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:
class Solution { public int solution(int N, int 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 also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int N, int M) {
// write your code in Java SE 8
}
private int getGcd(int num1, int num2) {
if (num1 % num2 == 0) {
return num2;
} else {
return getGcd(num2, nu)
}
}
}
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int N, int M) {
return N / getGcd(M, N);
}
private int getGcd(int num1, int num2) {
if (num1 % num2 == 0) {
return num2;
} else {
return getGcd(num2, num1 % num2);
}
}
}
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int N, int M) {
return N / getGcd(M, N);
}
// Euclidenan algorithm.
private int getGcd(int num1, int num2) {
if (num1 % num2 == 0) {
return num2;
} else {
return getGcd(num2, num1 % num2);
}
}
}
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int N, int M) {
return N / getGcd(M, N);
}
// Euclidean algorithm.
private int getGcd(int num1, int num2) {
if (num1 % num2 == 0) {
return num2;
} else {
return getGcd(num2, num1 % num2);
}
}
}
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int N, int M) {
return N / getGcd(M, N);
}
// Euclidean algorithm.
private int getGcd(int num1, int num2) {
if (num1 % num2 == 0) {
return num2;
} else {
return getGcd(num2, num1 % num2);
}
}
}
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int N, int M) {
return N / getGcd(M, N);
}
// Euclidean algorithm.
private int getGcd(int num1, int num2) {
if (num1 % num2 == 0) {
return num2;
} else {
return getGcd(num2, num1 % num2);
}
}
}
The solution obtained perfect score.