Find Saddle Point of a Matrix in Java
In this section, we will understand what is saddle point in a matrix, and how to find the saddle point of a matrix through a Java program.
What is the saddle point in a matrix?
In a matrix, an element is called the saddle point that is the minimum (or smallest) element row-wise and maximum (or largest) element column-wise. The term saddle point is widely used in game theory.
Note that a matrix may have more than one, and may not have saddle points. For example, consider the following matrix.
In the above matrix, 10 and 8 are the lowest in the respective column and highest in the respective row. Hence, the above matrix has two saddle points.
In the following matrix, there is no saddle point exists.
How to find saddle point?
Consider the following matrix and find the saddle point.
Let's find the saddle point.
Row 0: Minimum in row 0 is 4 (at index 0) and maximum in same column 0 is 7. Both elements are different, so row 0 does not contain any saddle point.
Row 1: Minimum in row 1 is 7 (at index 0) and maximum in same column 0 is 7. Both elements are the same, so 7 is the saddle point of the matrix.
Row 2: Minimum in row 2 is 1 (at index 1) and maximum in same column 1 is 8. Both elements are different, so row 2 does not contain any saddle point.
Java Program to Find the Saddle Point in a Matrix
Let's see another logic.
The saddle point of the matrix is: 7