### Monge array of m*n

An

*m*-by-*n*matrix is said to be a*Monge array*if, for all such thatone obtains

So whenever we pick two rows and two columns of a Monge array (a 2 × 2 sub-matrix) and consider the four elements at the intersection points, the sum of the upper-left and lower right elements (across the main diagonal) is less than or equal to the sum of the lower-left and upper-right elements (across the antidiagonal).

This matrix is a Monge array:

For example, take the intersection of rows 2 and 4 with columns 1 and 5. The four elements are:

- 17 + 7 = 24
- 23 + 11 = 34

The sum of the upper-left and lower right elements is less than or equal to the sum of the lower-left and upper-right elements.

Suggest an algorithm such that given an array of (m*n) ,it can give output whether it is

*Monge*or not.
What is a use of Monge array?

ReplyDelete