Codility. Train. Number-of-disc-intersections ★★★

Given an array A of N integers, we draw N discs in a 2D plane such that the I-th disc is centered on (0,I) and has a radius of A[I]. We say that the J-th disc and K-th disc intersect if J ≠ K and J-th and K-th discs have at least one common point.

Write a function:

def solution(A)

that, given an array A describing N discs as explained above, returns the number of pairs of intersecting discs. For example, given N=6 and:

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

intersecting discs appear in eleven pairs of elements:

• 0 and 1,
• 0 and 2,
• 0 and 4,
• 1 and 2,
• 1 and 3,
• 1 and 4,
• 1 and 5,
• 2 and 3,
• 2 and 4,
• 3 and 4,
• 4 and 5.

so the function should return 11.

The function should return −1 if the number of intersecting pairs exceeds 10,000,000.

Assume that:

• N is an integer within the range [0..100,000];
• each element of array A is an integer within the range [0..2147483647].

Complexity:

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

Elements of input arrays can be modified.

Codility. Train. Max-product-of-three ★★

A non-empty zero-indexed array A consisting of N integers is given. The product of triplet (P, Q, R) equates to A[P] * A[Q] * A[R] (0 ≤ P < Q < R < N).

For example, array A such that:

  A[0] = -3
  A[1] = 1
  A[2] = 2
  A[3] = -2
  A[4] = 5
  A[5] = 6

contains the following example triplets:

• (0, 1, 2), product is −3 * 1 * 2 = −6
• (1, 2, 4), product is 1 * 2 * 5 = 10
• (2, 4, 5), product is 2 * 5 * 6 = 60

Your goal is to find the maximal product of any triplet.

Write a function:

def solution(A)

that, given a non-empty zero-indexed array A, returns the value of the maximal product of any triplet.

For example, given array A such that:

  A[0] = -3
  A[1] = 1
  A[2] = 2
  A[3] = -2
  A[4] = 5
  A[5] = 6

the function should return 60, as the product of triplet (2, 4, 5) is maximal.

Assume that:

• N is an integer within the range [3..100,000];
• each element of array A is an integer within the range [−1,000..1,000].

Complexity:

• expected worst-case time complexity is O(N*log(N));
• expected worst-case space complexity is O(1), beyond input storage (not counting the storage required for input arguments).

Elements of input arrays can be modified.

Codility. Train. Triangle ★

A zero-indexed array A consisting of N integers is given. A triplet (P, Q, R) is triangular if 0 ≤ P < Q < R < N and:

• A[P] + A[Q] > A[R],
• A[Q] + A[R] > A[P],
• A[R] + A[P] > A[Q].

For example, consider array A such that:

  A[0] = 10    A[1] = 2    A[2] = 5
  A[3] = 1     A[4] = 8    A[5] = 20

Triplet (0, 2, 4) is triangular.

Write a function:

def solution(A)

that, given a zero-indexed array A consisting of N integers, returns 1 if there exists a triangular triplet for this array and returns 0 otherwise. For example, given array A such that:

  A[0] = 10    A[1] = 2    A[2] = 5
  A[3] = 1     A[4] = 8    A[5] = 20

the function should return 1, as explained above. Given array A such that:

  A[0] = 10    A[1] = 50    A[2] = 5
  A[3] = 1

the function should return 0.

Assume that:

• N is an integer within the range [0..1,000,000];
• each element of array A is an integer within the range [−2,147,483,648..2,147,483,647].

Complexity:

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

Elements of input arrays can be modified.