SGU 176 flow Construction (with Yuanhui upper and lower bounds minimum flow)

"Topic link"

http://acm.hust.edu.cn/vjudge/problem/viewProblem.action?id=11025

Model

There is a minimum flow of Yuanhui points in the upper and lower bounds. The minimum flow that satisfies both the upper and lower bounds and the flow balance.

Ideas

Construct the network according to the feasible flow. Not even the edge of the t->s. Add the maximum flow of the Yuanhui point, and then even t->s an INF edge and run the maximum stream over the residual network. The first time to seek the maximum flow so that can walk the edge is full, the second time to seek additional Yuanhui point maximum flow t->s flow will be as small as possible.

It is also possible to divide the lower bound mid, then the Edge (T,s,mid), if there is a viable flow, the mid is feasible.

Code

1#include <Set>2#include <cmath>3#include <queue>4#include <vector>5#include <cstdio>6#include <cstring>7#include <iostream>8#include <algorithm>9 #defineTrav (u,i) for (int i=front[u];i;i=e[i].nxt)Ten #definefor (A,B,C) for (int a= (b); a<= (c); a++) One using namespacestd; A  -typedefLong Longll; - Const intN = 5e4+Ten; the Const intINF =1e9; -  - ll Read () { -     CharC=GetChar (); +ll f=1, x=0; -      while(!IsDigit (c)) { +         if(c=='-') f=-1; C=GetChar (); A     } at      while(IsDigit (c)) -x=x*Ten+c-'0', c=GetChar (); -     returnx*F; - } -  - structEdge { in     intU,v,cap,flow; -Edge (intu=0,intv=0,intcap=0,intflow=0) to : U (u), V (v), cap (CAP), flow (flow) {} + }; - structDinic { the     intn,m,s,t; *     intD[n],cur[n],vis[n]; $vector<int>G[n];Panax NotoginsengVector<edge>es; -queue<int>Q; the     voidInitintN) { +          This->n=N; A es.clear (); thefor (I,0, N) g[i].clear (); +     } -     voidClear () { $for (I,0,(int) Es.size ()-1) es[i].flow=0; $     } -     voidAddedge (intUintVintW) { -Es.push_back (Edge (U,v,w,0)); theEs.push_back (Edge (V,u,0,0)); -m=es.size ();WuyiG[u].push_back (M-2); theG[v].push_back (M-1); -     } Wu     intBFs () { -memset (Vis,0,sizeof(Vis)); AboutQ.push (s); d[s]=0; vis[s]=1; $          while(!Q.empty ()) { -             intu=Q.front (); Q.pop (); -for (I,0,(int) G[u].size ()-1) { -edge& e=Es[g[u][i]]; A                 intv=e.v; +                 if(!vis[v]&&e.cap>e.flow) { thevis[v]=1; -d[v]=d[u]+1; $ Q.push (v); the                 } the             } the         } the         returnVis[t]; -     } in     intDfsintUinta) { the         if(U==t| |! AreturnA; the         intflow=0, F; About          for(int& I=cur[u];i<g[u].size (i++);) { theedge& e=Es[g[u][i]]; the             intv=e.v; the             if(d[v]==d[u]+1&& (F=dfs (V,min (a,e.cap-e.flow)) >0) { +e.flow+=F; -es[g[u][i]^1].flow-=F; theFlow+=f; a-=F;Bayi                 if(!a) Break; the             } the         } -         returnflow; -     } the     intMaxflow (intSintt) { the          This->s=s, This->t=T; the         intflow=0; the          while(BFS ()) { -memset (cur,0,sizeof(cur)); theflow+=DFS (s,inf); the         } the         returnflow;94     } the } DC; the  the intN,m,sum,down[n],inch[n],id[n];98  About intMain () - {101      while(SCANF ("%d%d", &n,&m) = =2) {102sum=0;103         ints=0, t=n+1;104Dc.init (t+2); theMemsetinch,0,sizeof(inch));106for (I,1, M) {107id[i]=-1;108             intX=read (), Y=read (), Z=read (), c=read ();109             if(c) down[i]=z,sum+=Z,DC. Addedge (s,y,z), DC. Addedge (x,t,z); the             Elsedown[i]=0, DC. Addedge (x, Y, z), Id[i]=dc.es.size ()-2;111         } the         intflow=DC. Maxflow (s,t);113dc. Addedge (N,1, INF); theflow+=DC. Maxflow (s,t); the         if(Flow!=sum) puts ("Impossible"); the         Else {117printf"%d\n", Dc.es[dc.es.size ()-2].flow);118for (I,1, M-1) 119                 if(id[i]>=0) printf ("%d", dc.es[id[i]].flow+down[i]); -                 Elseprintf"%d", Down[i]);121             if(id[m]>=0) printf ("%d\n", dc.es[id[m]].flow+down[m]);122             Elseprintf"%d\n", Down[m]);123         }124     } the     return 0;126}

SGU 176 flow Construction (with Yuanhui upper and lower bounds minimum flow)