【最大流】POJ 1145 PIGS

最新推荐文章于 2019-12-18 20:07:00 发布

原创最新推荐文章于 2019-12-18 20:07:00 发布 · 589 阅读

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本文介绍了一种通过构建直观且简单的网络流模型，然后逐步简化模型以揭示良好构图思路的方法。该方法特别适用于解决网络流问题，通过实例代码展示了如何使用基本的数据结构和算法实现这一过程。

如果一时想不出很好的构图方法,不如先构造一个最直观,或者说最“硬来”的模型,然后再用合并结点和边的方法来简化这个模型。

经过简化以后,好的构图思路自然就会涌现出来了。

这是解决网络流问题的一个好方法。

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <string>
#include <iostream>
#include <algorithm>
using namespace std;
#include <queue>
#include <stack>
#include <vector>
#include <deque>
#include <set>
#include <map>
#define IN     freopen ("in.txt" , "r" , stdin);
#define OUT  freopen ("out.txt" , "w" , stdout);
typedef long long LL;
const int MAXN = 111;//点数的最大值
const int MAXM = 1111;//边数的最大值
const LL INF = 1152921504;
struct Edge
{
    int to,next,cap,flow;
} edge[MAXM]; //注意是MAXM
int tol;
int head[MAXN];
int gap[MAXN],dep[MAXN],cur[MAXN];
void init()
{
    tol = 0;
    memset(head,-1,sizeof (head));
}
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 start,int end)
{
    memset(dep,-1,sizeof(dep));
    memset(gap,0,sizeof(gap));
    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 start,int end, int N)
{
    BFS(start,end);
    memcpy(cur,head,sizeof(head));
    int top = 0;
    int u = start;
    int ans = 0;
    int i;
    while(dep[start] < N)
    {
        if(u == end)
        {
            int Min = INF;
            int inser;
            for( 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( 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( 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( 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 != start)u = edge[S[--top]^1].to;
    }
    return ans;
}
int flag[MAXM];
int main()
{
    int n,m,a[MAXM],b,c;
    while(scanf("%d%d",&m,&n)!=EOF)
    {
        init();
        for(int i=1; i<=m; i++)
            scanf("%d",&a[i]);
        memset(flag,0,sizeof(flag));
        for(int i=1; i<=n; i++)
        {
            int sum=0;
            scanf("%d",&b);
            for(int j=0; j<b; j++)
            {
                scanf("%d",&c);
                if(flag[c]==0)
                {
                    flag[c]=i;
                    sum+=a[c];
                }
                else
                    addedge(flag[c],i,INF,0);
            }
            if(sum>0)
                addedge(0,i,sum,0);
            scanf("%d",&c);
            addedge(i,n+1,c,0);
        }
        printf("%d\n",sap(0,n+1,n+2));
    }
    return 0;
}