09. Maximum slice problem. MaxDoubleSliceSum.swift

import Foundation
import Glibc

// Solution @ Sergey Leschev, Belarusian State University

// 09. Maximum slice problem. MaxDoubleSliceSum.

// 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:
// class Solution { public int solution(int[] 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].

public func solution(_ A: inout [Int]) -> Int {
    let count = A.count
    if count == 3 { return 0 }
    var left = [Int](repeatElement(0, count: count))
    var right = [Int](repeatElement(0, count: count))
    var solution = 0

    for i in 1..<count {
        left[i] = max(A[i] + left[i - 1], 0)
        right[count - i - 1] = max(A[count - i - 1] + right[count - i], 0)
    }
    
    for i in 1..<count - 1 { solution = max(solution, left[i - 1] + right[i + 1]) }
    return solution
}