CODILITY - LESSON 4 - NumberOfDiscIntersections

PROBLEM:

We draw N discs on a plane. The discs are numbered from 0 to N − 1. A zero-indexed array A of N non-negative integers, specifying the radiuses of the discs, is given. The J-th disc is drawn with its center at (J, 0) and radius A[J].

We say that the J-th disc and K-th disc intersect if J ≠ K and the J-th and K-th discs have at least one common point (assuming that the discs contain their borders).

The figure below shows discs drawn for N = 6 and A as follows:

  A[0] = 1
  A[1] = 5
  A[2] = 2
  A[3] = 1
  A[4] = 4
  A[5] = 0

There are eleven (unordered) pairs of discs that intersect, namely:

• discs 1 and 4 intersect, and both intersect with all the other discs;
• disc 2 also intersects with discs 0 and 3.

Write a function:

class Solution { public int solution(int[] A); }

that, given an array A describing N discs as explained above, returns the number of (unordered) pairs of intersecting discs. The function should return −1 if the number of intersecting pairs exceeds 10,000,000.

Given array A shown above, the function should return 11, as explained above.

Assume that:

• N is an integer within the range [0..100,000];
• each element of array A is an integer within the range [0..2,147,483,647].

SOLUTION (93% score, time complexity O(N*log(N)) or O(N)) 
(click here to go to codility.com and see test results)

using System; using System.Collections.Generic; class Solution { public int solution(int[] A) { int N = A.Length; long [] AX = new long[N]; long [] AY = new long[N]; for (int i = 0; i < N; i++) { AX[Math.Max(0, i - A[i])]++; AY[Math.Min(N-1, i + A[i])]++; } long result = 0; long discsAtIndex = 0; for (int i = 0; i <N; i++) { if (AX[i] > 0) { result += discsAtIndex * AX[i] + (AX[i] * (AX[i] - 1) / 2); discsAtIndex += AX[i]; } discsAtIndex -= AY[i]; } if (result <= 10000000) return (int) result; else return -1; } }

This solution fails one test;

overflow arithmetic overflow tests	0.055 s	RUNTIME ERROR tested program terminated unexpectedly
stderr: Unhandled Exception: System.IndexOutOfRangeException: Array index is out of range. at Solution.solution (System.Int32[]

The solution is easier to understand if you see each pair XY as the start and end points of a line. You would be counting how many lines are at each index.

The array AX counts how many times a line (or circle) starts before or at the index. I.e. at position 0, 4 lines (or circles) have their starting point before or at 0.

The array AY counts how many times a line (or circle) ends at the index. I.e. at position 0 no line (or circle) ends there. At position 1, one line (or circle) ends.

There are two counts; the int result (which will be the answer) and we also need to count how many lines(discs) are at each index while we loop.

For this one, I had to check some forums in order to get the result count working properly,  as i wasn't accounting for pairs already counted in the result variable ((AX[i] * (AX[i] - 1) / 2);)

PR