中国剩余定理

中国剩余定理

对同余方程组：

x=a1(mod m1)

x=a2(mod m2)

.

x=ak(mod mk)

(m1,m2,...,mn互质)

则解x=M1*inv(M1,m1)+...+Mn*inv(Mn,mn) (mod m)

(其中m=m1*m2*...*mn=mi*Mi,   Mi=m/mi)

#include<iostream>

#include<cstdio>

#include<cstring>

#include<cstdlib>

#include<algorithm>

#include<vector>

#include<stack>

#include<queue>

#include<set>

#include<map>

#include<string>

#include<math.h>

#include<cctype>

#define ll long long

#define REP(i,a,b) for(int (i)=(a);(i)<=(b);(i)++)

#define REPP(i,a,b,t) for(int (i)=(a);(i)<=(b);(i)+=(t))

#define PII pair<int,int>

#define fst first

#define snd second

#define MP make_pair

#define PB push_back

#define RI(x) scanf("%d",&(x))

#define RII(x,y) scanf("%d%d",&(x),&(y))

#define RIII(x,y,z) scanf("%d%d%d",&(x),&(y),&(z))

#define DRI(x) int (x);scanf("%d",&(x))

#define DRII(x,y) int (x),(y);scanf("%d%d",&(x),&(y))

#define DRIII(x,y,z) int (x),(y),(z);scanf("%d%d",&(x),&(y),&(z))

#define RS(x) scanf("%s",s)

#define RSS(x,y) scanf("%s%s",x,y)

#define DRS(x) char x[maxn];scanf("%s",x)

#define DRSS(x,y) char x[maxn],y[maxn];scanf("%s%s",x,y)

#define MS0(a) memset((a),0,sizeof((a)))

#define MS1(a) memset((a),-1,sizeof((a)))

#define MS(a,b) memset((a),(b),sizeof((a)))

#define ALL(v) v.begin(),v.end()

#define SZ(v) (v).size()



using namespace std;



const int maxn=1000100;

const int INF=(1<<29);

const double EPS=0.0000000001;

const double Pi=acos(-1.0);



int n;

ll a[maxn],m[maxn];

ll x;

ll M,Mt[maxn];



ll qpow(ll n,ll k,ll p)

{

    ll res=1;

    while(k){

        if(k&1) res=(res%p)*(n%p)%p;

        n=(n%p)*(n%p)%p;

        k>>=1;

    }

    return res;

}



ll inv(ll a,ll m)

{

    return qpow(a,m-2,m);

}



int main()

{

    DRI(T);

    while(T--){

        RI(n);

        REP(i,0,n-1) cin>>a[i]>>m[i];

        M=1;

        REP(i,0,n-1) M*=m[i];

        REP(i,0,n-1) Mt[i]=M/m[i];

        x=0;

        REP(i,0,n-1) x=((x%M)+(Mt[i]*inv(Mt[i],m[i])*a[i]%M))%M;

        cout<<x<<endl;

    }

    return 0;

}

View Code