Python3 Program for Rotate matrix by 45 degrees

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
      8

Input: 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:

1. Store the diagonal elements in a list using a counter variable.
2. Print the number of spaces required to make the output look like the desired pattern.
3. Print the list elements after reversing the list.
4. Traverse through only diagonal elements to optimize the time taken by the operation.

Below is the implementation of the above approach:

Python3

# 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)

Output:

       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!