ZOJ1734-Power Network—ISAP算法-链式前向星存储结构_c++网络流isap算法链式前向星-优快云博客

本文链接：https://blog.youkuaiyun.com/zjutsunny/article/details/103017221

本文深入讲解了ISAP算法，一种高效的求解最大流问题的方法。通过详细的代码解析，介绍了算法的实现过程，包括节点预处理、增广路径查找、流量更新等关键步骤。适用于网络流问题的研究与应用。

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#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

#define inf 0x7fffffff
#define N 300
#define M 30000
int CurrentArc[N];
int pre[N];
int gap[N];
int dis[N];
int head[N];
int size;

struct Edge
{
    int v,w,next;
    Edge(){}
    Edge(int V,int W,int NEXT):v(V),w(W),next(NEXT){}
}edge[M];

void InsertEdge(int u,int v,int w)
{
    edge[size] = Edge(v,w,head[u]);
    head[u] = size++;
    edge[size] = Edge(u,0,head[v]);
    head[v] = size++;
}

int ISAP(int st,int ed,int n)
{
    for(int i=0; i<=n; i++)
    {
        CurrentArc[i] = head[i];
        gap[i] = dis[i] = 0;
    }
    int u = pre[st] = st;
    int minflow = inf;
	int maxflow = 0;
    while(dis[st] < n)
    {
        bool relabel = false;
        for(int &i=CurrentArc[u]; i!=-1; i=edge[i].next)
        {
            int v = edge[i].v;
            if(edge[i].w && dis[u]==dis[v]+1)
            {
                minflow = min(minflow,edge[i].w);
                pre[v] = u;
                u = v;
                if(v==ed)
                {
                    maxflow += minflow;
                    for(u=pre[u]; v!=st; v=u,u=pre[u])
                    {
                        edge[CurrentArc[u]].w -= minflow;
                        edge[CurrentArc[u]^1].w += minflow;
                    }
                    minflow = inf;
                }
                relabel = true;
            }
			if (relabel) break;
        }
		if (relabel) continue;
        int mindis = n;
        for(int i=head[u]; i!=-1; i=edge[i].next)
        {
            int v = edge[i].v;
            if(edge[i].w && dis[v] < mindis)
            {
                CurrentArc[u] = i;
                mindis = dis[v];
            }
        }
        if(--gap[dis[u]]==0) break;
        gap[dis[u]=mindis+1]++;
        u = pre[u];
    }
    return maxflow;
}

int main()
{
    int n,np,nc,m;
	int st,ed,nv;
	int u,v,w;
    while(scanf("%d%d%d%d",&n,&np,&nc,&m)!=EOF)
    {
		size = 0;
		memset(head,-1,sizeof(head));
		nv = n+2;
		st = n;
		ed = n+1;
        for(int i=1; i<=m; i++)
        {
            scanf(" (%d,%d)%d",&u,&v,&w); 
            InsertEdge(u,v,w);
        }
        for(int i=1; i<=np; i++)
        {
            scanf(" (%d)%d",&v,&w);
            InsertEdge(st,v,w);
        }
        
        for(int i=1; i<=nc; i++)
        {
            scanf(" (%d)%d",&u,&w);
            InsertEdge(u,ed,w);
        }
        printf("%d\n",ISAP(st,ed,nv));
    }
    return 0;
}