min_avg_two_slice.py

"""
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.
"""
import sys


def solution(A):
    n = len(A)
    pre_sum = [0] * (n + 1)
    min_slice_avg = sys.maxsize
    min_slice_idx = 0

    for i in range(1, n + 1):
        pre_sum[i] = pre_sum[i - 1] + A[i - 1]

        # calculate at least 2 prefix sums
        if i - 2 < 0:
            continue

        # check prev 3 slices if we have calculated 3 prefix sums
        if i >= 3:
            prev_3_slice_avg = (pre_sum[i] - pre_sum[i - 3]) / 3.0

            if prev_3_slice_avg < min_slice_avg:
                min_slice_avg = prev_3_slice_avg
                min_slice_idx = i - 3

        # check prev 2 slices
        prev_2_slice_avg = (pre_sum[i] - pre_sum[i - 2]) / 2.0

        if prev_2_slice_avg < min_slice_avg:
            min_slice_avg = prev_2_slice_avg
            min_slice_idx = i - 2

    return min_slice_idx