gcd与exgcd

最新推荐文章于 2022-09-20 23:30:39 发布

原创最新推荐文章于 2022-09-20 23:30:39 发布 · 151 阅读

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#exgcd

gcd与exgcd

#include<cmath>
#include<bits/stdc++.h>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<string>
using namespace std;
#define LL long long
LL read()
{
	LL x=0,w=1;
	char ch=0;
	while(ch<'0'||ch>'9')
	{
		if(ch=='-')
			w=-1;
		ch=getchar();
	}
	while(ch>='0'&&ch<='9')
	{
		x=x*10+ch-'0';
		ch=getchar();
	}
	return w*x;
}
int a,b,X,Y;
int gcd(int x,int y)
{
	while(y!=0)
	{
		int z=x;
		x=y;
		y=z%y;
	}
	return x;
}
int exgcd(int a,int b,int &x,int &y)//用来解a*x+b*y=gcd（a，b）的情况 
{
	if(b==0)
	{
		x=1;
		y=0;
		return a;
	}
	int r=exgcd(b,a%b,x,y);
	int t=x;
	x=y;
	y=t-a/b*y;
	return r;
}
int lcm(int a,int b)
{
	int ans=a/gcd(a,b);
	return ans*b;
}
int main()
{
	while(cin>>a>>b)
	{
		cout<<"GCD:"<<gcd(a,b)<<endl;
		int tt=exgcd(a,b,X,Y);
		cout<<"exGCD:"<<a<<"*"<<X<<'+'<<b<<'*'<<Y<<'='<<tt<<endl;
	}
	return 0;
 }