Max Double Slice Sum

Problem

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:

function 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].

My Solution

success O(N)
function solution(A) {
	let left = [...A].fill(0);
	let right = [...A].fill(0);

	for (let i = 1, j = A.length - 2; j >= 2; i++, j--) {
		left[i] = Math.max(0, left[i - 1] + A[i]);
		right[j] = Math.max(0, right[j + 1] + A[j]);
	}

	let max = left[0] + right[2];

	for (let i = 2; i < A.length - 1; i++) {
		max = Math.max(max, left[i - 1] + right[i + 1]);
	}

	return max;
}
`
``