Given a number N, the task is to create a square matrix of size N*N with values in range [1, N*N], such that the sum of each diagonal of an even sub-square matrix is even.
Input: N = 3
1 2 3
4 5 6
7 8 9
Explanation:For each even sub-square matrix the sum of each diagonal is a even number.
sum of each diagonal is 6 and 6 i.e even number.
Input: N = 4
1 2 3 4
6 5 8 7
9 10 11 12
14 13 16 15
For each even sub-square matrix the sum of each diagonal is a even number.
sum of each diagonal is 6 and 8 i.e even number.
Approach: The idea is to arrange elements from 1 to N*N in the below-given ways:
- Initialize odd and even by 1 and 2 elements respectively.
- Iterate two nested loop in the range [0, N].
- If the sum of indices in the two nested loops is even the print the value of odd and increment odd by 2 and if the sum is odd then print the value of even, and increment even by 2.
Below is the implementation of the above approach:
1 2 3 4 6 5 8 7 9 10 11 12 14 13 16 15
Time Complexity: O(N*N)
Auxiliary Space: O(1)
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