假设\(a\)是\(b\)的倍数,而且\(a / b\) 是质数
我们根据所含质数种类奇偶来建图,如果是奇数的话,就和\(s\)连边,如果是偶数的话就和\(t\)连边
\(s\)是源点,\(t\)是汇点
\(a\)如果能分解为奇数个质数相乘,那么\(a\)到\(b+n\)连一条容量为\(inf\),费用为\(c[a]*c[b]\)的边
\(a\)如果能分解为偶数个质数相乘,那么\(b\)到\(a+n\)连一条容量为\(inf\),费用为\(c[a]*c[b]\)的边
如果\(a\)能分解为奇数个质数相乘,那么源点到\(a\)连一条容量为\(sum[a]\),费用为\(0\)的边
如果\(a\)能分解为偶数个质数相乘,那么\(a\)到汇点连一条容量为\(sum[a]\),费用为\(0\)的边
剩下就是网络流的板子,然后需要注意的是,求的是费用不低于\(0\)的情况下的最大流
#include<cstdio> #include<cstring> #include<algorithm> #include<queue> #include<iostream> using namespace std; const int maxn=10020*30; #define int long long typedef long long ll; bool vis[maxn]; int n,m,s,t,x,y,z,f,cost[maxn],pre[maxn],last[maxn],flow[maxn],maxflow,mincost; //cost最小花费;pre每个点的前驱;last每个点的所连的前一条边;flow源点到此处的流量 //maxflow 最大流量 //mincost 最大流量的情况下的最小花费 struct Edge { int to,next,flow,cost;//flow流量 cost花费 } edge[maxn]; int head[maxn],num_edge; queue <int> q; int t1,m1,t2,m2; #define INF 2147483647 void add(int from,int to,int flow,int cost) { edge[++num_edge].next=head[from]; edge[num_edge].to=to; edge[num_edge].flow=flow; edge[num_edge].cost=cost; head[from]=num_edge; edge[++num_edge].next=head[to]; edge[num_edge].to=from; edge[num_edge].flow=0; edge[num_edge].cost=-cost; head[to]=num_edge; } bool spfa(int s,int t) { memset(cost,0x7f,sizeof(cost)); memset(flow,0x7f,sizeof(flow)); memset(vis,0,sizeof(vis)); q.push(s); vis[s]=1; cost[s]=0; pre[t]=-1; while (!q.empty()) { int now=q.front(); q.pop(); vis[now]=0; for (int i=head[now]; i!=-1; i=edge[i].next) { if (edge[i].flow>0 && cost[edge[i].to]>cost[now]+edge[i].cost) { //正边 cost[edge[i].to]=cost[now]+edge[i].cost; pre[edge[i].to]=now; last[edge[i].to]=i; flow[edge[i].to]=min(flow[now],edge[i].flow);// if (!vis[edge[i].to]) { vis[edge[i].to]=1; q.push(edge[i].to); } } } } return pre[t]!=-1; } void MCMF() { while (spfa(s,t)) { int now=t; while (now!=s) { //从源点一直回溯到汇点 edge[last[now]].flow-=flow[t];//flow和cost容易搞混 edge[last[now]^1].flow+=flow[t]; now=pre[now]; } if(mincost + flow[t]*cost[t] <= 0) maxflow+=flow[t], mincost+=flow[t]*cost[t]; else { maxflow += llabs(mincost)/llabs(cost[t]); break; } } } int top, pri[1000000], d[1000100], a[maxn], b[maxn], id[maxn]; int i, j, k; ll c[maxn]; void getprime() { int n = 1000000, i, j; top = 0; for(i=2; i<=n; i++) { if(!d[i])pri[top++] = i; for(j=0; j<top && i*pri[j]<=n; j++) { d[i*pri[j]] = 1; if(i%pri[j] == 0)break; } } } signed main() { getprime(); memset(head,-1,sizeof(head)); num_edge=-1; cin>>n; s = 0; t = n+n+2; for(i=1; i<=n; i++)scanf("%d", &a[i]); for(i=1; i<=n; i++)scanf("%d", &b[i]); for(i=1; i<=n; i++)scanf("%lld", &c[i]); for(i=1; i<=n; i++) { int num = 0, x= a[i]; for(j=0; (ll)pri[j]*pri[j]<=x; j++) { while(x%pri[j] == 0) x/=pri[j], num++; } if(x!=1)num++; if(num%2) { id[i] = i; // flow add(0, id[i], b[i], 0); } else { id[i] = i+n; add(id[i], t, b[i], 0); } } for(i=1; i<=n; i++) for(j=1; j<=n; j++) if(i!=j && a[i]>a[j] && a[i]%a[j] == 0) { int x = a[i]/a[j]; for(k=0; pri[k]*pri[k]<=x; k++) if(x % pri[k] == 0) break; if(pri[k]*pri[k] > x) { if(id[i]<id[j]) add(id[i], id[j], INF, -c[i]*c[j]); else add(id[j], id[i], INF, -c[i]*c[j]); } } MCMF(); cout<<maxflow<<endl; return 0; }