B - Mysterious Light
Time limit : 2sec / Stack limit : 256MB / Memory limit : 256MB
Score : 500 points
Problem Statement
Snuke is conducting an optical experiment using mirrors and his new invention, the rifle of Mysterious Light.
Three mirrors of length N are set so that they form an equilateral triangle. Let the vertices of the triangle be a,b and c.
Inside the triangle, the rifle is placed at the point p on segment ab such that ap=X. (The size of the rifle is negligible.) Now, the rifle is about to fire a ray of Mysterious Light in the direction of bc.
The ray of Mysterious Light will travel in a straight line, and will be reflected by mirrors, in the same ways as "ordinary" light. There is one major difference, though: it will be also reflected by its own trajectory as if it is a mirror! When the ray comes back to the rifle, the ray will be absorbed.
The following image shows the ray's trajectory where N=5 and X=2.
![btriangle.png](https://agc001.contest.atcoder.jp/img/agc/001/Gg9pvPKw/btriangle.png)
It can be shown that the ray eventually comes back to the rifle and is absorbed, regardless of the values of N and X. Find the total length of the ray's trajectory.
Constraints
- 2≦N≦1012
- 1≦X≦N−1
- N and X are integers.
Partial Points
- 300 points will be awarded for passing the test set satisfying N≦1000.
- Another 200 points will be awarded for passing the test set without additional constraints.
Input
The input is given from Standard Input in the following format:
N X
Output
Print the total length of the ray's trajectory.
Sample Input 1
5 2
Sample Output 1
12
Refer to the image in the Problem Statement section. The total length of the trajectory is 2+3+2+2+1+1+1=12.
欧几里得~题解后补,先上代码
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include <bits/stdc++.h> using namespace std; typedef long long ll; ll gcd(ll n, ll m) { if(n % m== 0) { return m; } return gcd(m, n%m); } int main() { ios :: sync_with_stdio(false); ll N, X, ans; cin >> N >> X; ans = 3*(N - gcd(N, X)); cout << ans << endl; }