Algorithm to calculate number of intersecting discs

Question

Given an array A of N integers we draw N discs in a 2D plane, such that i-th disc has center in (0,i) and a radius

Answer 1

An Implementation of Idea stated above in Java:

public class DiscIntersectionCount {


public int number_of_disc_intersections(int[] A) {
    int[] leftPoints = new int[A.length];
    for (int i = 0; i < A.length; i++) {
        leftPoints[i] = i - A[i];
    }

    Arrays.sort(leftPoints);
//      System.out.println(Arrays.toString(leftPoints));
    int count  = 0;
    for (int i = 0; i < A.length - 1; i++) {
        int rpoint = A[i] + i;

        int rrank = getRank(leftPoints, rpoint);

        //if disk has sifnificant radius, exclude own self
        if (rpoint > i) rrank -= 1;
        int rank = rrank; 
//          System.out.println(rpoint+" : "+rank);

        rank -= i;
        count += rank;
    }
    return count;

}

public int getRank(int A[], int num) {
    if (A==null || A.length == 0) return -1;        
    int mid = A.length/2;
    while ((mid >= 0) && (mid < A.length)) {

        if (A[mid] == num) return mid;

        if ((mid == 0) && (A[mid] > num)) return -1;
        if ((mid == (A.length - 1)) && (A[mid] < num)) return A.length;
        if (A[mid] < num && A[mid + 1] >= num) return mid + 1;
        if (A[mid] > num && A[mid - 1] <= num) return mid - 1;

        if (A[mid] < num) mid = (mid + A.length)/2;
        else  mid = (mid)/2;

    }

    return -1;
}

public static void main(String[] args) {
    DiscIntersectionCount d = new DiscIntersectionCount();
    int[] A = 
        //{1,5,2,1,4,0}
        //{0,0,0,0,0,0}
    //  {1,1,2}
    {3}
     ;
    int count = d.number_of_disc_intersections(A);
    System.out.println(count);
}
}