Integer Arrays A and B are grid line co-ordinates along x and y-axis respectively bounded by a rectangle of size X * Y. If the sizes of the sub-rectangles withing the bounding rectangle were arranged in the descending order, return the size of the Kth rectangle.                          

   

   public static int getKthRectangle(int X, int Y, int K, int [] A, int[] B){
        int[] width = calculateSideLength(A, X);
        int[] height = calculateSideLength(B, Y);

      Arrays.sort(width);
        Arrays.sort(height);
        int start = 1;
        int end = width[width.length-1] * height[height.length-1];
        int result = 0;
        while (start <= end) {
            int mid = (start + end)/2;
            if (greater(X, Y, mid, width, height) >= K) {
                start = mid+1;
                result = mid;
            } else {
                end = mid - 1;
            }
        }
        return result;
    }

    public static int greater(int X, int Y, int mid, int[] width, int[] height){
        int N = width.length;
        int result = 0;
        int j = N-1;
        for (int i = 0; i < N; i++){
            while (j >= 0 && width[i] * height[j] >= mid) {
                j--;
            }
            result += N-1-j;
        }
        return result;
    }

  public static int[] calculateSideLength(int[] X, int M) {
    int[] length = new int[X.length+1];
    for (int i = 0; i < X.length; i++){
        if ( i == 0) {
            length[i] = X[i] - 0;
        } else {
            length[i] = X[i] - X[i-1];
        }
    }
    length[X.length] = M - X[X.length-1];
    return length;
}

A: 1 3  X: 6

B: 1 5  Y: 7

width: 1 2 3

height: 1 4 2

K’th rectangle size: 6
The calculation of the side length remains the same for both X-axis and Y-axis.