OBJECT ORIENTED PROGAMMING

American Computer Science League 1993-94 p & Contest #2

Intermediate Division - PROGRAMMING

Back in the Saddle Again'

Problem: A matrix is a rectangular arrangement of numbers. The matrix below has 3 rows and 2 columns, and it's called a 3-by-2 matrix:

5 2

3 1

4 8

A saddle point of a matrix is any value of the matrix that is both the largest value in its row and the largest value in its column. There are two saddle points in the matrix above: 5 and 8. If the 4 in the last row of the matrix had been a 5, the matrix would have only one saddle point: 8. If the 4 in the last row had been an 8, the matrix would have no saddle points. Finally, if the 8 in the last row has been a 5, the matrix would have the single saddle point, 5. (This is tricky)

Input: Five matrices. Each matrix starts with the number of rows (r) and columns (c) of the matrix, followed by the r-by-c columns. The first data line below corresponds to the sample matrix above. All matrices will be smaller than 6-by-6, and all values will be positive integers.

Output: Print the saddle points of each matrix. If the matrix has no saddle points, print a message to that effect. If the matrix has more than one saddle point, they may be listed in any order; all must be listed in order to receive credit. If a saddle point appears more than once (as would happen if the 8 were changed to a 5 in the example above), it must be listed only once.

Sample Input:

Line #1: 3, 2, 5, 2, 3, 1, 4, 8 Line #2: 3, 3, 3, 2, 4, 1, 1, 6, 4, 2, 5 Line #3: 4, 2, 9, 3, 5, 8, 6, 3 2 1 Line #4: 4, 3, 1, 2, 3, 4, 2, 4, 6, 8, 1, 3, 5, 7 Line #5: 3, 2, 5, 2, 6, 8, 3, 8

Sample Output:

Output #1: 5 and 8 Output #2: 6 Output #3: 8 and 9 Output #4: 7 and 8 Output #5: none