BZOJ3129: [Sdoi2013]方程

拓展Lucas+容斥原理

  1 #include<cstdio>
  2 #include<cstdlib>
  3 #include<algorithm>
  4 #include<cstring>
  5 #include<vector>
  6 #include<cmath>
  7 #include<queue>
  8 #define MAXN 10000+10
  9 #define INF 0x7f7f7f7f
 10 #define LINF 0x7f7f7f7f7f7f7f7f
 11 #define ll long long
 12 #define pb push_back
 13 #define ft first
 14 #define sc second
 15 #define mp make_pair
 16 #define pil pair<int,ll>
 17 #define pll pair<ll,ll>
 18 using namespace std;
 19 struct Lucas{
 20     void extgcd(ll a,ll b,ll &x,ll &y){
 21         if(!b){x=1,y=0;}
 22         else{
 23             ll xx,yy;
 24             extgcd(b,a%b,xx,yy);
 25             x=yy;
 26             y=xx-a/b*yy;
 27         }
 28     }
 29     ll Inv(ll a,ll b){
 30         ll x,y;
 31         extgcd(a,b,x,y);
 32         x=(x%b+b)%b;
 33         if(!x)x+=b;
 34         return x;
 35     }
 36     ll Pow(ll a,ll b,ll p){
 37         ll ret=1LL;
 38         while(b){    
 39             if(b&1){(ret*=a)%=p;}
 40             (a*=a)%=p;
 41             b>>=1;
 42         }
 43         return ret;
 44     }
 45     ll fac(ll n,ll pi,ll pk){
 46         if(!n)return 1LL;
 47         ll ret=1LL;
 48         for(ll i=2;i<pk;i++){
 49             if(i%pi)(ret*=i)%=pk;    
 50         }
 51         ret=Pow(ret,n/pk,pk);
 52         for(ll i=2;i<=(n%pk);i++){
 53             if(i%pi)(ret*=i)%=pk;    
 54         }
 55         return ret*fac(n/pi,pi,pk)%pk;
 56     }
 57     ll C(ll n,ll m,ll pi,ll pk){
 58         ll a=fac(n,pi,pk),b=fac(m,pi,pk),c=fac(n-m,pi,pk);
 59         ll t=0LL;
 60         for(ll i=n/pi;i;i/=pi)t+=i;
 61         for(ll i=m/pi;i;i/=pi)t-=i;
 62         for(ll i=(n-m)/pi;i;i/=pi)t-=i;
 63         ll ret=a*Inv(b,pk)*Inv(c,pk)%pk;
 64         (ret*=Pow(pi,t,pk))%=pk;
 65         return ret;
 66     }
 67     ll n,m,p;
 68     vector<pll> pn;
 69     ll init(ll pp){
 70         p=pp;
 71         ll x=sqrt(pp*1.0);
 72         for(ll i=2;i<=x;i++){
 73             if(pp%i==0){
 74                 ll pk=1LL;
 75                 while(pp%i==0){
 76                     pp/=i;
 77                     pk*=i;
 78                 }
 79                 pn.pb(mp(i,pk));
 80             }
 81         }
 82         if(pp^1){
 83             pn.pb(mp(pp,pp));
 84         }
 85     }
 86     ll solve(ll n,ll m){
 87         ll ans=0LL,pi,pk;
 88         for(int i=0;i<pn.size();i++){
 89             pi=pn[i].ft,pk=pn[i].sc;
 90             ll t=C(n,m,pi,pk);
 91             (t*=(p/pk))%=p;
 92             (t*=Inv(p/pk,pk))%=p;
 93             (ans+=t)%=p;
 94         }
 95         return ans;
 96     }
 97 }L;
 98 int T,n,n1,n2,m;
 99 int a[10];
100 ll ans,p;
101 ll calc(ll n,ll m){
102     return L.solve(m+n-1,min(m,n-1));
103 }
104 void rc(int k,int m,int f){
105     if(m<0)return;
106     ans+=f*calc(n,m);
107     ans=(ans%p+p)%p;
108     for(int i=k+1;i<=n1;i++){
109         rc(i,m-a[i],-f);
110     }
111 }
112 void solve(){
113     scanf("%d%d%d%d",&n,&n1,&n2,&m);
114     m-=n;
115     for(int i=1;i<=n1;i++){
116         scanf("%d",&a[i]);
117     }
118     int t;
119     for(int i=1;i<=n2;i++){
120         scanf("%d",&t);
121         m-=(t-1);
122     }
123     if(m<0){
124         printf("0\n");
125         return;
126     }
127     ans=0LL;
128     rc(0,m,1);
129     printf("%lld\n",ans);
130 }
131 int main()
132 {
133     //freopen("data.in","r",stdin);
134     scanf("%d%lld",&T,&p);
135     L.init(p);
136     while(T--){
137         solve();
138     }
139     return 0;
140 }

 

posted @ 2018-01-26 13:15  white_hat_hacker  阅读(154)  评论(0)  编辑  收藏  举报