CodeForces 498C Array and Operations（最大流）

  1 #include<cstdio>
  2 #include<cstring>
  3 #include<queue>
  4 #include<algorithm>
  5 using namespace std;
  6 #define INF (1<<30)
  7 #define MAXN 111
  8 #define MAXM 111*111*2
  9 
 10 struct Edge{
 11     int v,cap,flow,next;
 12 }edge[MAXM];
 13 int vs,vt,NE,NV;
 14 int head[MAXN];
 15 
 16 void addEdge(int u,int v,int cap){
 17     edge[NE].v=v; edge[NE].cap=cap; edge[NE].flow=0;
 18     edge[NE].next=head[u]; head[u]=NE++;
 19     edge[NE].v=u; edge[NE].cap=0; edge[NE].flow=0;
 20     edge[NE].next=head[v]; head[v]=NE++;
 21 }
 22 
 23 int level[MAXN];
 24 int gap[MAXN];
 25 void bfs(){
 26     memset(level,-1,sizeof(level));
 27     memset(gap,0,sizeof(gap));
 28     level[vt]=0;
 29     gap[level[vt]]++;
 30     queue<int> que;
 31     que.push(vt);
 32     while(!que.empty()){
 33         int u=que.front(); que.pop();
 34         for(int i=head[u]; i!=-1; i=edge[i].next){
 35             int v=edge[i].v;
 36             if(level[v]!=-1) continue;
 37             level[v]=level[u]+1;
 38             gap[level[v]]++;
 39             que.push(v);
 40         }
 41     }
 42 }
 43 
 44 int pre[MAXN];
 45 int cur[MAXN];
 46 int ISAP(){
 47     bfs();
 48     memset(pre,-1,sizeof(pre));
 49     memcpy(cur,head,sizeof(head));
 50     int u=pre[vs]=vs,flow=0,aug=INF;
 51     gap[0]=NV;
 52     while(level[vs]<NV){
 53         bool flag=false;
 54         for(int &i=cur[u]; i!=-1; i=edge[i].next){
 55             int v=edge[i].v;
 56             if(edge[i].cap!=edge[i].flow && level[u]==level[v]+1){
 57                 flag=true;
 58                 pre[v]=u;
 59                 u=v;
 60                 //aug=(aug==-1?edge[i].cap:min(aug,edge[i].cap));
 61                 aug=min(aug,edge[i].cap-edge[i].flow);
 62                 if(v==vt){
 63                     flow+=aug;
 64                     for(u=pre[v]; v!=vs; v=u,u=pre[u]){
 65                         edge[cur[u]].flow+=aug;
 66                         edge[cur[u]^1].flow-=aug;
 67                     }
 68                     //aug=-1;
 69                     aug=INF;
 70                 }
 71                 break;
 72             }
 73         }
 74         if(flag) continue;
 75         int minlevel=NV;
 76         for(int i=head[u]; i!=-1; i=edge[i].next){
 77             int v=edge[i].v;
 78             if(edge[i].cap!=edge[i].flow && level[v]<minlevel){
 79                 minlevel=level[v];
 80                 cur[u]=i;
 81             }
 82         }
 83         if(--gap[level[u]]==0) break;
 84         level[u]=minlevel+1;
 85         gap[level[u]]++;
 86         u=pre[u];
 87     }
 88     return flow;
 89 }
 90 
 91 int n,m,a[111],x[111],y[111];
 92 bool isPrime(int x){
 93     if(x<2) return 0;
 94     for(int i=2; i*i<=x; ++i) if(x%i==0) return 0;
 95     return 1;
 96 }
 97 int main(){
 98     scanf("%d%d",&n,&m);
 99     for(int i=1; i<=n; ++i) scanf("%d",a+i);
100     for(int i=1; i<=m; ++i){
101         scanf("%d%d",x+i,y+i);
102         if(y[i]&1) swap(x[i],y[i]);
103     }
104     int res=0;
105     vs=0; vt=n+1; NV=vt+1;
106     for(int fact=2; fact*fact<=1000000000; ++fact){
107         if(!isPrime(fact)) continue;
108         NE=0;
109         memset(head,-1,sizeof(head));
110         for(int i=1; i<=m; ++i) addEdge(x[i],y[i],INF);
111         for(int i=1; i<=n; ++i){
112             int cnt=0;
113             while(a[i]%fact==0){
114                 a[i]/=fact;
115                 ++cnt;
116             }
117             if(i&1) addEdge(vs,i,cnt);
118             else addEdge(i,vt,cnt);
119         }
120         res+=ISAP();
121     }
122     for(int i=1; i<=n; ++i){
123         int fact=a[i];
124         if(!isPrime(fact)) continue;
125         NE=0;
126         memset(head,-1,sizeof(head));
127         for(int j=1; j<=m; ++j) addEdge(x[j],y[j],INF);
128         for(int j=1; j<=n; ++j){
129             if(a[j]!=fact) continue;
130             a[j]=1;
131             if(j&1) addEdge(vs,j,1);
132             else addEdge(j,vt,1);
133         }
134         res+=ISAP();
135     }
136     printf("%d",res);
137     return 0;
138 }