alg_problem: number_of_disc_intersections

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 A[i]. We say that k-th disc and j-th disc intersect, if and k-th and j-th discs have at least one common point.

Write a function

int number_of_disc_intersections(int[] A);

which given an array A describing N discs as explained above, returns the number of pairs of intersecting discs. For example, given N=6 and

there are 11 pairs of intersecting discs:

    0th and 1st
    0th and 2nd
    0th and 4th
    1st and 2nd
    1st and 3rd
    1st and 4th
    1st and 5th
    2nd and 3rd
    2nd and 4th
    3rd and 4th
    4th and 5th

so the function should return 11.

The function should return -1 if the number of intersecting pairs exceeds 10,000,000. The function may assume that N does not exceed 10,000,000.

#include <stdio.h>
#include <vector>

int number_of_disc_intersections ( const std::vector<int> &A ) {
   // write your code here
    size_t n = A.size();
    if(n==0) return -1;
    

    long long num=0;
    for(size_t i=0; i<n; i++)
    {
        for(size_t j=i+1; j<n; j++)
        {
            if( j-i<= A[i]+A[j] /*&& j -i + A[i] >= A[j] && j-i + A[j] >= A[i] */)
            {
                //printf("%d %d\n", i, j);
                num++;
                if(num>=10000000)
                    return -1;
            }
        }
    }

    return num;
}

int main()
{
    int a[]={1,5,2,1,4,0};
    std::vector<int> A(a, a+sizeof(a)/sizeof(a[0]));
    int i=number_of_disc_intersections(A);
    printf("%d\n",i);
}

http://stackoverflow.com/questions/4801242/algorithm-to-calculate-number-of-intersecting-discs

http://www.devcomments.com/q490073/Algorithm-to-calculate-number-intersecting-discs