Problema:

A non-empty zero-indexed array A consisting of N integers is given. A pair of integers (P, Q), such that 0 ≤ P < Q < N, is called a slice of array A (notice that the slice contains at least two elements). The average of a slice (P, Q) is the sum of A[P] + A[P + 1] + … + A[Q] divided by the length of the slice. To be precise, the average equals (A[P] + A[P + 1] + … + A[Q]) / (Q − P + 1).

For example, array A such that:

A[0] = 4 A[1] = 2 A[2] = 2 A[3] = 5 A[4] = 1 A[5] = 5 A[6] = 8

contains the following example slices:

  • slice (1, 2), whose average is (2 + 2) / 2 = 2;
  • slice (3, 4), whose average is (5 + 1) / 2 = 3;
  • slice (1, 4), whose average is (2 + 2 + 5 + 1) / 4 = 2.5.

The goal is to find the starting position of a slice whose average is minimal.

Write a function:

def solution(A)

that, given a non-empty zero-indexed array A consisting of N integers, returns the starting position of the slice with the minimal average. If there is more than one slice with a minimal average, you should return the smallest starting position of such a slice.

For example, given array A such that:

A[0] = 4 A[1] = 2 A[2] = 2 A[3] = 5 A[4] = 1 A[5] = 5 A[6] = 8

the function should return 1, as explained above.

Assume that:

  • N is an integer within the range [2..100,000];
  • each element of array A is an integer within the range [−10,000..10,000].

Complexity:

  • expected worst-case time complexity is O(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.

Solución:


def solution(A):
    list_size = len(A)
    min_index = 0
    min_avg = 9999999

    for x in xrange(list_size-1):
        slice_avg = (A[x] + A[x+1]) / 2.0
        if slice_avg < min_avg:
            min_index = x
            min_avg = slice_avg

        if x < list_size-2:
            slice_avg = (A[x] + A[x+1] + A[x+2]) / 3.0
            if slice_avg < min_avg:
                min_index = x
                min_avg = slice_avg

    return min_index

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