpose.
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16

Then we reverse elements of every column.
4 8 12 16
3 7 11 15
2 6 10 14
1 5  9 13

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

Then we reverse elements of every column again
16 15 14 13 
12 11 10 9 
8 7 6 5 
4 3 2 1

C++

// C++ program for left rotation of matrix by 180
#include <bits/stdc++.h>
using namespace std;
  
#define R 4
#define C 4
  
// Function to rotate the matrix by 180 degree
void reverseColumns(int arr[R][C])
{
    for (int i = 0; i < C; i++)
        for (int j = 0, k = C - 1; j < k; j++, k--)
            swap(arr[j][i], arr[k][i]);
}
  
// Function for transpose of matrix
void transpose(int arr[R][C])
{
    for (int i = 0; i < R; i++)
        for (int j = i; j < C; j++)
            swap(arr[i][j], arr[j][i]);
}
  
// Function for display the matrix
void printMatrix(int arr[R][C])
{
    for (int i = 0; i < R; i++) {
        for (int j = 0; j < C; j++)
            cout << arr[i][j] << " ";
        cout << ' ';
    }
}
  
// Function to anticlockwise rotate matrix
// by 180 degree
void rotate180(int arr[R][C])
{
    transpose(arr);
    reverseColumns(arr);
    transpose(arr);
    reverseColumns(arr);
}
  
// Driven code
int main()
{
    int arr[R][C] = { { 1, 2, 3, 4 },
                      { 5, 6, 7, 8 },
                      { 9, 10, 11, 12 },
                      { 13, 14, 15, 16 } };
    rotate180(arr);
    printMatrix(arr);
    return 0;
}

Java

// Java program for left
// rotation of matrix by 180
import java.util.*;
  
class GFG {
    static int R = 4, C = 4, t = 0;
  
    // Function to rotate the
    // matrix by 180 degree
    static void reverseColumns(int arr[][])
    {
        for (int i = 0; i < C; i++) {
            for (int j = 0, k = C - 1; j < k; j++, k--) {
                t = arr[j][i];
                arr[j][i] = arr[k][i];
                arr[k][i] = t;
            }
        }
    }
  
    // Function for transpose of matrix
    static void transpose(int arr[][])
    {
        for (int i = 0; i < R; i++) {
            for (int j = i; j < C; j++) {
                t = arr[i][j];
                arr[i][j] = arr[j][i];
                arr[j][i] = t;
            }
        }
    }
  
    // Function for display the matrix
    static void printMatrix(int arr[][])
    {
        for (int i = 0; i < R; i++) {
            for (int j = 0; j < C; j++)
                System.out.print(arr[i][j] + " ");
            System.out.println();
        }
    }
  
    // Function to anticlockwise
    // rotate matrix by 180 degree
    static void rotate180(int arr[][])
    {
        transpose(arr);
        reverseColumns(arr);
        transpose(arr);
        reverseColumns(arr);
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        int[][] arr = { { 1, 2, 3, 4 },
                        { 5, 6, 7, 8 },
                        { 9, 10, 11, 12 },
                        { 13, 14, 15, 16 } };
  
        rotate180(arr);
        printMatrix(arr);
    }
}
  
// This code is contributed by ChitraNayal

C#

// C# program for left
// rotation of matrix by 180
using System;
  
class GFG {
    static int R = 4, C = 4, t = 0;
  
    // Function to rotate the
    // matrix by 180 degree
    static void reverseColumns(int[, ] arr)
    {
        for (int i = 0; i < C; i++) {
            for (int j = 0, k = C - 1;
                 j < k; j++, k--) {
                t = arr[j, i];
                arr[j, i] = arr[k, i];
                arr[k, i] = t;
            }
        }
    }
  
    // Function for transpose of matrix
    static void transpose(int[, ] arr)
    {
        for (int i = 0; i < R; i++) {
            for (int j = i; j < C; j++) {
                t = arr[i, j];
                arr[i, j] = arr[j, i];
                arr[j, i] = t;
            }
        }
    }
  
    // Function for display the matrix
    static void printMatrix(int[, ] arr)
    {
        for (int i = 0; i < R; i++) {
            for (int j = 0; j < C; j++)
                Console.Write(arr[i, j] + " ");
            Console.WriteLine();
        }
    }
  
    // Function to anticlockwise
    // rotate matrix by 180 degree
    static void rotate180(int[, ] arr)
    {
        transpose(arr);
        reverseColumns(arr);
        transpose(arr);
        reverseColumns(arr);
    }
  
    // Driver Code
    static public void Main()
    {
        int[, ] arr = { { 1, 2, 3, 4 },
                        { 5, 6, 7, 8 },
                        { 9, 10, 11, 12 },
                        { 13, 14, 15, 16 } };
  
        rotate180(arr);
        printMatrix(arr);
    }
}
  
// This code is contributed by ajit

Python 3

# Python 3 program for left rotation of matrix by 180
   
R = 4
C = 4
   
# Function to rotate the matrix by 180 degree
def reverseColumns(arr):
    for i in range(C):
        j = 0
        k = C-1
        while j < k:
            t = arr[j][i]
            arr[j][i] = arr[k][i]
            arr[k][i] = t
            j += 1
            k -= 1
              
# Function for transpose of matrix
def transpose(arr):
    for i in range(R):
        for j in range(i, C):
            t = arr[i][j]
            arr[i][j] = arr[j][i]
            arr[j][i] = t
   
# Function for display the matrix
def printMatrix(arr):
    for i in range(R):
        for j in range(C):
            print(arr[i][j], end = " ");
        print();
   
# Function to anticlockwise rotate matrix
# by 180 degree
def rotate180(arr):
    transpose(arr);
    reverseColumns(arr);
    transpose(arr);
    reverseColumns(arr);
   
# Driven code
arr = [ [ 1, 2, 3, 4 ],
        [ 5, 6, 7, 8 ],
        [9, 10, 11, 12 ],
        [13, 14, 15, 16 ] ];
rotate180(arr);
printMatrix(arr);

PHP

<?php
// PHP program for left rotation of matrix by 180
  
$R = 4;
$C = 4;
   
// Function to rotate the matrix by 180 degree
function reverseColumns(&$arr)
{
    global $C;
    for ($i = 0; $i < $C; $i++)
    {
        for ($j = 0, $k = $C - 1; $j < $k; $j++, $k--)
        {
              $t = $arr[$j][$i];
              $arr[$j][$i] = $arr[$k][$i];
              $arr[$k][$i] = $t;
        }
    }    
}
   
// Function for transpose of matrix
function transpose(&$arr)
{
    global $R, $C;
    for ($i = 0; $i < $R; $i++)
    {
        for ($j = $i; $j < $C; $j++)
        {
            $t = $arr[$i][$j];
            $arr[$i][$j] = $arr[$j][$i];
            $arr[$j][$i] = $t;
        }
    }
}
   
// Function for display the matrix
function printMatrix(&$arr)
{
    global $R, $C;
    for ($i = 0; $i < $R; $i++) {
        for ($j = 0; $j < $C; $j++)
        {
            echo $arr[$i][$j]." ";
        }
        echo " ";
    }
}
   
// Function to anticlockwise rotate matrix
// by 180 degree
function rotate180(&$arr)
{
      
    transpose($arr);
    reverseColumns($arr);
    transpose($arr);
    reverseColumns($arr);
}
   
// Driven code
  
$arr = array( array( 1, 2, 3, 4 ),
                 array( 5, 6, 7, 8 ),
                 array( 9, 10, 11, 12 ),
                 array( 13, 14, 15, 16 ) );
rotate180($arr);
printMatrix($arr);
return 0;
?>


Output :

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

Time complexity : O(R*C)
Auxiliary Space : O(1)



This article is attributed to GeeksforGeeks.org

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