Given a square matrix, the task is that turn it by 180 degrees in an 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
Python Program for Rotate a Matrix by 180 degree
The solution of this problem is that to rotate a matrix by 180 degrees 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 the 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 degrees then we will have to print the given matrix in a reverse manner.
Python3
# Python3 program to# rotate a matrix by# 180 degreesN = 3# Function to Rotate# the matrix by 180 degreedef 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 codemat = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]rotateMatrix(mat) |
9 8 7 6 5 4 3 2 1
Time complexity: O(N*N)
Auxiliary Space: O(1)
In-place rotation for Rotate a Matrix by 180 degree
There are four steps :
1- Find transpose of a matrix.
2- Reverse columns of the transpose.
3- Find transpose of a 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
Python3
# Python3 program for left rotation of matrix by 180R = 4C = 4# Function to rotate the matrix by 180 degreedef 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 matrixdef 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 matrixdef 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 degreedef rotate180(arr): transpose(arr) reverseColumns(arr) transpose(arr) reverseColumns(arr)# Driven codearr = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]rotate180(arr)printMatrix(arr) |
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)
In the code above, the transpose of the matrix has to be found twice, and also, columns have to be reversed twice.
So, we can have a better solution.
Position swapping for Rotate a Matrix by 180 degree
Here, we swap the values in the respective positions.
Python3
# Reverse Row at specified index in the matrixdef reverseRow(data, index): cols = len(data[index]) for i in range(cols // 2): temp = data[index][i] data[index][i] = data[index][cols - i - 1] data[index][cols - i - 1] = temp return data# Print Matrix datadef printMatrix(data): for i in range(len(data)): for j in range(len(data[0])): print(data[i][j], end=' ') print()# Rotate Matrix by 180 degreesdef rotateMatrix(data): rows = len(data) cols = len(data[0]) if (rows % 2): # If N is odd reverse the middle # row in the matrix data = reverseRow(data, len(data) // 2) # Swap the value of matrix [i][j] with # [rows - i - 1][cols - j - 1] for half # the rows size. for i in range(rows // 2): for j in range(cols): temp = data[i][j] data[i][j] = data[rows - i - 1][cols - j - 1] data[rows - i - 1][cols - j - 1] = temp return data# Driver Codedata = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]# Rotate Matrixdata = rotateMatrix(data)# Print MatrixprintMatrix(data) |
25 24 23 22 21 20 19 18 17 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)
Rotate a Matrix by 180 degree Reversing all rows using slicing
Python3
# Rotate Matrix by 180 degreesdef rotateMatrix(data): rows = len(data) cols = len(data[0]) # Reversing all rows for i in range(len(data)): data[i] = data[i][::-1] # Reversing all rows of the matrix data = data[::-1] for i in range(rows): for j in range(cols): print(data[i][j], end=' ') print()# Driver Codedata = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]# Rotate MatrixrotateMatrix(data) |
25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Please refer complete article on Rotate a Matrix by 180 degree for more details!
