lesson9_3_MaxDoubleSliceSum.rb

# A non-empty 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 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.

# Write an efficient algorithm for the following assumptions:

# 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].

def solution(a)
  max_starting =(a.length - 2).downto(0).each.inject([[],0]) do |(acc,max), i|
    [acc, acc[i]= [0, a[i] + max].max ]
  end.first

  max_ending =1.upto(a.length - 3).each.inject([[],0]) do |(acc,max), i|
    [acc, acc[i]= [0, a[i] + max].max ]
  end.first

  max_ending.each_with_index.inject(0) do |acc, (el,i)|
    [acc, el.to_i + max_starting[i+2].to_i].max
  end
end