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

This is a ruby solution that scored 100/100 on codility. I'm posting it now because I'm finding it difficult to follow the already posted ruby answer.

def solution(a)
    end_points = []
    a.each_with_index do |ai, i|
        end_points << [i - ai, i + ai]
    end
    end_points = end_points.sort_by { |points| points[0]}

    intersecting_pairs = 0
    end_points.each_with_index do |point, index|
        lep, hep = point
        pairs = bsearch(end_points, index, end_points.size - 1, hep)
        return -1 if 10000000 - pairs + index < intersecting_pairs
        intersecting_pairs += (pairs - index)
    end
    return intersecting_pairs
end

# This method returns the maximally appropriate position
# where the higher end-point may have been inserted.
def bsearch(a, l, u, x)
    if l == u
        if x >= a[u][0]
            return u
        else
            return l - 1 
        end
    end
    mid = (l + u)/2

    # Notice that we are searching in higher range
    # even if we have found equality.
    if a[mid][0] <= x
        return bsearch(a, mid+1, u, x)
    else
        return bsearch(a, l, mid, x)
    end
end