QuestionB.java

package Q10_09_Sorted_Matrix_Search;
import CtCILibrary.*;

public class QuestionB {
	
	public static Coordinate partitionAndSearch(int[][] matrix, Coordinate origin, Coordinate dest, Coordinate pivot, int x) {
		Coordinate lowerLeftOrigin = new Coordinate(pivot.row, origin.column);
		Coordinate lowerLeftDest = new Coordinate(dest.row, pivot.column - 1);
		Coordinate upperRightOrigin = new Coordinate(origin.row, pivot.column);
		Coordinate upperRightDest = new Coordinate(pivot.row - 1, dest.column);
		
		Coordinate lowerLeft = findElement(matrix, lowerLeftOrigin, lowerLeftDest, x);
		if (lowerLeft == null) {
			return findElement(matrix, upperRightOrigin, upperRightDest, x);
		}
		return lowerLeft;
	}
	
	public static Coordinate findElement(int[][] matrix, Coordinate origin, Coordinate dest, int x) {
		if (!origin.inbounds(matrix) || !dest.inbounds(matrix)) {
			return null;
		}
		if (matrix[origin.row][origin.column] == x) {
			return origin;
		} else if (!origin.isBefore(dest)) {
			return null;
		}
		
		/* Set start to start of diagonal and end to the end of the diagonal. Since
		 * the grid may not be square, the end of the diagonal may not equal dest.
		 */
		Coordinate start = (Coordinate) origin.clone();
		int diagDist = Math.min(dest.row - origin.row, dest.column - origin.column);
		Coordinate end = new Coordinate(start.row + diagDist, start.column + diagDist);
		Coordinate p = new Coordinate(0, 0);
		
		/* Do binary search on the diagonal, looking for the first element greater than x */
		while (start.isBefore(end)) {
			p.setToAverage(start, end);
			if (x > matrix[p.row][p.column]) {
				start.row = p.row + 1;
				start.column = p.column + 1;
			} else {
				end.row = p.row - 1;
				end.column = p.column - 1;
			}
		}
		
		/* Split the grid into quadrants. Search the bottom left and the top right. */ 
		return partitionAndSearch(matrix, origin, dest, start, x);
	}
	
	public static Coordinate findElement(int[][] matrix, int x) {
		Coordinate origin = new Coordinate(0, 0);
		Coordinate dest = new Coordinate(matrix.length - 1, matrix[0].length - 1);
		return findElement(matrix, origin, dest, x);
	}
	
	public static void main(String[] args) {
		int[][] matrix = {{15, 30,  50,  70,  73}, 
				 	 	  {35, 40, 100, 102, 120},
				 	 	  {36, 42, 105, 110, 125},
				 	 	  {46, 51, 106, 111, 130},
				 	 	  {48, 55, 109, 140, 150}};
	
		AssortedMethods.printMatrix(matrix);
		int m = matrix.length;
		int n = matrix[0].length;
		
		int count = 0;
		int littleOverTheMax = matrix[m - 1][n - 1] + 10;
		for (int i = 0; i < littleOverTheMax; i++) {
			Coordinate c = findElement(matrix, i);
			if (c != null) {
				System.out.println(i + ": (" + c.row + ", " + c.column + ")");
				count++;
			}
		}
		System.out.println("Found " + count + " unique elements.");
	}

}