欧几里德专场

欧几里德 扩展欧几里德  博客视频参考：

http://www.cnblogs.com/void/archive/2011/04/18/2020357.html

https://www.nowcoder.com/live/153/4/1

poj  1061 青蛙约会 

点击就送一刀99

#include<iostream>
using namespace std;
#define LL long long
LL exgcd(LL a,LL b,LL &x,LL &y){
    if(b==0){
       x=1;
       y=0;
       return a;
    }
    LL r=exgcd(b,a%b,x,y);
    int temp=x;
    x=y;
    y=temp-a/b*y;
    return r;
}
LL xxx(LL a,LL b,LL c){
    LL x,y;
    LL gcd=exgcd(a,b,x,y);
    if(c%gcd!=0) return -1;
    x*=c/gcd;
    b/=gcd;
    if(b<0) b=-b;
    LL ans=x%b;
    if(ans<=0){
       ans+=b;
    }
    return ans;
}
int main(){
   int x,y,m,n,l;
   cin>>x>>y>>m>>n>>l;
   if(xxx(m-n,l,y-x)==-1) cout<<"Impossible"<<endl;   //要注意 n-m 和 y-x 要同步 
   else cout<<xxx(n-m,l,x-y)<<endl;

   return 0;
}

hdu 1756 

点击   点击打开链接

/*
设A=9973*y+n，因为A%B=0，所以(9973*y+n)=B*x，其中x=A/B

移项，有B*x+9973*(-y)=n。

联想到扩展GCD的式子：B*X+9973*Y=1，两边都乘以n，B*(nX)+9973*(nY)=n。

这样x=nX，y=-nY，只要求出X和Y就行了，套扩展GCD模板即可
*/

#include<iostream>
using namespace std;
#define LL long long
LL exgcd(LL a,LL b,LL &x,LL &y){
    if(b==0){
       x=1;
       y=0;
       return a;
    }
    LL r=exgcd(b,a%b,x,y);
    int temp=x;
    x=y;
    y=temp-a/b*y;
    return r;
}
LL xxx(LL a,LL b,LL c){
    LL x,y;
    LL gcd=exgcd(a,b,x,y);
    if(c%gcd!=0) return -1;
    x*=c/gcd;
    b/=gcd;
    if(b<0) b=-b;
    LL ans=x%b;
    if(ans<=0){
       ans+=b;
    }
    return ans;
}

int main(){
   int t;
   cin>>t;
   while(t--){
     LL n,b;
     cin>>n>>b;
     LL ans=xxx(b,9973,n);
     cout<<ans<<endl;
   }
   return 0;
}

hdu 2669 

点击打开链接

#include<iostream>
using namespace std;
#define LL long long
LL exgcd(LL a,LL b,LL &x,LL &y){
    if(b==0){
       x=1;
       y=0;
       return a;
    }
    LL r=exgcd(b,a%b,x,y);
    int temp=x;
    x=y;
    y=temp-a/b*y;
    return r;
}
LL xxx(LL a,LL b,LL c){
    LL x,y;
    LL gcd=exgcd(a,b,x,y);
    if(c%gcd!=0) return -1;
    x*=c/gcd;
    b/=gcd;
    if(b<0) b=-b;
    LL ans=x%b;
    if(ans<=0){
       ans+=b;
    }
    return ans;
}
int main(){
   LL a,b;
   while(cin>>a>>b){
       LL ans=xxx(a,b,1);
       if(ans==-1) cout<<"sorry"<<endl;
       else cout<<ans<<" "<<(1-ans*a)/b<<endl;
   }
   return 0;
}

zoj  3609

点击打开链接

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <vector>
#include <string>
#include <queue>
#include <stack>
#include <algorithm>

#define INF 0x7fffffff
#define EPS 1e-12
#define MOD 1000000007
#define PI 3.141592653579798
#define N 100000

using namespace std;

typedef long long LL;
typedef double DB;

LL e_gcd(LL a,LL b,LL &x,LL &y)
{
    if(b==0)
    {
        x=1;
        y=0;
        return a;
    }
    LL ans=e_gcd(b,a%b,x,y);
    LL temp=x;
    x=y;
    y=temp-a/b*y;
    return ans;
}

LL cal(LL a,LL b,LL c)
{
    LL x,y;
    LL gcd=e_gcd(a,b,x,y);
    if(c%gcd!=0) return -1;
    x*=c/gcd;
    b*=c/gcd;
    if(b<0) b=-b;
    LL ans=x%b;
    if(ans<=0) ans=ans+b;
    return ans;
}

int main()
{
    LL a,b,t;
    scanf("%lld",&t);
    while(t--)
    {
        scanf("%lld%lld",&a,&b);
        LL ans=cal(a,b,1);
        if(ans==-1) printf("Not Exist\n");
        else printf("%lld\n",ans);
    }
    return 0;
}

牛客 

点击打开链接

#include<bits/stdc++.h>
using namespace std;
#define maxn 100000+100
#define LL long long
LL l[maxn];
LL r[maxn];
LL exgcd(LL a,LL b,LL &x,LL &y){
   if(b==0){
      x=1;
      y=0;
      return a;
   }
   LL ans=exgcd(b,a%b,x,y);
   LL t=x;
   x=y;
   y=t-a/b*y;

   return ans;
}
LL xxx(int n){
   LL aa=l[0],bb=r[0];
   for(int j=1;j<n;j++){
      LL x,y;
      LL k=r[j]-bb;
      LL ans=exgcd(aa,l[j],x,y);
      if(k%ans){
         return -1;
      }
      x=k/ans*x;
      LL t=l[j]/ans;
      x=(x%t+t)%t;
     // cout<<x<<" "<<bb<<endl;
      bb=bb+x*aa;
      aa=aa*l[j]/ans;
      //cout<<aa<<" "<<bb<<endl;
   }
   return bb;
}
int main(){
   int n;
   cin>>n;
   for(int j=0;j<n;j++){
     scanf("%lld%lld",&l[j],&r[j]);
   }
   cout<<xxx(n)<<endl;
}