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最新推荐文章于 2024-08-05 23:05:49 发布

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最新推荐文章于 2024-08-05 23:05:49 发布

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本文介绍了一种改进的最短增广路径算法(ISAP)，该算法用于解决最大流问题，特别适用于寻找复杂网络中的最大流值。通过使用间隙数组来记录不同距离节点的数量，并在搜索过程中动态调整节点的距离值，从而提高算法效率。

#include <queue>
#include <stdio.h>
#include <string.h>
#include<iostream>
using namespace std;
#define N 1005
#define M 40005
#define INF 0x7fffffff
#define min(a,b) a < b ?  a : b
#define CLR(a,v) memset(a,v,sizeof(a))
struct Vertex
{
    int head;
}V[N];
struct Edge
{
    int v,c,f,next;
    Edge(){}
    Edge(int v,int c,int f,int ne):v(v),c(c),f(f),next(ne){}
}E[M];
int d[N],pre[N],cur[N],gap[N];
int top,s,t,n,m;
void Init()
{
    top = 0;
    CLR(V,-1);
}
void Add_edge(int u,int v,int c)
{
    E[top] = Edge(v,c,0,V[u].head);
    V[u].head = top++;
    E[top] = Edge(u,0,0,V[v].head);
    V[v].head = top++;
}
void set_d()
{
    queue<int> Q;
    CLR(d,-1);
    CLR(gap,0);
    d[t] = 0;
    Q.push(t);
    while(!Q.empty())
    {
        int v = Q.front();
        Q.pop();
        ++gap[ d[v] ];
        for(int i=V[v].head;i!=-1;i=E[i].next)
        {
            int u = E[i].v;
           // cout<<u<<endl;
            if(d[u] == -1)
            {
                d[u] = d[v]+1;
                Q.push(u);
            }
        }
    }
}
int Sap()
{
    set_d();                                        //You can replace it with "CLR(d,0)" if you feel it trouble
    int MaxFlow = 0, u = s;
    int flow = INF;// cout<<s<<endl;
   // cout<<d[s]<<n<<endl;
    memcpy(cur,V,sizeof(V));                        //current arc
    while(d[s] < n)
    {
        int &i = cur[u];                            //reference
        for(;i!=-1;i=E[i].next)
        {
            int v = E[i].v;
            if(E[i].c > E[i].f && d[u] == d[v]+1)  //admissible arc
            {
                u = v;
                pre[v] = i;
                flow = min(flow,E[i].c-E[i].f);
               ;
                if(u == t)
                {
                    while(u != s)
                    {
                        int j = pre[u];
                        E[j].f   += flow;
                        E[j^1].f -= flow;
                        u = E[j^1].v;
                    }
                   // cout<<flow<<endl;
                    MaxFlow = max(MaxFlow,flow);
                    flow = INF;
                }
                break;
            }
        }
        if(i == -1)                                //there's no admissible arc.
        {
            if(--gap[ d[u] ] == 0)
                break;
            int dmin = n-1;
            cur[u] = V[u].head;
            for(int j=V[u].head;j!=-1;j=E[j].next)
                if(E[j].c > E[j].f)                //not full arc
                    dmin = min(dmin,d[ E[j].v ]);
            d[u] = dmin+1;
            ++gap[ d[u] ];
            if(u != s)
                u = E[ pre[u]^1 ].v;
        }
    }
   // cout<<MaxFlow<<endl;
    return MaxFlow;
}
char str[1008][100];
int cn;
int fun(char a[])
{
    for(int i=1;i<=cn;i++)
    {
        if(strcmp(a,str[i]) == 0)
            return i;
    }
    strcpy(str[++cn],a);
    return  cn;
}
int main()
{   int cas = 1;
    char a[1000],b[1000];
    while(~scanf("%d%d",&n,&m),n||m)
    {
        int w;
        cn = 0;
        Init();
        while(m--)
        {
            scanf("%s%s%d",a,b,&w);
            int x = fun(a);
            int y = fun(b);
            Add_edge(x,y,w);
            Add_edge(y,x,w);
            // cout<<x<<y<<endl;
        }
        scanf("%s%s",a,b);
        s = fun(a);
        t = fun(b);
        printf("Scenario #%d\n",cas++);
        printf("%d tons\n",Sap());
        puts("");
    }
}

#include<cstdio>#include<cstring>#include<queue>#include<algorithm>#define N 505#define inf 999999999using namespace std;int n,m,s,t,dis[N],pre[N],gap[N],flow[N][N];struct edge{int v,w;edge *next,*rev;edge(){next=0;}edge(int vv,int ww,edge *e){v=vv;w=ww;next=e;}}*adj[N],*path[N],*e;void insert(int u,int v,int w){edge *p=new edge(v,w,adj[u]);adj[u]=p;edge *q=new edge(u,0,adj[v]);adj[v]=q;p->rev=q;q->rev=p;}void bfs(){memset(dis,0x7f,sizeof(dis));memset(gap,0,sizeof(gap));queue<int> q;dis[t]=0;gap[0]=1;q.push(t);while(q.size()){int x=q.front();q.pop();for(e=adj[x];e;e=e->next){if(e->rev->w==0||dis[e->v]<t)continue;dis[e->v]=dis[x]+1;++gap[dis[e->v]];q.push(e->v);}}}int ISAP(){memset(dis,0,sizeof(dis));memset(gap,0,sizeof(gap));//bfs();int ans=0,u=s,d;while(dis[s]<=t){if(u==t){int minflow=-1u>>1;for(e=path[u];u!=s;e=path[u=pre[u]])minflow=min(minflow,e->w);for(e=path[u=t];u!=s;e=path[u=pre[u]]){e->w-=minflow;e->rev->w+=minflow;flow[pre[u]][u]+=minflow;flow[u][pre[u]]-=minflow;}ans+=minflow;}for(e=adj[u];e;e=e->next)if(e->w>0&&dis[u]==dis[e->v]+1)break;if(e){pre[e->v]=u;path[e->v]=e;u=e->v;}else{if(--gap[dis[u]]==0)break;for(d=t,e=adj[u];e;e=e->next)if(e->w>0)d=min(d,dis[e->v]);dis[u]=d+1;++gap[dis[u]];if(u!=s)u=pre[u];}}return ans;}int main(){int u,v,w;while(~scanf("%d%d",&m,&n)){memset(adj,0,sizeof(adj));while(m--){scanf("%d%d%d",&u,&v,&w);insert(u,v,w);//insert(v,u,w);//无向边}s=1;t=n;printf("%d\n",ISAP());}}