05. Prefix Sums. CountDiv.swift

import Foundation
import Glibc

// Solution @ Sergey Leschev, Belarusian State University

// 05. Prefix Sums. CountDiv.

// Write a function:
// class Solution { public int solution(int A, int B, int K); }
// that, given three integers A, B and K, returns the number of integers within the range [A..B] that are divisible by K, i.e.:
// { i : A ≤ i ≤ B, i mod K = 0 }
// For example, for A = 6, B = 11 and K = 2, your function should return 3, because there are three numbers divisible by 2 within the range [6..11], namely 6, 8 and 10.

// Write an efficient algorithm for the following assumptions:
// A and B are integers within the range [0..2,000,000,000];
// K is an integer within the range [1..2,000,000,000];
// A ≤ B.

public func solution(_ A: Int, _ B: Int, _ K: Int) -> Int {
    if B == 0 { return 1 }
    let aDivisors = Int(A / K)
    let bDivisors = Int(B / K)

    let result = bDivisors - aDivisors
    return A % K == 0 ? result + 1 : result
}