【网络流】 HDU 3157 Crazy Circuits 有源汇上下界最小流

来源：互联网发布：驾驶行为大数据分析编辑：程序博客网时间：2024/05/16 18:44

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;}

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