Python Program for Mirror of matrix across diagonal
Given a 2-D array of order N x N, print a matrix that is the mirror of the given tree across the diagonal. We need to print the result in a way: swap the values of the triangle above the diagonal with the values of the triangle below it like a mirror image swap. Print the 2-D array obtained in a matrix layout.
Examples:
Input : int mat[][] = {{1 2 4 }
{5 9 0}
{ 3 1 7}}
Output : 1 5 3
2 9 1
4 0 7
Input : mat[][] = {{1 2 3 4 }
{5 6 7 8 }
{9 10 11 12}
{13 14 15 16} }
Output : 1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
A simple solution to this problem involves extra space. We traverse all right diagonal (right-to-left) one by one. During the traversal of the diagonal, first, we push all the elements into the stack and then we traverse it again and replace every element of the diagonal with the stack element.
Below is the implementation of the above idea.
Python3
MAX = 100
def imageSwap(mat, n):
row = 0
for j in range (n):
s = []
i = row
k = j
while (i < n and k > = 0 ):
s.append(mat[i][k])
i + = 1
k - = 1
i = row
k = j
while (i < n and k > = 0 ):
mat[i][k] = s[ - 1 ]
k - = 1
i + = 1
s.pop()
column = n - 1
for j in range ( 1 , n):
s = []
i = j
k = column
while (i < n and k > = 0 ):
s.append(mat[i][k])
i + = 1
k - = 1
i = j
k = column
while (i < n and k > = 0 ):
mat[i][k] = s[ - 1 ]
i + = 1
k - = 1
s.pop()
def printMatrix(mat, n):
for i in range (n):
for j in range (n):
print (mat[i][j], end = " " )
print ()
mat = [[ 1 , 2 , 3 , 4 ], [ 5 , 6 , 7 , 8 ],
[ 9 , 10 , 11 , 12 ], [ 13 , 14 , 15 , 16 ]]
n = 4
imageSwap(mat, n)
printMatrix(mat, n)
|
Output
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
Time complexity: O(n*n)
Method 2:
we just have to swap (mat[i][j] to mat[j][i]).
Below is the implementation of the above idea.
Python3
from builtins import range
MAX = 100
def imageSwap(mat, n):
for i in range (n):
for j in range (i + 1 ):
t = mat[i][j]
mat[i][j] = mat[j][i]
mat[j][i] = t
def printMatrix(mat, n):
for i in range (n):
for j in range (n):
print (mat[i][j], end = " " )
print ()
if __name__ = = '__main__' :
mat = [ 1 , 2 , 3 , 4 ], \
[ 5 , 6 , 7 , 8 ], \
[ 9 , 10 , 11 , 12 ], \
[ 13 , 14 , 15 , 16 ]
n = 4
imageSwap(mat, n)
printMatrix(mat, n)
|
Output:
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
Time complexity: O(n*n)
Auxiliary space: O(1) as it is using constant space.
Method 3: Using List Comprehension
Python3
def printMatrix(mat, n):
for i in range (n):
for j in range (n):
print (mat[i][j], end = " " )
print ()
mat = [[ 1 , 2 , 3 , 4 ], [ 5 , 6 , 7 , 8 ],
[ 9 , 10 , 11 , 12 ], [ 13 , 14 , 15 , 16 ]]
n = 4
mat = [[(mat[j][i]) for j in range (n)] for i in range (n)]
printMatrix(mat, n)
|
Output
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
Time Complexity: O(n*n)
Space Complexity: O(n)
Please refer complete article on Mirror of matrix across diagonal for more details!
Last Updated :
24 Mar, 2023
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