## 2017年2月24日 星期五

### 【Python】Codility in Python : Lesson 9 - Maximum slice problem【MaxDoubleSliceSum】

Maximum slice problem 第一題：【MaxDoubleSliceSum】
Find the maximal sum of any double slice.

A non-empty zero-indexed array A consisting of N integers is given.

A triplet (X, Y, Z), such that 0 ≤ X < Y < Z < N, is called a double slice.

The sum of double slice (X, Y, Z) is the total of
A[X + 1] + A[X + 2] + ... + A[Y − 1] + A[Y + 1] + A[Y + 2] + ... + A[Z − 1].

For example, array A such that:

A = 3
A = 2
A = 6
A = -1
A = 4
A = 5
A = -1
A = 2

contains the following example double slices:

double slice (0, 3, 6), sum is 2 + 6 + 4 + 5 = 17,
double slice (0, 3, 7), sum is 2 + 6 + 4 + 5 − 1 = 16,
double slice (3, 4, 5), sum is 0.

The goal is to find the maximal sum of any double slice.

Write a function:

def solution(A)

that, given a non-empty zero-indexed array A consisting of N integers,
returns the maximal sum of any double slice.

For example, given:

A = 3
A = 2
A = 6
A = -1
A = 4
A = 5
A = -1
A = 2

the function should return 17,
because no double slice of array A has a sum of greater than 17.

Assume that:

N is an integer within the range [3..100,000];
each element of array A is an integer within the range [−10,000..10,000].

Correctness：100%、Performance：100%
```python def solution(S): length = len(A) start =  * length end =  * length for i in reversed(range(length-1)): start[i] = max(0, start[i+1] + A[i]) for i in range(1, length): end[i] = max(0, end[i-1] + A[i]) maxDoubleSlice = 0 for i in range(1, length-1): 　maxDoubleSlice = max(maxDoubleSlice, start[i+1] + end[i-1]) return maxDoubleSlice ```