洛谷P3980：[NOI2008]志愿者招募

Posted 2020-10-24 white_hat_hacker

线性规划：

  1 #include<cstdio>
  2 #include<cstdlib>
  3 #include<algorithm>
  4 #include<cstring>
  5 #include<vector>
  6 #include<queue>
  7 #define rint register int
  8 #define ll long long
  9 #define MAXN 1000+10
 10 #define pb push_back
 11 #define INF 0x7f7f7f7f
 12 #define oo 0x7f7f7f7f7f7f7f7f
 13 #define pil pair<int,ll>
 14 #define mp make_pair
 15 using namespace std;
 16 int read(){
 17     int x=0,f=1;char ch=getchar();
 18     while(ch<‘0‘||ch>‘9‘){if(‘-‘==ch)f=-1;ch=getchar();}
 19     while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();}
 20     return x*f;
 21 }
 22 struct E{
 23     int from,to,cap,flow;
 24     ll cost;
 25     E(int x=0,int y=0,int c=0,int f=0,ll w=0LL){
 26         from=x,to=y,cap=c,flow=f,cost=w;
 27     }
 28 };
 29 struct Dinic{
 30     int n,m,s,t;
 31     vector<E> es;
 32     vector<int> G[MAXN];
 33     void init(int n,int s,int t){
 34         this->n=n;
 35         this->s=s,this->t=t;
 36         es.clear();
 37         for(int i=0;i<=n;i++)G[i].clear();
 38     }
 39     void add(int x,int y,int cap,ll cost){
 40         es.pb(E(x,y,cap,0,cost));
 41         es.pb(E(y,x,0,0,-cost));
 42         m=es.size();
 43         G[x].pb(m-2),G[y].pb(m-1);
 44     }
 45     int p[MAXN],a[MAXN];
 46     ll d[MAXN];
 47     int b[MAXN];
 48     bool SPFA(int &flow,ll &cost){
 49         p[s]=0,a[s]=INF;
 50         memset(d,0x7f,sizeof(d));
 51         d[s]=0;
 52         memset(b,0,sizeof(b));
 53         b[s]=1;
 54         queue<int> q;
 55         q.push(s);
 56         while(!q.empty()){
 57             int x=q.front();q.pop();b[x]=0;
 58             for(rint i=0;i<G[x].size();i++){
 59                 E &e=es[G[x][i]];
 60                 if(e.cap>e.flow&&d[e.to]>d[x]+e.cost){
 61                     p[e.to]=G[x][i];
 62                     a[e.to]=min(a[x],e.cap-e.flow);
 63                     d[e.to]=d[x]+e.cost;
 64                     if(!b[e.to]){
 65                         b[e.to]=1;
 66                         q.push(e.to);
 67                     }
 68                 }
 69             }
 70         }
 71         if(oo==d[t]){
 72             return 0;
 73         }
 74         flow+=a[t];
 75         cost+=a[t]*d[t];
 76         for(rint i=t;i!=s;i=es[p[i]].from){
 77             es[p[i]].flow+=a[t];
 78             es[p[i]^1].flow-=a[t];
 79         }
 80         return 1;
 81     }
 82     pil MaxfMinc(){
 83         int flow=0;
 84         ll cost=0LL;
 85         while(SPFA(flow,cost));
 86         return mp(flow,cost);
 87     }
 88 }D;
 89 int n,m,s=0,t=MAXN-1;
 90 int a[MAXN];
 91 void init(){
 92     D.init(t,s,t);
 93     n=read(),m=read();
 94     for(rint i=1;i<=n;i++){
 95         a[i]=read();
 96     }
 97     int x,y,z;
 98     for(rint i=1;i<=m;i++){
 99         x=read(),y=read(),z=read();
100         D.add(x,y+1,INF,1LL*z);
101     }
102     for(rint i=1;i<=n+1;i++){
103         x=a[i]-a[i-1];
104         if(x>0)D.add(s,i,x,0LL);
105         else D.add(i,t,-x,0LL);
106         if(i>1)D.add(i,i-1,INF,0LL);
107     }
108 }
109 int main()
110 {
111     init();
112     printf("%lld\n",D.MaxfMinc().second);
113     return 0;
114 }

转化为最小费用最大流

  1 #include<cstdio>
  2 #include<cstdlib>
  3 #include<algorithm>
  4 #include<cstring>
  5 #include<vector>
  6 #include<queue>
  7 #define rint register int
  8 #define ll long long
  9 #define MAXN 1000+10
 10 #define pb push_back
 11 #define INF 0x7f7f7f7f
 12 #define oo 0x7f7f7f7f7f7f7f7f
 13 #define pil pair<int,ll>
 14 #define mp make_pair
 15 using namespace std;
 16 int read(){
 17     int x=0,f=1;char ch=getchar();
 18     while(ch<‘0‘||ch>‘9‘){if(‘-‘==ch)f=-1;ch=getchar();}
 19     while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();}
 20     return x*f;
 21 }
 22 struct E{
 23     int from,to,cap,flow;
 24     ll cost;
 25     E(int x=0,int y=0,int c=0,int f=0,ll w=0LL){
 26         from=x,to=y,cap=c,flow=f,cost=w;
 27     }
 28 };
 29 struct Dinic{
 30     int n,m,s,t;
 31     vector<E> es;
 32     vector<int> G[MAXN];
 33     void init(int n,int s,int t){
 34         this->n=n;
 35         this->s=s,this->t=t;
 36         es.clear();
 37         for(int i=0;i<=n;i++)G[i].clear();
 38     }
 39     void add(int x,int y,int cap,ll cost){
 40         es.pb(E(x,y,cap,0,cost));
 41         es.pb(E(y,x,0,0,-cost));
 42         m=es.size();
 43         G[x].pb(m-2),G[y].pb(m-1);
 44     }
 45     int p[MAXN],a[MAXN];
 46     ll d[MAXN];
 47     int b[MAXN];
 48     bool SPFA(int &flow,ll &cost){
 49         p[s]=0,a[s]=INF;
 50         memset(d,0x7f,sizeof(d));
 51         d[s]=0;
 52         memset(b,0,sizeof(b));
 53         b[s]=1;
 54         queue<int> q;
 55         q.push(s);
 56         while(!q.empty()){
 57             int x=q.front();q.pop();b[x]=0;
 58             for(rint i=0;i<G[x].size();i++){
 59                 E &e=es[G[x][i]];
 60                 if(e.cap>e.flow&&d[e.to]>d[x]+e.cost){
 61                     p[e.to]=G[x][i];
 62                     a[e.to]=min(a[x],e.cap-e.flow);
 63                     d[e.to]=d[x]+e.cost;
 64                     if(!b[e.to]){
 65                         b[e.to]=1;
 66                         q.push(e.to);
 67                     }
 68                 }
 69             }
 70         }
 71         if(oo==d[t]){
 72             return 0;
 73         }
 74         flow+=a[t];
 75         cost+=a[t]*d[t];
 76         for(rint i=t;i!=s;i=es[p[i]].from){
 77             es[p[i]].flow+=a[t];
 78             es[p[i]^1].flow-=a[t];
 79         }
 80         return 1;
 81     }
 82     pil MaxfMinc(){
 83         int flow=0;
 84         ll cost=0LL;
 85         while(SPFA(flow,cost));
 86         return mp(flow,cost);
 87     }
 88 }D;
 89 int n,m,s=0,t=MAXN-1;
 90 int main()
 91 {
 92     D.init(t,s,t);
 93     int k;
 94     n=read(),m=read();
 95     for(rint i=1;i<=n;i++){
 96         k=read();
 97         D.add(i,i+1,INF-k,0LL);
 98     }
 99     D.add(s,1,INF,0LL);
100     D.add(n+1,t,INF,0LL);
101     int x,y;
102     for(rint i=1;i<=m;i++){
103         x=read(),y=read(),k=read();
104         D.add(x,y+1,INF,1LL*k);
105     }
106     printf("%lld\n",D.MaxfMinc().second);
107     return 0;
108 }