[poj1006]Biorhythms

题意：

$left{ {egin{array}{*{20}{l}}
{res = {r_1}\,mod \,{m_1}}\
{res = {r_2}\,mod \,{m_2}}\
{res = {r_3}\,mod \,{m_3}}
end{array}} ight.$

解题关键：由于模数互质，直接crt即可。

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cstdlib>
#include<cmath>
#include<iostream>
using namespace std;
typedef long long ll;
ll x,y,r[10],m[10],n=3;
ll extgcd(ll a,ll b,ll &x,ll &y){
    ll d=a;
    if(b)   d=extgcd(b,a%b,y,x),y-=a/b*x;
    else  x=1,y=0;
    return d;
}
ll inv(ll t,ll mod){ extgcd(t,mod,x,y);return (x+mod)%mod;}
ll crt(int n,ll *r,ll *m){
    ll M=1,ret=0;
    for(int i=0;i<n;i++) M*=m[i];
    for(int i=0;i<n;i++){
        ll w=M/m[i];
        ret+=w*inv(w,m[i])*r[i];
        ret%=M;
    }
    return (ret+M)%M;
}
int main(){
    ll a,Case=1;
    m[0]=23,m[1]=28,m[2]=33;
    while(cin>>r[0]>>r[1]>>r[2]>>a){
        if(a==-1&&r[0]==-1&&r[1]==-1&&r[2]==-1) break;
        printf("Case %d: ",Case++);
        ll tmp=23*28*33;
        ll ans=((crt(3,r,m)-a)%tmp+tmp)%tmp;
        if(ans==0) ans+=tmp;
        printf("the next triple peak occurs in %lld days.
",ans);
    }
}