Max double slice sum

Question

Recently, I tried to solve the Max Double Slice Sum problem in codility which is a variant of max slice problem. My Solution was to look for a slice that has maximum value w

Answer 1

Here is my solution https://github.com/dinkar1708/coding_interview/blob/master/codility/max_slice_problem_max_double_slice_sum.py

Codility 100% in Python

def solution(A):
"""
Idea is use two temporary array and store sum using Kadane’s algorithm
ending_here_sum[i] -  the maximum sum contiguous sub sequence ending at index i
starting_here_sum[i] - the maximum sum contiguous sub sequence starting with index i

Double slice sum should be the maximum sum of ending_here_sum[i-1]+starting_here_sum[i+1]

Reference -
https://rafal.io/posts/codility-max-double-slice-sum.html

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].
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.
"""
ar_len = len(A)
ending_here_sum = [0] * ar_len
starting_here_sum = [0] * ar_len

# the maximum sum contiguous sub sequence ending at index i
for index in range(1, ar_len - 2):  # A[X + 1] + A[X + 2] + ... + A[Y - 1]
    ending_here_sum[index] = max(ending_here_sum[index - 1] + A[index], 0)

# the maximum sum contiguous sub sequence starting with index i
for index in range(ar_len - 2, 1, -1):  # A[Y + 1] + A[Y + 2] + ... + A[Z - 1]
    starting_here_sum[index] = max(starting_here_sum[index + 1] + A[index], 0)

# Double slice sum should be the maximum sum of ending_here_sum[i-1]+starting_here_sum[i+1]
max_slice_sum = ending_here_sum[0] + starting_here_sum[2]
for index in range(1, ar_len - 1):
    max_slice_sum = max(max_slice_sum, ending_here_sum[index - 1] + starting_here_sum[index + 1])

return max_slice_sum