UVA 11478 halum (differential constraint)

Title Link: http://acm.hust.edu.cn/vjudge/problem/viewProblem.action?id=34651

Ideas

Differential constraint system.

Set the operation on node U and Sum[u], then the Edge (u,v) weight is d-sum[v]+sum[u]. For the biggest problem with the minimum value we think of the two-point answer, set two points to X, then the problem becomes the question whether there is a solution to determine the minimum value of x. For weights we have inequalities d-sum[v]+sum[u]>=x = = sum[v]<=sum[u]+ (d-x), so that a differential constraint system can be established.

No solution: If the minimum value of 1 o'clock is still not true.

Arbitrary solution: True if the minimum value is r+1.

Otherwise, the maximum value of the two-part answer, when the graph has a negative weight loop time Division constraint system without solution that is two-point answer is not established.

Code

1#include <cstdio>2#include <cstring>3#include <vector>4#include <queue>5 using namespacestd;6 7 Const intMAXN = ++Ten;8 9 intn,m;Ten structEdge {intu,v,w; One }; Avector<int>G[MAXN]; -Vector<edge>es; - voidAddedge (intUintVintW) { the Es.push_back (Edge) {u,v,w}); -     intM=es.size (); G[u].push_back (M-1); - } - BOOLSPFA () { +queue<int>Q; -     intINQ[MAXN],D[MAXN],CNT[MAXN]; +memset (INQ,0,sizeof(INQ)); Amemset (CNT,0,sizeof(CNT)); at      for(intI=1; i<=n;i++) -d[i]=0, inq[i]=1, Q.push (i); -      while(!Q.empty ()) { -         intU=q.front (); Q.pop (); inq[u]=0; -          for(intI=0; I<g[u].size (); i++) { -Edge e=Es[g[u][i]]; in             intv=e.v; -             if(d[v]>d[u]+e.w) { tod[v]=d[u]+E.W; +                 if(!Inq[v]) { -inq[v]=1, Q.push (v); the                     if(++cnt[v]> (n))return false; *                 } $             }Panax Notoginseng         } -     } the     return true; + } A BOOLCanintx) { the      for(intI=0; I<es.size (); i++) es[i].w-=x; +     BOOLans=SPFA (); -      for(intI=0; I<es.size (); i++) es[i].w+=x; $     returnans; $ } -  - intMain () { the      while(SCANF ("%d%d", &n,&m) = =2) { - es.clear ();Wuyi          for(intI=1; i<=n;i++) g[i].clear (); the         intu,v,w; -         intL=0, r=0; Wu          for(intI=0; i<m;i++) { -scanf"%d%d%d",&u,&v,&W); AboutAddedge (U,V,W); R=Max (r,w); $         } -         if(Can (r+1)) printf ("infinite\n"); -         Else if(!can (1)) printf ("No solution\n"); -         Else { A              while(l<R) { +                 intm=l+ (r-l+1)/2; the                 if(Can (M)) L=m;Elser=m-1; -             } $printf"%d\n", L); the         } the     } the     return 0; the}

UVA 11478 halum (differential constraint)