Question

Im trying to get the min value in a column in the row of the max value. Im trying to using for loops but its not working.

Let say a matrix A:

3 4 5
2 3 4
1 2 3

I want the program to find the max value in the [0]th row then find the min value in the colunm of the max.
So result should be : max of row [0] = 5, min of column [2] = 3.
I then want it to do the same of all the rows, that why I ysed a while loop.

Here is the matrix:

public int[][] createMatrix(int a, int b){
    Scanner  inputm = new Scanner(System.in);
  A = new int[a][b];  
System.out.println("Enter elements for matrix A : ");
for (int i=0 ; i < A.length ; i++){
    System.out.println("Enter numbers for " + i +"th row");
for  (int j=0 ; j < A[i].length ; j++){
A[i][j] = inputm.nextInt();

    }

}
return A;
}

public int[][] displayMatrix(){
 System.out.println("Matrix A: ");

    for (int i=0 ; i < A.length ; i++)
    {     System.out.println();
        for  (int j=0 ; j < A[i].length ; j++){
            System.out.print(A[i][j]+" ");
              }
    }


return A;

}


public int getMaximumOfEveryRow (int c){ 
    a=c;
int i= 0;
int j;
 while(i < A[a].length){

    max = Integer.MIN_VALUE;
    for (  j = 0; j < A [ i ].length; j++ )
        if ( A [ i ] [ j ] > max ){
            max = A [ i ] [ j ];
        }



            for (  i = 0; i < A [ i ].length; i++ )// e
        if ( A [ i ] [ j ] < min ){
            min = A [ i ] [ j ];
        }

        System.out.println( "\n Maximum of row " + j + " = " + max );
    System.out.println( "Minimum of column " + i + " = " + min );        
    if(max == min){
    System.out.println( min+ " = " + max );
    System.out.println( "This is a saddle point. ");
    }




    i++;

 }     
return max;


}

and this is what I have so far:

public int getMaximumOfEveryRow (int c){ 
    a=c;
int i= 0;
int j;
 while(i < A[a].length){

    max = Integer.MIN_VALUE;
    for (  j = 0; j < A [ i ].length; j++ )
        if ( A [ i ] [ j ] > max ){
            max = A [ i ] [ j ];
        }


    int e = j;  
    int r;
            for (  i = 0; i < A [ i ].length; i++ )// e
        if ( A [ i ] [ j ] < min ){
            min = A [ i ] [ j ];
        }

        System.out.println( "\n Maximum of row " + j + " = " + max );
    System.out.println( "Minimum of column " + i + " = " + min );        
    if(max == min){
    System.out.println( min+ " = " + max );
    System.out.println( "This is a saddle point. ");
    }




    i++;

 }     
return max;


}
public int getMaximumOfEveryColumn ()
{
for ( int i = 0; i < A.length; i++ )
{
    maxc = Integer.MIN_VALUE;
    for ( int j = 0; j < A [ i ].length; j++ )
        if ( A [ j ] [ i ] > maxc )
            maxc = A [ j ] [ i ];
    System.out.println( "Maximum of column " + i + " = " + maxc );
}
return maxc;
}

public int getMinimumOfEveryColumn_(){
for ( int i = 0; i < A.length; i++ )
{
    minc = Integer.MAX_VALUE;
    for ( int j = 0; j < A [ i ].length; j++ )
        if ( A [ j ] [ i ] < minc )
            minc = A [ j ] [ i ];
    System.out.println( "Minimum of column " + i + " = " + minc );
}
return minc;
}
public int getMaximumOfEveryRow ()
{
for ( int i = 0; i < A.length; i++ )
{
    maxr = Integer.MIN_VALUE;
    for ( int j = 0; j < A [ i ].length; j++ )
        if ( A [ i ] [ j ] > maxr )
            maxr = A [ i ] [ j ];
    System.out.println( "Maximum of row " + i + " = " + maxr );
}
return maxr;
}

code for finding the max value in colunm and then finding the min value in the row of that max value.

public void get_max_of_the_row_of_local_min ()
{
 for ( int i = 0; i < A.length; i++ )
 {
    min = Integer.MAX_VALUE;
    max = Integer.MIN_VALUE;
    int index_of_min_in_its_col = 0;



    //maxc = Integer.MIN_VALUE;
    for ( int j = 0; j < A [ i ].length; j++ )

        if ( A [ j ] [ i ] > max ){
            max = A [ j ] [ i ];
            index_of_min_in_its_col = i;
            System.out.println( " Maximum of col [" + i + "] = " + max);
        }

   for ( int j = 0; j < A [ index_of_min_in_its_col ].length; j++ )

        if ( A [ index_of_min_in_its_col ] [ index_of_min_in_its_col ] < min ){
            min = A [ index_of_min_in_its_col ] [ index_of_min_in_its_col ];
   a =j;
        }
    //System.out.print( " Maximum of col [" + j + "] = " + max);
    System.out.println( " Minimum of rol [" + index_of_min_in_its_col + "] = " + min );

    if(max == min){
    System.out.println("This is a saddle point.");
    }

 }

Answer 1

Here is the solution:

public void get_minimum_of_the_column_of_local_maximum ()
{
    for ( int i = 0; i < A.length; i++ )
    {
        min = Integer.MAX_VALUE;
        max = Integer.MIN_VALUE;
        int index_of_maximum_in_its_row = 0;

        for ( int j = 0; j < A [ i ].length; j++ )
            if ( A [ i ] [ j ] > max )
                {
                    max = A [ i ] [ j ];
                    index_of_maximum_in_its_row = j;
                }

        for ( int j = 0; j < A [ index_of_maximum_in_its_row ].length; j++ )
            if ( A [ j ] [ index_of_maximum_in_its_row ] < min )
                min = A [ j ] [ index_of_maximum_in_its_row ];

        System.out.print( " Maximum of row [" + i + "] = " + max);
        System.out.println( " Minimum of column [" + index_of_maximum_in_its_row + "] = " + min );
    }
}

What does this code snippet do?

You have min = Integer.MAX_VALUE, max = Integer.MIN_VALUE variables. The reason we assign these values to this numbers is to make finding max/min possible. How? Initially min has the greatest integer value but as far as we find a value less than it we update our minimum so the min‘s value decreases. Same technique with max variable but of course it goes the other direction by increasing in value after comparisons.

First inner for loop determines the maximum of row i, then marks the index of maximum in that row by using variable index_of_maximum_in_its_row. It is required to be used later on in the second inner loop.

Second inner loop determines the minimum of column number index_of_maximum_in_its_row with one iteration over that column. Than the method prints the results.