Problem 1634. Kurchan Square - Evaluation Function

Evaluate a Kurchan square. An NxN square with values 1:N^2.

Given a square matrix determine the products of each row, column, diagonal, and anti-diagonal.

The K-value is the Max minus the Minimum of the these products.

Example: m=[5 1 8;3 9 4;7 2 6]

Row Products: 40,108, and 84. Column products 105, 18, and 192.

Diagonal Products: 270, 1*4*7=28, and 8*3*2=48.

Anti-Diagonal Products: 8*9*7=504, 1*3*6=18, and 5*4*2=40.

K is thus 504-18 = 486. [ Max of all products - Min of all products ]

Input: Square Matrix

Output: Kurchan Score

Related Challenges:

1) Minimize Kurchan Squares (N=4:9)

2) Minimize Kurchan Squares (N=10:20) [Very large numbers]

3) Maximize Sum of Products (N=4:9) and a Large number Challenge

4) Minimize Sum of Products (N=4:9) and a Large number Challenge