05. Prefix Sums. MinAvgTwoSlice.swift

import Foundation
import Glibc

// Solution @ Sergey Leschev, Belarusian State University

// 05. Prefix Sums. MinAvgTwoSlice.

// A non-empty array A consisting of N integers is given. A pair of integers (P, Q), such that 0 ≤ P < Q < N, is called a slice of array A (notice that the slice contains at least two elements). The average of a slice (P, Q) is the sum of A[P] + A[P + 1] + ... + A[Q] divided by the length of the slice. To be precise, the average equals (A[P] + A[P + 1] + ... + A[Q]) / (Q − P + 1).

// For example, array A such that:
//     A[0] = 4
//     A[1] = 2
//     A[2] = 2
//     A[3] = 5
//     A[4] = 1
//     A[5] = 5
//     A[6] = 8
// contains the following example slices:
// slice (1, 2), whose average is (2 + 2) / 2 = 2;
// slice (3, 4), whose average is (5 + 1) / 2 = 3;
// slice (1, 4), whose average is (2 + 2 + 5 + 1) / 4 = 2.5.
// The goal is to find the starting position of a slice whose average is minimal.

// Write a function:
// class Solution { public int solution(int[] A); }
// that, given a non-empty array A consisting of N integers, returns the starting position of the slice with the minimal average. If there is more than one slice with a minimal average, you should return the smallest starting position of such a slice.

// For example, given array A such that:
//     A[0] = 4
//     A[1] = 2
//     A[2] = 2
//     A[3] = 5
//     A[4] = 1
//     A[5] = 5
//     A[6] = 8
// the function should return 1, as explained above.

// Write an efficient algorithm for the following assumptions:
// N is an integer within the range [2..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 == 2 { return 0 }
    var sliceMinIndex = 0
    var sliceMinAvg = Double(Int.max)

    for i in 0...count - 2 {
        let slice2 = A[i] + A[i + 1]
        let slice3 = i < count - 2 ? (slice2 + A[i + 2]) : Int.max
        let avg = min(Double(slice2) / 2.0, Double(slice3) / 3.0)
        if avg < sliceMinAvg {
            sliceMinIndex = i
            sliceMinAvg = avg
        }
    }
    return sliceMinIndex
}