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.

Solution:

def solution(A):
  A.sort()
  for i in xrange(len(A) - 2):
    P, Q, R = A[i], A[i + 1], A[i + 2]
    if P + Q > R and Q + R > P and R + P > Q:
      return 1
  else:
    return 0