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

I know that this is an old questions but it is still active on codility.

    private int solution(int[] A)
    {
        int openedCircles = 0;
        int intersectCount = 0;

We need circles with their start and end values. For that purpose I have used Tuple. True/False indicates if we are adding Circle Starting or Circle Ending value.

        List> circles = new List>();
        for(int i = 0; i < A.Length; i ++)
        {
            // Circle start value
            circles.Add(new Tuple((decimal)i - (decimal)A[i], true));

            // Circle end value
            circles.Add(new Tuple((decimal)i + (decimal)A[i], false));
        }

Order "circles" by their values. If one circle is ending at same value where other circle is starting, it should be counted as intersect (because of that "opening" should be in front of "closing" if in same point)

        circles = circles.OrderBy(x => x.Item1).ThenByDescending(x => x.Item2).ToList();

Counting and returning counter

        foreach (var circle in circles)
        {
            // We are opening new circle (within existing circles)
            if(circle.Item2 == true)
            {
                intersectCount += openedCircles;

                if (intersectCount > 10000000)
                { 
                    return -1;
                }

                openedCircles++;
            }
            else
            {
                // We are closing circle
                openedCircles--;
            }
        }

        return intersectCount;
    }