понедельник, 13 января 2014 г.

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.

Solution:
def solution(A):
   L, A = len(A), list(A); A.sort()
   return (lambda x, y: x if x > y else y)\
   (A[L-1]*A[L-2]*A[L-3], A[0]*A[1]*A[L-1])

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