UVA11478 halum [differential constraint system]

https://vjudge.net/problem/UVA-11478

Given a graph, each edge has a weighted value. Each time you can select a node v and an integer d, reduce the weight of all edges at the end of the V by D, increase the weight of all edges starting at V by D, and finally let the minimum value of all edges be greater than 0 and as large as possible.

Damn, the book was wrong. >0 not nonnegative wa several times because of this

Considering the constraints of each edge, Di represents the Halum amount of I

W-dv+du>0

Dv-du<w

However, solving this differential constraint system only makes this set of inequalities, the longest and shortest-path control is the maximum value of a single d rather than the minimum value

How is the minimum maximum?

Two-point answer ...

Then the inequality becomes dv-du<w-mid, which means that after operation the right can be larger than mid

No solution is mid=1, unbounded words is mid= maximum Benquan (can not use 1e9, overflow) is also established

#include <iostream>#include<cstdio>#include<algorithm>#include<cstring>using namespaceStd;typedefLong Longll;Const intn=505, m=3005, inf=1e9;inlineintRead () {CharC=getchar ();intx=0, f=1;  while(c<'0'|| C>'9'){if(c=='-') f=-1; c=GetChar ();}  while(c>='0'&&c<='9') {x=x*Ten+c-'0'; c=GetChar ();} returnx*F;}intn,m,u,v,w;structedge{intV,ne; DoubleW;} E[M];intH[n],cnt=0; inlinevoidInsintUintVintW) {CNT++; E[CNT].V=v;e[cnt].w=w;e[cnt].ne=h[u];h[u]=CNT;}intQ[n],head,tail,inq[n],num[n],d[n];inlinevoidLopint&AMP;X) {if(x==n) x=1;Else if(x==0) x=n-1;}BOOLSPFA (intmid) {Head=tail=1; memset (INQ,0,sizeof(INQ)); memset (num,0,sizeof(num));  for(intI=1; i<=n;i++) q[tail++]=i,inq[i]=1, d[i]=0;  while(head!=tail) {        intu=q[head++];inq[u]=0; Lop (head);  for(intI=h[u];i;i=e[i].ne) {            intv=e[i].v,w=e[i].w-mid; if(d[v]>d[u]+W) {D[v]=d[u]+W; if(!Inq[v]) {Inq[v]=1; if(++num[v]>n)return true; if(D[v]<d[q[head]]) head--, Lop (head), q[head]=v; Elseq[tail++]=v,lop (tail); }            }        }    }    return false;}intMain () { while(SCANF ("%d%d", &n,&m)! =EOF) {CNT=0; Memset (H,0,sizeof(h)); intL=1, r=0, ans=0;  for(intI=1; i<=m;i++) U=read (), V=read (), W=read (), Ins (u,v,w), r=Max (R,W); if(SPFA (L)) {Puts ("No Solution");Continue;} Else if(!SPFA (R)) {Puts ("Infinite");Continue;} Else{             while(l<=R) {                intMid= (l+r) >>1; if(!SPFA (mid)) ans=mid,l=mid+1; Elser=mid-1; } printf ("%d\n", ans); }    }}

UVA11478 Halum [differential constrained system]