【网络流】 HDU 3157 Crazy Circuits 有源汇上下界最小流
最小流解法:先按照【上下界可行流】建图 但先不建end --> star 边
MAXFlow=按新建的源点和汇点跑一次最大流
再建end->star的边
MAXFlow+=再按新建的源点和汇点跑一次最大流
如果MAXFlow == 新建源点流出的sum值
则 有ans = end->star的流量
否则无ans
#include <cstdio> #include <cstring> #include <cstdlib> #include <string> #include <iostream> #include <algorithm> #include <sstream> #include <cmath> using namespace std; #include <queue> #include <stack> #include <vector> #include <deque> #include <set> #include <map> #include <time.h>; #define cler(arr, val) memset(arr, val, sizeof(arr)) #define FOR(i,a,b) for(int i=a;i<=b;i++) #define IN freopen ("in.txt" , "r" , stdin); #define OUT freopen ("out.txt" , "w" , stdout); typedef long long LL; const int MAXN = 100; const int MAXM = 1500; const int INF = 0x3f3f3f3f; //const int INF = 22222; const int mod = 1000000007; struct Edge { int to,next,cap,flow; } edge[MAXM]; int tol,head[MAXN]; int gap[MAXN],dep[MAXN],cur[MAXN]; void init() { tol=0; cler(head,-1); } void addedge(int u,int v,int w,int rw=0) { edge[tol].to=v,edge[tol].cap=w,edge[tol].flow=0,edge[tol].next=head[u]; head[u]=tol++; edge[tol].to=u,edge[tol].cap=rw,edge[tol].flow=0,edge[tol].next=head[v]; head[v]=tol++; } int Q[MAXN]; void BFS(int star,int end) { cler(dep,-1); cler(gap,0); gap[0]=-1; int front= 0, rear = 0; dep[end]=0; Q[rear++] = end; while(front!= rear) { int u=Q[front++]; for(int i = head[u]; i!=-1; i=edge[i].next) { int v=edge[i].to; if(dep[v]!= -1) continue; Q[rear++]= v; dep[v]=dep[u]+1; gap[dep[v]]++; } } } int S[MAXN]; int sap(int star,int end,int N) { BFS(star,end); memcpy(cur,head,sizeof(head)); int top=0, u=star,ans=0; while(dep[star]<N) { if(u==end) { int Min=INF; int inser; for(int i=0; i<top; i++) if(Min>edge[S[i]].cap-edge[S[i]].flow) { Min=edge[S[i]].cap-edge[S[i]].flow; inser=i; } for(int i=0; i<top; i++) { edge[S[i]].flow+=Min; edge[S[i]^1].flow-=Min; } ans+=Min; top=inser; u=edge[S[top]^1].to; continue; } bool flag = false; int v; for(int i=cur[u]; i!=-1; i=edge[i].next) { v=edge[i].to; if(edge[i].cap-edge[i].flow&&dep[v]+1==dep[u]) { flag = true; cur[u]=i; break; } } if(flag) { S[top++] = cur[u]; u=v; continue; } int Min=N; for(int i= head[u]; i!=-1; i=edge[i].next) if(edge[i].cap-edge[i].flow&&dep[edge[i].to]<Min) { Min=dep[edge[i].to]; cur[u]=i; } gap[dep[u]]--; if(!gap[dep[u]]) return ans; dep[u]=Min+1; gap[dep[u]]++; if(u!=star) u=edge[S[--top]^1].to; } return ans; } char s[10]; int low[MAXN],star,end,sum; int getnum(char *s) { if(strcmp(s,"+")==0) return star; else if(strcmp(s,"-")==0) return end; else return atoi(s); } int main() { #ifndef ONLINE_JUDGE freopen("in.txt", "r", stdin); //freopen("out.txt", "w", stdout); #endif int n , m; while(~scanf("%d%d",&n,&m),n+m) { cler(low,0); init(); star=0,end=n+1,sum=0; for(int i=0; i<m; i++) { int d; char s1[5],s2[5]; scanf("%s %s %d",s1,s2,&d); int l=getnum(s1),r=getnum(s2); addedge(l,r,INF); low[r]+=d; low[l]-=d; } int Star=n+2,End=n+3; for(int i=0;i<=n+1;i++) { if(low[i]>0) { addedge(Star,i,low[i]); sum+=low[i]; } else addedge(i,End,-low[i]); } int maxflow=sap(Star,End,n+4); addedge(end,star,INF); maxflow+=sap(Star,End,n+4); if(maxflow!=sum) printf("impossible\n"); else printf("%d\n",edge[tol-2].flow); } return 0; }