poj 2987——最大闭权图运用最大流dinic

火碳黑 — Sat, 09 Apr 2011 05:44:00 GMT

Firing

Description

You’ve finally got mad at “the world’s most stupid” employees of yours and decided to do some firings. You’re now simply too mad to give response to questions like “Don’t you think it is an even more stupid decision to have signed them?”, yet calm enough to consider the potential profit and loss from firing a good portion of them. While getting rid of an employee will save your wage and bonus expenditure on him, termination of a contract before expiration costs you funds for compensation. If you fire an employee, you also fire all his underlings and the underlings of his underlings and those underlings’ underlings’ underlings… An employee may serve in several departments and his (direct or indirect) underlings in one department may be his boss in another department. Is your firing plan ready now?

Input

The input starts with two integers n (0 < n ≤ 5000) and m (0 ≤ m ≤ 60000) on the same line. Next follows n + m lines. The first n lines of these give the net profit/loss from firing the i-th employee individually b_i (|b_i| ≤ 10⁷, 1 ≤ i ≤ n). The remaining m lines each contain two integers i and j (1 ≤ i, j ≤ n) meaning the i-th employee has the j-th employee as his direct underling.

Output

Output two integers separated by a single space: the minimum number of employees to fire to achieve the maximum profit, and the maximum profit.

Sample Input

Sample Output

2 2

Hint

As of the situation described by the sample input, firing employees 4 and 5 will produce a net profit of 2, which is maximum.

题意：
公司要裁员，裁掉一个员工，他的下属也得裁掉。裁掉一个员工可以少发一定的工资，但他已经他的下属全被裁掉，所以这个partment会减少一定的生产利润。显然，裁掉一个人就可能得到收益（正的或者负的）；
给出裁掉一个员工能获得的收益（正或负）。
给出公司里员工的依赖关系。表示A有下属B
问得到的最大利益以及裁掉的最少人数。
分析：在这些人中选若干人，使得收益最大。如果A有下属B，那我裁掉A就得裁掉B。所以裁掉B成了裁掉A的必要条件，即A依赖于B。所以让A连向B，A->B容量为正无穷。
那么选若干人事效益最大就是求这个权闭合图的最大值。
之后对于收益是正的人，s->x容量为收益值，对于收益是负的人x->t，容量为收益值得绝对值。
结果就是正权值和-最小割值（最大流：图中切割最小的值）=最大权闭合图的值。
这个图从s出发的边都是收益，从x->t的边都是消耗。那求最小割就是对于给出的这么多的收益，通过多少消耗能让取得的收益最大。
那最后的利润就是：总利润和-取得利润最大所需的消耗。

#include <iostream>
#include <stdlib.h>
using namespace std;
const int maxn= 20010;
const __int64 inf=0x7fffffff;
struct node
{
    __int64 v,next;
    __int64 w;
}fn[500010];
__int64 level[maxn],g[maxn],que[maxn],out[maxn],th, tip, visit[maxn];
inline void add(__int64 u,__int64 v,__int64 w)
{
    fn[th].v = v, fn[th].w = w, fn[th].next = g[u], g[u] = th++;
    fn[th].v = u, fn[th].w = 0, fn[th].next = g[v], g[v] = th++;
}
void build_level(__int64  n,__int64 s,__int64  e)
{
    __int64 h=0,r=0,i,u;
    for (i = 0; i <= n; i++) level[i]=0;
    level[s] = 1;
    que[0] = s;
    while(h <= r)
    {
        u = que[h++];
        for (i = g[u]; i != -1; i = fn[i].next)
        {
            if (fn[i].w && level[fn[i].v] == 0)
            {
                que[++r] = fn[i].v;
                level[fn[i].v] = level[u] + 1;
             }
        }
    }
}
__int64 dinic(__int64 n,__int64 s,__int64 e)
{
    __int64 ret=0,i;
    while(1)
    {
        build_level(n,s,e);
        if (level[e] == 0) break;
        for (i = 0; i < n; ++i) out[i] = g[i];
        __int64 q = -1;
        while(1)
        {
            if (q < 0)
            {
                for (i = out[s]; i != -1; i = fn[i].next)
                {
                    if (fn[i].w && out[fn[i].v] != -1 && level[fn[i].v] == 2)
                    {
                        que[++q] = i;
                        out[s] = fn[i].next;
                        break;
                    }
                }
                if (i == -1)
                {
                    break;
                }
            }
            __int64 u = fn[que[q]].v;
            if(u == e)
            {
                __int64 tmp=inf;
                for(i = 0;i <= q; i++)
                    if(tmp > fn[que[i]].w)tmp = fn[que[i]].w;
                ret += tmp;
                for(i=0;i<=q;i++)
                {
                    fn[que[i]].w -= tmp;
                    fn[que[i]^1].w += tmp;
                }
                for (i = 0; i <= q; i++)
                {
                    if(fn[que[i]].w == 0)
                    {
                        q = i-1;
                        break;
                    }
                }
            }
            else
            {
                for (i = out[u]; i != -1; i = fn[i].next)
                {
                    if (fn[i].w && out[fn[i].v] !=-1 && level[u] + 1 == level[fn[i].v])
                    {
                        que[++q] = i, out[u] = fn[i].next;
                        break;
                    }
                }
                if(i==-1)
                {
                    out[u] = -1, q--;
                 }

            }
        }
    }
    return ret;
}
void dfs(int s, int e)
{
    int i;
    if (s == e)
    {
        return;
    }
    for (i = g[s]; i != -1; i++)
    {
        if (!visit[fn[i].v] && fn[i].w)
        {
            dfs(fn[i].v, e);
        }
    }
}
int main()
{
    __int64 m, n, t, u, v, i, j, start, end, sum, num, w, ans;
    int k = 0;
    while (scanf("%I64d%I64d", &n, &m) - EOF)
    {
        k++;
        start = 0, end = n + 1, th = 0;
        for (i = 0; i <= end; i++)
        {
            g[i] = -1;
        }
        for (i = 1, sum = 0; i <= n; i++)
        {
            scanf("%I64d", &num);
            if (num >= 0)
            {
                add(start, i, num);
                sum += num;
            }
            else
            {
                add(i, end, -num);
            }
        }
        for (j = 1; j <= m; j++)
        {
            scanf("%I64d%I64d", &u, &v);
            add(u, v, inf);
        }
        sum -= dinic(end + 1, start, end);
        tip = 0;
        for (i = 0; i <= end + 1; i++)
        {
            visit[i] = 0;
        }
        dfs(0, end);
        for (i = 0, tip = 0; i <= end + 1; i++)
        {
            if (visit[i])
            {
                tip++;
            }
        }
        printf("%I64d %I64d\n", tip, ans);
    }
    //system("pause");
    return 0;
}

火碳黑 2011-04-09 13:44 发表评论

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poj 2987——最大闭权图 运用最大流dinic

poj 2987——最大闭权图运用最大流dinic