max_double_slice_sum.py

"""
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[0] = 3
    A[1] = 2
    A[2] = 6
    A[3] = -1
    A[4] = 4
    A[5] = 5
    A[6] = -1
    A[7] = 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[0] = 3
    A[1] = 2
    A[2] = 6
    A[3] = -1
    A[4] = 4
    A[5] = 5
    A[6] = -1
    A[7] = 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].
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)
    left = [0] * n
    for i in range(1, n - 1):
        left[i] = max(0, left[i - 1] + A[i])

    right = [0] * n
    for i in range(n - 2, 1, -1):
        right[i] = max(0, right[i + 1] + A[i])

    max_sum = -sys.maxsize
    for i in range(1, n - 1):
        max_sum = max(max_sum, left[i - 1] + right[i + 1])
    return max_sum