## Monday, 29 August 2016

### Chapter 8 Exercise 35, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

8.35 (Largest block) Given a square matrix with the elements 0 or 1, write a program
to find a maximum square submatrix whose elements are all 1s. Your program
should prompt the user to enter the number of rows in the matrix. The program
then displays the location of the first element in the maximum square submatrix
and the number of the rows in the submatrix. Here is a sample run:
Enter the number of rows in the matrix: 5
Enter the matrix row by row:
1 0 1 0 1
1 1 1 0 1
1 0 1 1 1
1 0 1 1 1
1 0 1 1 1
The maximum square submatrix is at (2, 2) with size 3
Your program should implement and use the following method to find the maxi-
mum square submatrix:
public static int[] findLargestBlock(int[][] m)
The return value is an array that consists of three values. The first two values are
the row and column indices for the first element in the submatrix, and the third
value is the number of the rows in the submatrix.

import java.util.Scanner;

public class Exercise_35 {

public static void main(String[] args) {

Scanner input = new Scanner(System.in);
System.out.print("Enter the number of rows in the matrix: ");
int size = input.nextInt();
int[][] m = new int[size][size];

System.out.println("Enter the matrix row by row: ");
for (int i = 0; i < m.length; i++)
for (int j = 0; j < m[i].length; j++)
m[i][j] = input.nextInt();

int[] location = findLargestBlock(m);

if (location != null) {
System.out.printf("The maximum square submatrix is at (%d, %d) with size %d",
location[0], location[1], location[2]);
}

}

public static int[] findLargestBlock(int[][] m) {

int[] highestSquare = null;
int highestSize = 0;
for (int i = 0; i < m.length; i++) {

for (int j = 0; j < m[0].length; j++) {

int occurrence = getOccurrence(m, i, j);

if (occurrence < 2) continue; // not a square

if (scanPossibleSquare(m, i, j, occurrence) && occurrence > highestSize) {

highestSize = occurrence;
highestSquare = new int[]{i,j,occurrence};
}
}
}
return highestSquare;
}

public static int getOccurrence(int[][] m, int row, int column) {

int occurrence = 0;

if (column == m[0].length - 1) return 0;

for (int j = column; j < m[0].length; j++) {

if (m[row][j] == 1) {
occurrence++;
if (j == m[0].length - 1) return occurrence; // if in the end of grid

} else if (occurrence > 1) return occurrence;

else return 0;
}
return 0;
}

public static boolean scanPossibleSquare(int[][] m, int row, int column, int occurrence) {

if (row + occurrence > m.length) return false; // out of range

for (int i = row; i < occurrence + row; i++) {

for (int j = column; j < occurrence + column; j++) {
if (m[i][j] == 0) return false;
}
}
return true;
}
}