洛谷P3980：[NOI2008]志愿者招募

线性规划：

 #include<cstdio>
 #include<cstdlib>
 #include<algorithm>
 #include<cstring>
 #include<vector>
 #include<queue>
 #define rint register int
 #define ll long long
 #define MAXN 1000+10
 #define pb push_back
 #define INF 0x7f7f7f7f
 #define oo 0x7f7f7f7f7f7f7f7f
 #define pil pair<int,ll>
 #define mp make_pair
 using namespace std;
 int read(){
     int x=,f=;char ch=getchar();
     while(ch<''||ch>''){if('-'==ch)f=-;ch=getchar();}
     while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
     return x*f;
 }
 struct E{
     int from,to,cap,flow;
     ll cost;
     E(int x=,int y=,int c=,int f=,ll w=0LL){
         from=x,to=y,cap=c,flow=f,cost=w;
     }
 };
 struct Dinic{
     int n,m,s,t;
     vector<E> es;
     vector<int> G[MAXN];
     void init(int n,int s,int t){
         this->n=n;
         this->s=s,this->t=t;
         es.clear();
         for(int i=;i<=n;i++)G[i].clear();
     }
     void add(int x,int y,int cap,ll cost){
         es.pb(E(x,y,cap,,cost));
         es.pb(E(y,x,,,-cost));
         m=es.size();
         G[x].pb(m-),G[y].pb(m-);
     }
     int p[MAXN],a[MAXN];
     ll d[MAXN];
     int b[MAXN];
     bool SPFA(int &flow,ll &cost){
         p[s]=,a[s]=INF;
         memset(d,0x7f,sizeof(d));
         d[s]=;
         memset(b,,sizeof(b));
         b[s]=;
         queue<int> q;
         q.push(s);
         while(!q.empty()){
             int x=q.front();q.pop();b[x]=;
             for(rint i=;i<G[x].size();i++){
                 E &e=es[G[x][i]];
                 if(e.cap>e.flow&&d[e.to]>d[x]+e.cost){
                     p[e.to]=G[x][i];
                     a[e.to]=min(a[x],e.cap-e.flow);
                     d[e.to]=d[x]+e.cost;
                     if(!b[e.to]){
                         b[e.to]=;
                         q.push(e.to);
                     }
                 }
             }
         }
         if(oo==d[t]){
             return ;
         }
         flow+=a[t];
         cost+=a[t]*d[t];
         for(rint i=t;i!=s;i=es[p[i]].from){
             es[p[i]].flow+=a[t];
             es[p[i]^].flow-=a[t];
         }
         return ;
     }
     pil MaxfMinc(){
         int flow=;
         ll cost=0LL;
         while(SPFA(flow,cost));
         return mp(flow,cost);
     }
 }D;
 int n,m,s=,t=MAXN-;
 int a[MAXN];
 void init(){
     D.init(t,s,t);
     n=read(),m=read();
     for(rint i=;i<=n;i++){
         a[i]=read();
     }
     int x,y,z;
     for(rint i=;i<=m;i++){
         x=read(),y=read(),z=read();
         D.add(x,y+,INF,1LL*z);
     }
     for(rint i=;i<=n+;i++){
         x=a[i]-a[i-];
         if(x>)D.add(s,i,x,0LL);
         else D.add(i,t,-x,0LL);
         if(i>)D.add(i,i-,INF,0LL);
     }
 }
 int main()
 {
     init();
     printf("%lld\n",D.MaxfMinc().second);
     return ;
 }

转化为最小费用最大流

 #include<cstdio>
 #include<cstdlib>
 #include<algorithm>
 #include<cstring>
 #include<vector>
 #include<queue>
 #define rint register int
 #define ll long long
 #define MAXN 1000+10
 #define pb push_back
 #define INF 0x7f7f7f7f
 #define oo 0x7f7f7f7f7f7f7f7f
 #define pil pair<int,ll>
 #define mp make_pair
 using namespace std;
 int read(){
     int x=,f=;char ch=getchar();
     while(ch<''||ch>''){if('-'==ch)f=-;ch=getchar();}
     while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
     return x*f;
 }
 struct E{
     int from,to,cap,flow;
     ll cost;
     E(int x=,int y=,int c=,int f=,ll w=0LL){
         from=x,to=y,cap=c,flow=f,cost=w;
     }
 };
 struct Dinic{
     int n,m,s,t;
     vector<E> es;
     vector<int> G[MAXN];
     void init(int n,int s,int t){
         this->n=n;
         this->s=s,this->t=t;
         es.clear();
         for(int i=;i<=n;i++)G[i].clear();
     }
     void add(int x,int y,int cap,ll cost){
         es.pb(E(x,y,cap,,cost));
         es.pb(E(y,x,,,-cost));
         m=es.size();
         G[x].pb(m-),G[y].pb(m-);
     }
     int p[MAXN],a[MAXN];
     ll d[MAXN];
     int b[MAXN];
     bool SPFA(int &flow,ll &cost){
         p[s]=,a[s]=INF;
         memset(d,0x7f,sizeof(d));
         d[s]=;
         memset(b,,sizeof(b));
         b[s]=;
         queue<int> q;
         q.push(s);
         while(!q.empty()){
             int x=q.front();q.pop();b[x]=;
             for(rint i=;i<G[x].size();i++){
                 E &e=es[G[x][i]];
                 if(e.cap>e.flow&&d[e.to]>d[x]+e.cost){
                     p[e.to]=G[x][i];
                     a[e.to]=min(a[x],e.cap-e.flow);
                     d[e.to]=d[x]+e.cost;
                     if(!b[e.to]){
                         b[e.to]=;
                         q.push(e.to);
                     }
                 }
             }
         }
         if(oo==d[t]){
             return ;
         }
         flow+=a[t];
         cost+=a[t]*d[t];
         for(rint i=t;i!=s;i=es[p[i]].from){
             es[p[i]].flow+=a[t];
             es[p[i]^].flow-=a[t];
         }
         return ;
     }
     pil MaxfMinc(){
         int flow=;
         ll cost=0LL;
         while(SPFA(flow,cost));
         return mp(flow,cost);
     }
 }D;
 int n,m,s=,t=MAXN-;
 int main()
 {
     D.init(t,s,t);
     int k;
     n=read(),m=read();
     for(rint i=;i<=n;i++){
         k=read();
         D.add(i,i+,INF-k,0LL);
     }
     D.add(s,,INF,0LL);
     D.add(n+,t,INF,0LL);
     int x,y;
     for(rint i=;i<=m;i++){
         x=read(),y=read(),k=read();
         D.add(x,y+,INF,1LL*k);
     }
     printf("%lld\n",D.MaxfMinc().second);
     return ;
 }