【Python】Codility in Python : Lesson 5 - Prefix Sums【MinAvgTwoSlice】

Prefix Sums 第四題：【MinAvgTwoSlice】
Find the minimal average of any slice containing at least two elements.

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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.

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方法一：用 Prefix Sums 的方法
Correctness：100%、Performance：100%

import sys

def solution(A):
  result = 0
  length = len(A)
  valueList = [0]
  for i in range(length):
    valueList.append(valueList[i] + A[i])

  minAvg = sys.float_info.max
  for i in range(length - 1):
    index1 = i + 1
    index2 = i + 2
    avg = (valueList[index1 + 1] - valueList[i]) / 2.0
    if(avg < minAvg):
      minAvg = avg
      result = i

    if(i < length - 2):
      avg = (valueList[index2 + 1] - valueList[i]) / 3.0
      if(avg < minAvg):
        minAvg = avg
        result = i

  return result

完整練習題 source code 請參閱：github