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) {
// write your code in C# 6.0 with .NET 4.5 (Mono)
}
}
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) {
int count = A.Length;
int[] rangeMin = new int[count];
int[] rangeMax = new int[count];
for (int i=0; i<count; i++)
{
rangeMin[i] = i - A[i];
rangeMax[i] = i + A[i];
}
int lower = 0;
int intersections = 0;
for(int k=0;k<count; k++)
{
while ((lower < count) && (rangeMax[k] >= rangeMin[lower])){
lower++;
}
intersections += lower - k - 1;
if (intersections > 10000000)
return -1;
}
return intersections;
}
}
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) {
int count = A.Length;
int[] rangeMin = new int[count];
int[] rangeMax = new int[count];
for (int i=0; i<count; i++)
{
rangeMin[i] = i - A[i];
rangeMax[i] = i + A[i];
}
int lower = 0;
int intersections = 0;
for(int k=0;k<count; k++)
{
while ((lower < count) && (rangeMax[k] >= rangeMin[lower])){
lower++;
}
intersections += lower - k - 1;
if (intersections > 10000000)
return -1;
}
return intersections;
}
}
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) {
int count = A.Length;
int[] rangeMin = new int[count];
int[] rangeMax = new int[count];
for (int i=0; i<count; i++)
{
rangeMin[i] = i - A[i];
rangeMax[i] = i + A[i];
}
int lower = 0;
int intersections = 0;
for(int k=0;k<count; k++)
{
while ((lower < count) && (rangeMax[k] >= rangeMin[lower])){
lower++;
}
intersections += lower - k - 1;
if (intersections > 10000000)
return -1;
}
return intersections;
}
}
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) {
int count = A.Length;
int[] rangeMin = new int[count];
int[] rangeMax = new int[count];
for (int i=0; i<count; i++)
{
rangeMin[i] = i - A[i];
rangeMax[i] = i + A[i];
}
Array.Sort(rangeMax);
Array.Sort(rangeMin);
int lower = 0;
int intersections = 0;
for(int k=0;k<count; k++)
{
while ((lower < count) && (rangeMax[k] >= rangeMin[lower])){
lower++;
}
intersections += lower - k - 1;
if (intersections > 10000000)
return -1;
}
return intersections;
}
}
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) {
int count = A.Length;
int[] rangeMin = new int[count];
int[] rangeMax = new int[count];
for (int i=0; i<count; i++)
{
rangeMin[i] = i - A[i];
rangeMax[i] = i + A[i];
}
Array.Sort(rangeMax);
Array.Sort(rangeMin);
int lower = 0;
int intersections = 0;
for(int k=0;k<count; k++)
{
while ((lower < count) && (rangeMax[k] >= rangeMin[lower])){
lower++;
}
intersections += lower - k - 1;
if (intersections > 10000000)
return -1;
}
return intersections;
}
}
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) {
int count = A.Length;
int[] rangeMin = new int[count];
int[] rangeMax = new int[count];
for (int i=0; i<count; i++)
{
rangeMin[i] = i - A[i];
rangeMax[i] = i + A[i];
}
Array.Sort(rangeMax);
Array.Sort(rangeMin);
int lower = 0;
int intersections = 0;
for(int k=0;k<count; k++)
{
while ((lower < count) && (rangeMax[k] >= rangeMin[lower])){
lower++;
}
intersections += lower - k - 1;
if (intersections > 10000000)
return -1;
}
return intersections;
}
}
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) {
int count = A.Length;
int[] rangeMin = new int[count];
int[] rangeMax = new int[count];
for (int i=0; i<count; i++)
{
rangeMin[i] = i - A[i];
rangeMax[i] = i + A[i];
}
Array.Sort(rangeMax);
Array.Sort(rangeMin);
int lower = 0;
int intersections = 0;
for(int k=0;k<count; k++)
{
while ((lower < count) && (rangeMax[k] >= rangeMin[lower])){
lower++;
}
intersections += lower - k - 1;
if (intersections > 10000000)
return -1;
}
return intersections;
}
}
[0, 12, 5, 3, 7, 18, 22, 16, 9, 5]
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) {
int count = A.Length;
int[] rangeMin = new int[count];
int[] rangeMax = new int[count];
for (int i=0; i<count; i++)
{
rangeMin[i] = i - A[i];
rangeMax[i] = i + A[i];
}
Array.Sort(rangeMax);
Array.Sort(rangeMin);
int lower = 0;
int intersections = 0;
for(int k=0;k<count; k++)
{
while ((lower < count) && (rangeMax[k] >= rangeMin[lower])){
lower++;
}
intersections += lower - k - 1;
if (intersections > 10000000)
return -1;
}
return intersections;
}
}
[0, 12, 5, 3, 7, 18, 22, 16, 9, 5]
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) {
int count = A.Length;
int[] rangeMin = new int[count];
int[] rangeMax = new int[count];
for (int i=0; i<count; i++)
{
rangeMin[i] = i - A[i];
rangeMax[i] = i + A[i];
}
Array.Sort(rangeMax);
Array.Sort(rangeMin);
int lower = 0;
int intersections = 0;
for(int k=0;k<count; k++)
{
while ((lower < count) && (rangeMax[k] >= rangeMin[lower])){
lower++;
}
intersections += lower - k - 1;
if (intersections > 10000000)
return -1;
}
return intersections;
}
}
The following issues have been detected: wrong answers.
For example, for the input [1, 2147483647, 0] the solution returned a wrong answer (got -1 expected 2).