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Compute the number of intersections in a sequence of discs.

Programming language:
Spoken language:

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:

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:

int solution(int A[], int N);

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

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:

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:

int solution(vector<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].

Complexity:

- expected worst-case time complexity is O(N*log(N));
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

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:

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

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

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:

func Solution(A []int) int

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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); }

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

function solution(A);

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

function solution(A)

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

Note: All arrays in this task are zero-indexed, unlike the common Lua convention. You can use `#A` to get the length of the array A.

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

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:

int solution(NSMutableArray *A);

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

function solution(A: array of longint; N: longint): longint;

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

function solution($A);

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

sub solution { my (@A)=@_; ... }

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

def solution(A)

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

def solution(a)

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

object Solution { def solution(a: Array[Int]): Int }

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

public func solution(inout A : [Int]) -> Int

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

public func solution(_ A : inout [Int]) -> Int

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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

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:

Private Function solution(A As Integer()) As Integer

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].

Complexity:

- expected worst-case time complexity is O(N*log(N));

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