count_triangles.py

"""
A zero-indexed array A consisting of N integers is given.
A triplet (P, Q, R) is triangular if it is possible to build a triangle
 with sides of lengths A[P], A[Q] and A[R].
 In other words, 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] = 12
There are four triangular triplets that can be constructed from elements of this array,
 namely (0, 2, 4), (0, 2, 5), (0, 4, 5), and (2, 4, 5).

Write a function:

    def solution(A)

that, given a zero-indexed array A consisting of N integers,
 returns the number of triangular triplets in this array.

For example, given array A such that:

  A[0] = 10    A[1] = 2    A[2] = 5
  A[3] = 1     A[4] = 8    A[5] = 12
the function should return 4, as explained above.

Assume that:
    N is an integer within the range [0..1,000];
    each element of array A is an integer within the range [1..1,000,000,000].

Complexity:
    expected worst-case time complexity is O(N2);
    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.
"""


def solution(A):
    n = len(A)
    result = 0

    A.sort()

    for first in range(n - 2):
        third = first + 2
        for second in range(first + 1, n - 1):
            while third < n and A[first] + A[second] > A[third]:
                third += 1
            result += third - second - 1

    return result