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:
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:
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;
}
`
``