Given an integer N, the task is to construct a matrix of size N2 using positive and negative integers and excluding 0, such that the sum of the matrix is equal to the sum of the diagonal of the matrix.
Input: N = 2
Diagonal sum = (1 + 4) = 5
Matrix sum = (1 – 2 + 2 + 4) = 5
Input: N = 5
1 2 3 5 10
3 1 4 -9 1
-19 6 1 5 -8
4 -7 2 1 12
-17 1 1 1 1
Diagonal sum = (1 + 1 + 1 + 1 + 1) = 5
Matrix sum = 5
The approach to solving the problem is to traverse all indices of the matrix and print a positive element(say y) at the N diagonal positions and equally distribute a single-valued positive and negative integer(say x and -x) in the remaining N2 – N positions.
Below is the implementation of the above approach:
1 2 -2 2 -2 2 1 -2 2 -2 2 -2 1 2 -2 2 -2 2 1 -2 2 -2 2 -2 1
Time Complexity: O(N2)
Auxiliary Space: O(1)
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