CC150 - 11.6

Question:

Given an M x N matrix in which each row and each column is sorted in ascending order, write a method to find an element.

 

package POJ;

public class Main {

    /**
     * 
     * 11.6 Given an M x N matrix in which each row and each column is sorted in
     * ascending order, write a method to find an element.
     * 
     */
    public static void main(String[] args) {
        Main so = new Main();
    }

    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 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;
        if (!origin.isBefore(dest))
            return null;
        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);

        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;
            }
        }
        return partitionAndSearch(matrix, origin, dest, start, x);
    }

    private static Coordinate partitionAndSearch(int[][] matrix,
            Coordinate origin, Coordinate dest, Coordinate pivot, int elem) {
        // TODO Auto-generated method stub
        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, elem);
        if (lowerLeft == null)
            return findElement(matrix, upperRightOrigin, upperRightDest, elem);
        return lowerLeft;
    }
}

class Coordinate implements Cloneable {
    int row;
    int column;

    public Coordinate(int r, int c) {
        row = r;
        column = c;
    }

    public boolean inbounds(int[][] matrix) {
        return row >= 0 && column >= 0 && row < matrix.length
                && column < matrix[0].length;
    }

    public boolean isBefore(Coordinate p) {
        return row <= p.row && column <= p.column;
    }

    public Object clone() {
        return new Coordinate(row, column);
    }

    public void setToAverage(Coordinate min, Coordinate max) {
        row = (min.row + max.row) / 2;
        column = (min.column + max.column) / 2;
    }
}