Given a matrix mat[][] of size N*N, the task is to rotate the matrix by 45 degrees and print the matrix.
Examples:
Input: N = 6,
mat[][] = {{3, 4, 5, 1, 5, 9, 5},
{6, 9, 8, 7, 2, 5, 2},
{1, 5, 9, 7, 5, 3, 2},
{4, 7, 8, 9, 3, 5, 2},
{4, 5, 2, 9, 5, 6, 2},
{4, 5, 7, 2, 9, 8, 3}}
Output:
3
6 4
1 9 5
4 5 8 1
4 7 9 7 5
4 5 8 7 2 9
5 2 9 5 5
7 9 3 3
2 5 5
9 6
8Input: N = 4,
mat[][] = {{2, 5, 7, 2},
{9, 1, 4, 3},
{5, 8, 2, 3},
{6, 4, 6, 3}}Output:
2
9 5
5 1 7
6 8 4 2
4 2 3
6 3
3
Approach: Follow the steps given below in order to solve the problem:
- Store the diagonal elements in a list using a counter variable.
- Print the number of spaces required to make the output look like the desired pattern.
- Print the list elements after reversing the list.
- Traverse through only diagonal elements to optimize the time taken by the operation.
Below is the implementation of the above approach:
# Python3 program for the above approach # Function to rotate matrix by 45 degree def matrix(n, m, li):
# Counter Variable
ctr = 0
while (ctr < 2 * n - 1 ):
print ( " " * abs (n - ctr - 1 ), end = "")
lst = []
# Iterate [0, m]
for i in range (m):
# Iterate [0, n]
for j in range (n):
# Diagonal Elements
# Condition
if i + j = = ctr:
# Appending the
# Diagonal Elements
lst.append(li[i][j])
# Printing reversed Diagonal
# Elements
lst.reverse()
print ( * lst)
ctr + = 1
# Driver Code # Dimensions of Matrix n = 8
m = n
# Given matrix li = [[ 4 , 5 , 6 , 9 , 8 , 7 , 1 , 4 ],
[ 1 , 5 , 9 , 7 , 5 , 3 , 1 , 6 ],
[ 7 , 5 , 3 , 1 , 5 , 9 , 8 , 0 ],
[ 6 , 5 , 4 , 7 , 8 , 9 , 3 , 7 ],
[ 3 , 5 , 6 , 4 , 8 , 9 , 2 , 1 ],
[ 3 , 1 , 6 , 4 , 7 , 9 , 5 , 0 ],
[ 8 , 0 , 7 , 2 , 3 , 1 , 0 , 8 ],
[ 7 , 5 , 3 , 1 , 5 , 9 , 8 , 5 ]]
# Function Call matrix(n, m, li) |
4 1 5 7 5 6 6 5 9 9 3 5 3 7 8 3 5 4 1 5 7 8 1 6 7 5 3 1 7 0 6 4 8 9 1 4 5 7 4 8 9 8 6 3 2 7 9 3 0 1 3 9 2 7 5 1 5 1 9 0 0 8 8 5
Time Complexity: O(N2)
Auxiliary Space: O(N) since using list for auxiliary space
Please refer complete article on Rotate matrix by 45 degrees for more details!