Question.java

package Question20_12;

import CareerCupLibrary.*;

public class Question {
	public static int getMaxMatrix(int[][] original) {
		int maxArea = Integer.MIN_VALUE; // Important! Max could be < 0
		int rowCount = original.length;
		int columnCount = original[0].length;
		int[][] matrix = precomputeMatrix(original);
		for (int row1 = 0; row1 < rowCount; row1++) {
			for (int row2 = row1; row2 < rowCount; row2++) {
				for (int col1 = 0; col1 < columnCount; col1++) {
					for (int col2 = col1; col2 < columnCount; col2++) {
						int sum = computeSum(matrix, row1, row2, col1, col2);
						if (sum > maxArea) {
							System.out.println("New Max of " + sum + ": (rows " + row1 + " to " + row2 + ") and (columns " + col1 + " to " + col2 + ")");
							maxArea = sum;
						}
						
					}
				}
			}
		}
		return maxArea;
	}
		
	private static int[][] precomputeMatrix(int[][] matrix) {
		int[][] sumMatrix = new int[matrix.length][matrix[0].length];
		for (int i = 0; i < matrix.length; i++) {
			for (int j = 0; j < matrix.length; j++) {
				if (i == 0 && j == 0) { // first cell
					sumMatrix[i][j] = matrix[i][j];
				} else if (j == 0) { // cell in first column
					sumMatrix[i][j] = sumMatrix[i - 1][j] + matrix[i][j];
				} else if (i == 0) { // cell in first row
					sumMatrix[i][j] = sumMatrix[i][j - 1] + matrix[i][j];
				} else {
					sumMatrix[i][j] = sumMatrix[i - 1][j] + 
					  sumMatrix[i][j - 1] - sumMatrix[i - 1][j - 1] +
					  matrix[i][j];
				}
			}
		}
		return sumMatrix;
	}
	
	private static int computeSum(int[][] sumMatrix, int i1, int i2, 
								  int j1, int j2) {
		if (i1 == 0 && j1 == 0) { // starts at row 0, column 0
			return sumMatrix[i2][j2];
		} else if (i1 == 0) { // starts at row 0
			return sumMatrix[i2][j2] - sumMatrix[i2][j1 - 1];
		} else if (j1 == 0) { // starts at column 0
			return sumMatrix[i2][j2] - sumMatrix[i1 - 1][j2];
		} else {
			return sumMatrix[i2][j2] - sumMatrix[i2][j1 - 1] - sumMatrix[i1 - 1][j2] + sumMatrix[i1 - 1][j1 - 1];
		}
	}
	
	public static void main(String[] args) {
		int[][] matrix = AssortedMethods.randomMatrix(10, 10, -5, 5);
		AssortedMethods.printMatrix(matrix);
		System.out.println(getMaxMatrix(matrix));
	}

}