Two positive integers N and M are given. Integer N represents the number of chocolates arranged in a circle, numbered from 0 to N − 1.
You start to eat the chocolates. After eating a chocolate you leave only a wrapper.
You begin with eating chocolate number 0. Then you omit the next M − 1 chocolates or wrappers on the circle, and eat the following one.
More precisely, if you ate chocolate number X, then you will next eat the chocolate with number (X + M) modulo N (remainder of division).
You stop eating when you encounter an empty wrapper.
For example, given integers N = 10 and M = 4. You will eat the following chocolates: 0, 4, 8, 2, 6.
The goal is to count the number of chocolates that you will eat, following the above rules.
Write a function:
function solution(N, M);
that, given two positive integers N and M, returns the number of chocolates that you will eat.
For example, given integers N = 10 and M = 4. the function should return 5, as explained above.
Write an efficient algorithm for the following assumptions:
- N and M are integers within the range [1..1,000,000,000].
// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(N, M) {
// write your code in JavaScript (Node.js 8.9.4)
const findGCD = (m, n) => {
if (m === n || n === 0) return m;
if (m > n) return findGCD(n, m % n);
return findGCD(m, n % m);
};
const findLCD = (m, n) => (m * n) / findGCD(m, n);
return findLCD(N, M);
}
// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(N, M) {
// write your code in JavaScript (Node.js 8.9.4)
const findGCD = (m, n) => {
if (m === n || n === 0) return m;
if (m > n) return findGCD(n, m % n);
return findGCD(m, n % m);
};
const findLCD = (m, n) => (m * n) / findGCD(m, n);
return findLCD(N, M);
}
// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(N, M) {
// write your code in JavaScript (Node.js 8.9.4)
const findGCD = (m, n) => {
if (m === n || n === 0) return m;
if (m > n) return findGCD(n, m % n);
return findGCD(m, n % m);
};
const findLCD = (m, n) => (m * n) / findGCD(m, n);
return findLCD(N, M)/M;
}// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(N, M) {
// write your code in JavaScript (Node.js 8.9.4)
const findGCD = (m, n) => {
if (m === n || n === 0) return m;
if (m > n) return findGCD(n, m % n);
return findGCD(m, n % m);
};
const findLCD = (m, n) => (m * n) / findGCD(m, n);
return findLCD(N, M)/M;
}// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(N, M) {
// write your code in JavaScript (Node.js 8.9.4)
const findGCD = (m, n) => {
if (m === n || n === 0) return m;
if (m > n) return findGCD(n, m % n);
return findGCD(m, n % m);
};
const findLCD = (m, n) => (m * n) / findGCD(m, n);
return findLCD(N, M)/M;
}// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(N, M) {
// write your code in JavaScript (Node.js 8.9.4)
const findGCD = (m, n) => {
if (m === n || n === 0) return m;
if (m > n) return findGCD(n, m % n);
return findGCD(m, n % m);
};
const findLCD = (m, n) => (m * n) / findGCD(m, n);
return findLCD(N, M)/M;
}The solution obtained perfect score.