We draw N discs on a plane. The discs are numbered from 0 to N − 1. An 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] = 0There 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.
Write an efficient algorithm for the following assumptions:
- 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].
using System;
// you can also use other imports, for example:
// using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution
{
public int solution(int[] A)
{
if (A == null || A.Length <= 1)
{
return 0;
}
// this solution has a time complexity of O(N*N)
int intersectingPairs = 0;
var coordinatesMap = new List<DiscCoordinates>();
for (int i = 0; i < A.Length; i++)
{
coordinatesMap.Add(new DiscCoordinates((long)i-(long)A[i], 1));
coordinatesMap.Add(new DiscCoordinates((long)i+(long)A[i], -1));
}
coordinatesMap.Sort((coord1, coord2) => coord1.CompareTo(coord2));
int runningDiscs = 0;
foreach (var discCoordinates in coordinatesMap)
{
if (discCoordinates.DiscRunningIncrement == 1)
{
intersectingPairs += runningDiscs;
if (intersectingPairs > 10000000) return -1;
}
runningDiscs += discCoordinates.DiscRunningIncrement;
}
return intersectingPairs;
}
private class DiscCoordinates : IComparable<DiscCoordinates>
{
public DiscCoordinates(long xCoord, sbyte discRunningIncrement)
{
XCoordinate = xCoord;
DiscRunningIncrement = discRunningIncrement;
}
public long XCoordinate { get; private set; }
public sbyte DiscRunningIncrement { get; private set; }
public int CompareTo(DiscCoordinates other)
{
if (this.XCoordinate.Equals(other.XCoordinate))
{
return (-1) * this.DiscRunningIncrement.CompareTo(other.DiscRunningIncrement);
}
return this.XCoordinate.CompareTo(other.XCoordinate);
}
}
}
Compilation failed: 1 error(s), 0 warnings Solution.cs(20,35): error CS0246: The type or namespace name `List' could not be found. Are you missing `System.Collections.Generic' using directive?
using System;
// you can also use other imports, for example:
using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution
{
public int solution(int[] A)
{
if (A == null || A.Length <= 1)
{
return 0;
}
// this solution has a time complexity of O(N*N)
int intersectingPairs = 0;
var coordinatesMap = new List<DiscCoordinates>();
for (int i = 0; i < A.Length; i++)
{
coordinatesMap.Add(new DiscCoordinates((long)i-(long)A[i], 1));
coordinatesMap.Add(new DiscCoordinates((long)i+(long)A[i], -1));
}
coordinatesMap.Sort((coord1, coord2) => coord1.CompareTo(coord2));
int runningDiscs = 0;
foreach (var discCoordinates in coordinatesMap)
{
if (discCoordinates.DiscRunningIncrement == 1)
{
intersectingPairs += runningDiscs;
if (intersectingPairs > 10000000) return -1;
}
runningDiscs += discCoordinates.DiscRunningIncrement;
}
return intersectingPairs;
}
private class DiscCoordinates : IComparable<DiscCoordinates>
{
public DiscCoordinates(long xCoord, sbyte discRunningIncrement)
{
XCoordinate = xCoord;
DiscRunningIncrement = discRunningIncrement;
}
public long XCoordinate { get; private set; }
public sbyte DiscRunningIncrement { get; private set; }
public int CompareTo(DiscCoordinates other)
{
if (this.XCoordinate.Equals(other.XCoordinate))
{
return (-1) * this.DiscRunningIncrement.CompareTo(other.DiscRunningIncrement);
}
return this.XCoordinate.CompareTo(other.XCoordinate);
}
}
}
using System;
// you can also use other imports, for example:
using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution
{
public int solution(int[] A)
{
if (A == null || A.Length <= 1)
{
return 0;
}
// this solution has a time complexity of O(N*N)
int intersectingPairs = 0;
var coordinatesMap = new List<DiscCoordinates>();
for (int i = 0; i < A.Length; i++)
{
coordinatesMap.Add(new DiscCoordinates((long)i-(long)A[i], 1));
coordinatesMap.Add(new DiscCoordinates((long)i+(long)A[i], -1));
}
coordinatesMap.Sort((coord1, coord2) => coord1.CompareTo(coord2));
int runningDiscs = 0;
foreach (var discCoordinates in coordinatesMap)
{
if (discCoordinates.DiscRunningIncrement == 1)
{
intersectingPairs += runningDiscs;
if (intersectingPairs > 10000000) return -1;
}
runningDiscs += discCoordinates.DiscRunningIncrement;
}
return intersectingPairs;
}
private class DiscCoordinates : IComparable<DiscCoordinates>
{
public DiscCoordinates(long xCoord, sbyte discRunningIncrement)
{
XCoordinate = xCoord;
DiscRunningIncrement = discRunningIncrement;
}
public long XCoordinate { get; private set; }
public sbyte DiscRunningIncrement { get; private set; }
public int CompareTo(DiscCoordinates other)
{
if (this.XCoordinate.Equals(other.XCoordinate))
{
return (-1) * this.DiscRunningIncrement.CompareTo(other.DiscRunningIncrement);
}
return this.XCoordinate.CompareTo(other.XCoordinate);
}
}
}
using System;
// you can also use other imports, for example:
using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution
{
public int solution(int[] A)
{
if (A == null || A.Length <= 1)
{
return 0;
}
// this solution has a time complexity of O(N*N)
int intersectingPairs = 0;
var coordinatesMap = new List<DiscCoordinates>();
for (int i = 0; i < A.Length; i++)
{
coordinatesMap.Add(new DiscCoordinates((long)i-(long)A[i], 1));
coordinatesMap.Add(new DiscCoordinates((long)i+(long)A[i], -1));
}
coordinatesMap.Sort((coord1, coord2) => coord1.CompareTo(coord2));
int runningDiscs = 0;
foreach (var discCoordinates in coordinatesMap)
{
if (discCoordinates.DiscRunningIncrement == 1)
{
intersectingPairs += runningDiscs;
if (intersectingPairs > 10000000) return -1;
}
runningDiscs += discCoordinates.DiscRunningIncrement;
}
return intersectingPairs;
}
private class DiscCoordinates : IComparable<DiscCoordinates>
{
public DiscCoordinates(long xCoord, sbyte discRunningIncrement)
{
XCoordinate = xCoord;
DiscRunningIncrement = discRunningIncrement;
}
public long XCoordinate { get; private set; }
public sbyte DiscRunningIncrement { get; private set; }
public int CompareTo(DiscCoordinates other)
{
if (this.XCoordinate.Equals(other.XCoordinate))
{
return (-1) * this.DiscRunningIncrement.CompareTo(other.DiscRunningIncrement);
}
return this.XCoordinate.CompareTo(other.XCoordinate);
}
}
}
The solution obtained perfect score.