# Bzoj 1449 [JSOI2009] team benefits (cost split, minimum cost flow)

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Author: User

1449: [JSOI2009] Team earnings time limit:5 Sec Memory limit:64 MB
submit:547 solved:302
[Submit] [Status] [Discuss] Descriptioninputoutput An integer that represents the minimum value of the sum of all the teams in the league. Sample Input3 3
1 0 2 1
1 1 10 1
0 1 3 3
0 S
2 3
3 1
Sample Output43
HINT

Source

Ideas

Cost split, minimum cost maximum flow.

By S to each match the Edge (1,0), which is connected by each match to both teams (1,0).

Consider winning a win W Field defeated L field, then increase the cost = ci*w^2+di*l^2-ci* (w+1) ^2-di* (l+1) ^2=2*ci*w+ci+di+2*di*l revenue. When W increases, the cost is monotonically increasing, so you can connect one (1,cost) side at a time and then w++,l--again until the game is all won, assuming that the remaining races are all lost at the beginning.

Code

`1#include <cstdio>2#include <cstring>3#include <queue>4#include <vector>5 #definefor (A,B,C) for (int a= (b);a< (c); a++)6 using namespacestd;7 8typedefLong LongLL;9 Const intMAXN =8000+Ten;Ten Const intINF =1e9; One  A structedge{intU,v,cap,flow,cost; - }; - structzkw { the     intn,m,s,t; -     intVIS[MAXN],D[MAXN]; -vector<int>G[MAXN]; -Vector<edge>es; +      -     voidInitintN) { +          This->n=N; A es.clear (); at          for(intI=0; i<n;i++) g[i].clear (); -     } -     voidAddedge (intUintVintCapintCost ) { -Es.push_back (Edge) {u,v,cap,0, cost}); -Es.push_back (Edge) {v,u,0,0,-Cost }); -m=es.size (); inG[u].push_back (M-2); -G[v].push_back (M-1); to     } +     BOOLSPFA () { -memset (Vis,0,sizeof(Vis)); the          for(intI=0; i<n;i++) d[i]=INF; *queue<int>Q; \$d[t]=0, vis[t]=1, Q.push (t);Panax Notoginseng          while(!Q.empty ()) { -             intU=q.front (); Q.pop (), vis[u]=0; the              for(intI=0; I<g[u].size (); i++) { +edge& e=Es[g[u][i]]; A                 intv=e.v; the                 if(es[g[u][i]^1].cap && d[v]>d[u]-e.cost) { +d[v]=d[u]-E.cost; -                     if(!Vis[v]) { \$vis[v]=1; \$ Q.push (v); -                     } -                 } the             } -         }Wuyi         returnd[s]!=INF; the     } -     intDfsintUinta,ll&Cost ) { Wuvis[u]=1;if(u==t)returnA; -         intUsed=0, W; About          for(intI=0; I<g[u].size (); i++) { \$edge& e=Es[g[u][i]]; -             intv=e.v; -             if(D[u]-e.cost==d[v] &&!vis[v] &&e.cap) { -W=dfs (V,min (A-used,e.cap), cost); Acost+=w*E.cost; +E.cap-=w, es[g[u][i]^1].cap+=W; theUsed+=w;if(used==a)returnA; -             } \$         } the         returnused; the     } the     intMincost (intSintt,ll&Cost ) { the          This->s=s, This->t=T; -         intflow=0; cost=0; in          while(SPFA ()) { thevis[t]=1; the              while(Vis[t]) { Aboutmemset (Vis,0,sizeof(Vis)); theflow+=DFS (s,inf,cost); the             } the         } +         returnflow; -     } the } MC;Bayi  the  the intn,m; - intC[MAXN],D[MAXN],WIN[MAXN],LOSE[MAXN],inch[MAXN]; -  the intMain () { thescanf"%d%d",&n,&m); theMc.init (n+m+2); the     ints=n+m,t=s+1; -for (I,0, N) thescanf"%d%d%d%d",&win[i],&lose[i],&c[i],&d[i]); the     intu,v; thefor (I,0, M) {94scanf"%d%d",&u,&v); theU--, v--;  the         inch[U]++,inch[v]++; theMc. Addedge (S,i,1,0);98Mc. Addedge (I,m+u,1,0); AboutMc. Addedge (I,m+v,1,0); -     }101LL ans=0;102for (I,0, N) {103lose[i]+=inch[i];104ans+=c[i]*win[i]*win[i]+d[i]*lose[i]*Lose[i]; the     }106for (I,0, N) {107For (J,0,inch[i]) {108Mc. Addedge (M+i,t,1,2*c[i]*win[i]+c[i]+d[i]-2*d[i]*lose[i]);109Lose[i]--, win[i]++; the         }111     } the LL cost;113 MC. Mincost (s,t,cost); theprintf"%lld", cost+ans); the     return 0; the}`

Bzoj 1449 [JSOI2009] team benefits (cost split, minimum cost flow)

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