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

A Python answer

from bisect import bisect_right

def number_of_disc_intersections(li):
    pairs = 0
    # treat as a series of intervals on the y axis at x=0
    intervals = sorted( [(i-li[i], i+li[i]) for i in range(len(li))] )
    # do this by creating a list of start points of each interval
    starts = [i[0] for i in intervals]
    for i in range(len(starts)):
        # find the index of the rightmost value less than or equal to the interval-end
        count = bisect_right(starts, intervals[i][1])
        # subtract current position to exclude previous matches, and subtract self
        count -= (i+1)
        pairs += count
        if pairs > 10000000:
            return -1
    return pairs