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11 Feb 2019

How to find Saddle point of a matrix in java?

Saddle point of a matrix is an element in the matrix which is smallest in its row and largest in its column. A matrix can have many or no saddle points. For example,

6    3     1
9    7     8
 2    4    5

In this matrix, 7 is the saddle point. Because it is the smallest in its row (2nd row) and largest in its column (2nd column).

Algorithm To Find Saddle Point Of A Matrix In Java

Step 1 : For each row of the matrix, find the smallest element in a row and store it in rowMin and also store its column index in colIndex.

for (int i = 0; i < matrix.length; i++) 
        int rowMin = matrix[i][0];
        int colIndex = 0;

        for (int j = 1; j < matrix[i].length; j++)
                if(matrix[i][j] < rowMin)
                        rowMin = matrix[i][j];
                        colIndex = j;

Step 2 : Check whether rowMin is also the largest element in its column i.e colIndex.

for (int j = 0; j < matrix.length; j++)
        if(matrix[j][colIndex] > rowMin)
                saddlePoint = false;

Step 3 : If rowMin is also the largest element in its column, then declare that element as saddle point.

Step 4 : Repeat above steps for all the rows of a matrix.