Count Div

Problem

Write a function:

function solution(A, B, 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.

My Solution

failed O(B-A)

function solution(A, B, K) {
	let cnt = 0;
	for (let i = A; i < B + 1; i++) {
		if (i % K === 0) cnt++;
	}

	return cnt;
}

failed

function solution(A, B, K) {
	let min = 0;
	let cnt = 0;

	while (min < A && min + K < A) min += K;

	while (min < B && min + K < B) {
		min += K;
		cnt++;
	}

	return cnt;
}

success O(N) or O(N * log(N))

function solution(A, B, K) {
	return Math.floor(B / K) - Math.ceil(A / K) + 1;
}