agc001B 模拟

Description

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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.

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.

Solution

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传说中的诡异的光。。

可以发现每次都会形成一个平行四边形，而三角形的边长则是所在平行四边形的短边。我们用取模加速模拟的过程就可以了

Code

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#include 
#include 
#include 
#define rep(i,st,ed) for (int i=st;i<=ed;++i)

typedef long long LL;

int main(void) {
	LL n,x; scanf("%lld%lld",&n,&x);
	x=std:: min(x,n-x);
	LL y=std:: max(x,n-x),ans=n;
	while (x) {
		if (y%x==0) {
			ans+=(y/x)*2*x;
			ans-=x;
			break;
		} else {
			ans+=(y/x)*2*x;
			LL tmp=y; y=x;
			x=tmp%x;
		}
	} printf("%lld\n", ans);
	return 0;
}