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
# Python3 program for the above approach# Function to rotate matrix by 45 degreedef 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 Matrixn = 8m = n# Given matrixli = [[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 Callmatrix(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!
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