Inplace rotate square matrix by 90 degrees | Set 1
Given a square matrix, turn it by 90 degrees in anti-clockwise direction without using any extra space.
Examples :
Input: Matrix: 1 2 3 4 5 6 7 8 9 Output: 3 6 9 2 5 8 1 4 7 The given matrix is rotated by 90 degree in anti-clockwise direction. Input: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Output: 4 8 12 16 3 7 11 15 2 6 10 14 1 5 9 13 The given matrix is rotated by 90 degree in anti-clockwise direction.
An approach that requires extra space is already discussed here.
Approach: To solve the question without any extra space, rotate the array in form of squares, dividing the matrix into squares or cycles. For example,
A 4 X 4 matrix will have 2 cycles. The first cycle is formed by its 1st row, last column, last row and 1st column. The second cycle is formed by 2nd row, second-last column, second-last row and 2nd column. The idea is for each square cycle, swap the elements involved with the corresponding cell in the matrix in anti-clockwise direction i.e. from top to left, left to bottom, bottom to right and from right to top one at a time using nothing but a temporary variable to achieve this.
Demonstration:
First Cycle (Involves Red Elements) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Moving first group of four elements (First elements of 1st row, last row, 1st column and last column) of first cycle in counter clockwise. 4 2 3 16 5 6 7 8 9 10 11 12 1 14 15 13 Moving next group of four elements of first cycle in counter clockwise 4 8 3 16 5 6 7 15 2 10 11 12 1 14 9 13 Moving final group of four elements of first cycle in counter clockwise 4 8 12 16 3 6 7 15 2 10 11 14 1 5 9 13 Second Cycle (Involves Blue Elements) 4 8 12 16 3 6 7 15 2 10 11 14 1 5 9 13 Fixing second cycle 4 8 12 16 3 7 11 15 2 6 10 14 1 5 9 13
Algorithm:
- There is N/2 squares or cycles in a matrix of side N. Process a square one at a time. Run a loop to traverse the matrix a cycle at a time, i.e loop from 0 to N/2 – 1, loop counter is i
- Consider elements in group of 4 in current square, rotate the 4 elements at a time. So the number of such groups in a cycle is N – 2*i.
- So run a loop in each cycle from x to N – x – 1, loop counter is y
- The elements in the current group is (x, y), (y, N-1-x), (N-1-x, N-1-y), (N-1-y, x), now rotate the these 4 elements, i.e (x, y) <- (y, N-1-x), (y, N-1-x)<- (N-1-x, N-1-y), (N-1-x, N-1-y)<- (N-1-y, x), (N-1-y, x)<- (x, y)
- Print the matrix.
C++
// C++ program to rotate a matrix
// by 90 degrees
#include <bits/stdc++.h>
#define N 4
using namespace std;
void displayMatrix(
int mat[N][N]);
// An Inplace function to
// rotate a N x N matrix
// by 90 degrees in
// anti-clockwise direction
void rotateMatrix(int mat[][N])
{
// Consider all squares one by one
for (int x = 0; x < N / 2; x++) {
// Consider elements in group
// of 4 in current square
for (int y = x; y < N - x - 1; y++) {
// Store current cell in
// temp variable
int temp = mat[x][y];
// Move values from right to top
mat[x][y] = mat[y][N - 1 - x];
// Move values from bottom to right
mat[y][N - 1 - x]
= mat[N - 1 - x][N - 1 - y];
// Move values from left to bottom
mat[N - 1 - x][N - 1 - y]
= mat[N - 1 - y][x];
// Assign temp to left
mat[N - 1 - y][x] = temp;
}
}
}
// Function to print the matrix
void displayMatrix(int mat[N][N])
{
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++)
printf("%2d ", mat[i][j]);
printf("\n");
}
printf("\n");
}
/* Driver program to test above functions */
int main()
{
// Test Case 1
int mat[N][N] = {
{ 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 },
{ 13, 14, 15, 16 }
};
// Test Case 2
/* int mat[N][N] = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
*/
// Test Case 3
/*int mat[N][N] = {
{1, 2},
{4, 5}
};*/
// displayMatrix(mat);
rotateMatrix(mat);
// Print rotated matrix
displayMatrix(mat);
return 0;
}
Java
// Java program to rotate a
// matrix by 90 degrees
import java.io.*;
class GFG {
// An Inplace function to
// rotate a N x N matrix
// by 90 degrees in
// anti-clockwise direction
static void rotateMatrix(
int N, int mat[][])
{
// Consider all squares one by one
for (int x = 0; x < N / 2; x++) {
// Consider elements in group
// of 4 in current square
for (int y = x; y < N - x - 1; y++) {
// Store current cell in
// temp variable
int temp = mat[x][y];
// Move values from right to top
mat[x][y] = mat[y][N - 1 - x];
// Move values from bottom to right
mat[y][N - 1 - x]
= mat[N - 1 - x][N - 1 - y];
// Move values from left to bottom
mat[N - 1 - x][N - 1 - y] = mat[N - 1 - y][x];
// Assign temp to left
mat[N - 1 - y][x] = temp;
}
}
}
// Function to print the matrix
static void displayMatrix(
int N, int mat[][])
{
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++)
System.out.print(
" " + mat[i][j]);
System.out.print("\n");
}
System.out.print("\n");
}
/* Driver program to test above functions */
public static void main(String[] args)
{
int N = 4;
// Test Case 1
int mat[][] = {
{ 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 },
{ 13, 14, 15, 16 }
};
// Test Case 2
/* int mat[][] = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
*/
// Test Case 3
/*int mat[][] = {
{1, 2},
{4, 5}
};*/
// displayMatrix(mat);
rotateMatrix(N, mat);
// Print rotated matrix
displayMatrix(N, mat);
}
}
// This code is contributed by Prakriti Gupta
Python3
# Python3 program to rotate a matrix by 90 degrees
N = 4
# An Inplace function to rotate
# N x N matrix by 90 degrees in
# anti-clockwise direction
def rotateMatrix(mat):
# Consider all squares one by one
for x in range(0, int(N / 2)):
# Consider elements in group
# of 4 in current square
for y in range(x, N-x-1):
# store current cell in temp variable
temp = mat[x][y]
# move values from right to top
mat[x][y] = mat[y][N-1-x]
# move values from bottom to right
mat[y][N-1-x] = mat[N-1-x][N-1-y]
# move values from left to bottom
mat[N-1-x][N-1-y] = mat[N-1-y][x]
# assign temp to left
mat[N-1-y][x] = temp
# Function to print the matrix
def displayMatrix( mat ):
for i in range(0, N):
for j in range(0, N):
print (mat[i][j], end = ' ')
print ("")
# Driver Code
mat = [[0 for x in range(N)] for y in range(N)]
# Test case 1
mat = [ [1, 2, 3, 4 ],
[5, 6, 7, 8 ],
[9, 10, 11, 12 ],
[13, 14, 15, 16 ] ]
'''
# Test case 2
mat = [ [1, 2, 3 ],
[4, 5, 6 ],
[7, 8, 9 ] ]
# Test case 3
mat = [ [1, 2 ],
[4, 5 ] ]
'''
rotateMatrix(mat)
# Print rotated matrix
displayMatrix(mat)
# This code is contributed by saloni1297
C#
// C# program to rotate a
// matrix by 90 degrees
using System;
class GFG {
// An Inplace function to
// rotate a N x N matrix
// by 90 degrees in anti-
// clockwise direction
static void rotateMatrix(int N,
int[, ] mat)
{
// Consider all
// squares one by one
for (int x = 0; x < N / 2; x++) {
// Consider elements
// in group of 4 in
// current square
for (int y = x; y < N - x - 1; y++) {
// store current cell
// in temp variable
int temp = mat[x, y];
// move values from
// right to top
mat[x, y] = mat[y, N - 1 - x];
// move values from
// bottom to right
mat[y, N - 1 - x] = mat[N - 1 - x,
N - 1 - y];
// move values from
// left to bottom
mat[N - 1 - x,
N - 1 - y]
= mat[N - 1 - y, x];
// assign temp to left
mat[N - 1 - y, x] = temp;
}
}
}
// Function to print the matrix
static void displayMatrix(int N,
int[, ] mat)
{
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++)
Console.Write(" " + mat[i, j]);
Console.WriteLine();
}
Console.WriteLine();
}
// Driver Code
static public void Main()
{
int N = 4;
// Test Case 1
int[, ] mat = {
{ 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 },
{ 13, 14, 15, 16 }
};
// Tese Case 2
/* int mat[][] =
{
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
*/
// Tese Case 3
/*int mat[][] =
{
{1, 2},
{4, 5}
};*/
// displayMatrix(mat);
rotateMatrix(N, mat);
// Print rotated matrix
displayMatrix(N, mat);
}
}
// This code is contributed by ajit
PHP
<?php
// PHP program to rotate a
// matrix by 90 degrees
$N = 4;
// An Inplace function to
// rotate a N x N matrix
// by 90 degrees in
// anti-clockwise direction
function rotateMatrix(&$mat)
{
global $N;
// Consider all
// squares one by one
for ($x = 0; $x < $N / 2; $x++)
{
// Consider elements
// in group of 4 in
// current square
for ($y = $x;
$y < $N - $x - 1; $y++)
{
// store current cell
// in temp variable
$temp = $mat[$x][$y];
// move values from
// right to top
$mat[$x][$y] = $mat[$y][$N - 1 - $x];
// move values from
// bottom to right
$mat[$y][$N - 1 - $x] =
$mat[$N - 1 - $x][$N - 1 - $y];
// move values from
// left to bottom
$mat[$N - 1 - $x][$N - 1 - $y] =
$mat[$N - 1 - $y][$x];
// assign temp to left
$mat[$N - 1 - $y][$x] = $temp;
}
}
}
// Function to
// print the matrix
function displayMatrix(&$mat)
{
global $N;
for ($i = 0; $i < $N; $i++)
{
for ($j = 0; $j < $N; $j++)
echo $mat[$i][$j] . " ";
echo "\n";
}
echo "\n";
}
// Driver code
// Test Case 1
$mat = array(array(1, 2, 3, 4),
array(5, 6, 7, 8),
array(9, 10, 11, 12),
array(13, 14, 15, 16));
// Tese Case 2
/* $mat = array(array(1, 2, 3),
array(4, 5, 6),
array(7, 8, 9));
*/
// Tese Case 3
/*$mat = array(array(1, 2),
array(4, 5));*/
// displayMatrix($mat);
rotateMatrix($mat);
// Print rotated matrix
displayMatrix($mat);
// This code is contributed
// by ChitraNayal
?>
Javascript
<script>
// Javascript program to rotate a
// matrix by 90 degrees
// An Inplace function to
// rotate a N x N matrix
// by 90 degrees in
// anti-clockwise direction
function rotateMatrix(N,mat)
{
// Consider all squares one by one
for (let x = 0; x < N / 2; x++)
{
// Consider elements in group
// of 4 in current square
for (let y = x; y < N - x - 1; y++)
{
// Store current cell in
// temp variable
let temp = mat[x][y];
// Move values from right to top
mat[x][y] = mat[y][N - 1 - x];
// Move values from bottom to right
mat[y][N - 1 - x]
= mat[N - 1 - x][N - 1 - y];
// Move values from left to bottom
mat[N - 1 - x][N - 1 - y] = mat[N - 1 - y][x];
// Assign temp to left
mat[N - 1 - y][x] = temp;
}
}
}
// Function to print the matrix
function displayMatrix(N,mat)
{
for (let i = 0; i < N; i++)
{
for (let j = 0; j < N; j++)
document.write(
" " + mat[i][j]);
document.write("<br>");
}
document.write("<br>");
}
/* Driver program to test above functions */
let N = 4;
let mat=[[1, 2, 3, 4],[ 5, 6, 7, 8 ],[9, 10, 11, 12 ],[13, 14, 15, 16]];
// displayMatrix(mat);
rotateMatrix(N, mat);
// Print rotated matrix
displayMatrix(N, mat);
// This code is contributed by rag2127.
</script>Output
4 8 12 16 3 7 11 15 2 6 10 14 1 5 9 13
Complexity Analysis:
- Time Complexity: O(n*n), where n is side of array.
A single traversal of the matrix is needed. - Space Complexity: O(1).
As a constant space is needed
Easy to understand and apply
Another Approach:
1.Reverse every individual row
2. Perform Transpose
C++
// C++ program to rotate a matrix
// by 90 degrees
#include <bits/stdc++.h>
#define N 4
using namespace std;
void displayMatrix(
int mat[N][N]);
// An Inplace function to
// rotate a N x N matrix
// by 90 degrees in
// anti-clockwise direction
void rotateMatrix(int mat[][N])
{ //REVERSE every row
for(int i=0;i<N;i++)
reverse(mat[i],mat[i]+N);
// Performing Transpose
for(int i=0;i<N;i++)
{ for(int j=i;j<N;j++)
swap(mat[i][j],mat[j][i]);
}
}
// Function to print the matrix
void displayMatrix(int mat[N][N])
{
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++)
printf("%2d ", mat[i][j]);
printf("\n");
}
printf("\n");
}
/* Driver program to test above functions */
int main()
{
// Test Case 1
int mat[N][N] = {
{ 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 },
{ 13, 14, 15, 16 }
};
// Test Case 2
/* int mat[N][N] = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
*/
// Test Case 3
/*int mat[N][N] = {
{1, 2},
{4, 5}
};*/
// displayMatrix(mat);
rotateMatrix(mat);
// Print rotated matrix
displayMatrix(mat);
return 0;
}
Python3
# Python3 program to rotate a matrix by 90 degrees
N = 4
# An Inplace function to rotate
# N x N matrix by 90 degrees in
# anti-clockwise direction
def rotateMatrix(mat):
# Consider all squares one by one
for x in range(0, int(N / 2)):
# Consider elements in group
# of 4 in current square
for y in range(x, N-x-1):
# store current cell in temp variable
temp = mat[x][y]
# move values from right to top
mat[x][y] = mat[y][N-1-x]
# move values from bottom to right
mat[y][N-1-x] = mat[N-1-x][N-1-y]
# move values from left to bottom
mat[N-1-x][N-1-y] = mat[N-1-y][x]
# assign temp to left
mat[N-1-y][x] = temp
# Function to print the matrix
def displayMatrix( mat ):
for i in range(0, N):
for j in range(0, N):
print (mat[i][j], end = ' ')
print ("")
# Driver Code
mat = [[0 for x in range(N)] for y in range(N)]
# Test case 1
mat = [ [1, 2, 3, 4 ],
[5, 6, 7, 8 ],
[9, 10, 11, 12 ],
[13, 14, 15, 16 ] ]
'''
# Test case 2
mat = [ [1, 2, 3 ],
[4, 5, 6 ],
[7, 8, 9 ] ]
# Test case 3
mat = [ [1, 2 ],
[4, 5 ] ]
'''
rotateMatrix(mat)
# Print rotated matrix
displayMatrix(mat)
# This code is contributed by code_hunt.Output
4 8 12 16 3 7 11 15 2 6 10 14 1 5 9 13
Complexity Analysis:
Time Complexity: O(n*n) + 0(n*n) where n is size of array.
Auxiliary Space: O(1). As a constant space is needed
Exercise: Turn 2D matrix by 90 degrees in clockwise direction without using extra space.
Rotate a matrix by 90 degree without using any extra space | Set 2
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