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POJ 3498 拆点 最大流

2014年02月17日 ⁄ 综合 ⁄ 共 2791字 ⁄ 字号 评论关闭

大概题意:

在南极的海洋上, 有一些企鹅站在一些浮冰上,这些企鹅想聚在一块,也就是到某块浮冰上聚会, 但是它们不想游泳,只想从一块浮冰跳到另一块上,自身的跳跃距离题中已经给出来了,然后是每个浮冰的坐标,该浮冰上已经有个多少个企鹅,以及浮冰的承受能力,所谓承受能力不是指能载动多少企鹅,题目中说了每个浮冰载企鹅是没有问题的,但是从浮冰往外跳会导致浮冰破损,这里的承受能力就是能跳出去多少次企鹅。

那么这题是一道网络流,题目要求的是最后能够成为聚会地点的浮冰标号,这里可以联想到需要枚举汇点,并且可以根据跳跃距离的限制N2枚举进行建边,但是每个浮冰的承受能力是点的容量,怎样转化为边的容量? 一般平时碰到的点的容量,可以直接连到汇点上, 要么你就拆点,将其变为两个点,中间的边容量就是点容量, 那么本题由于每块浮冰是可以去往多块浮冰的,所以直接连接汇点肯定不行,那么就需要进行拆点了

#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>
#include <cstdio>
#include <cmath>
#include <queue>
#include <map>
#include <set>
#define eps 1e-5
#define MAXN 222
#define MAXM 55555
#define INF 100000007
using namespace std;
struct node
{
    int v;    // vtex
    int c;    // cacity
    int f;   // current f in this arc
    int next, r;
}edge[MAXM];
int dist[MAXN], nm[MAXN], src, des, n;
int head[MAXN], e;
void add(int x, int y, int c)
{
    edge[e].v = y;
    edge[e].c = c;
    edge[e].f = 0;
    edge[e].r = e + 1;
    edge[e].next = head[x];
    head[x] = e++;
    edge[e].v = x;
    edge[e].c = 0;
    edge[e].f = 0;
    edge[e].r = e - 1;
    edge[e].next = head[y];
    head[y] = e++;
}
void rev_BFS()
{
    int Q[MAXN], h = 0, t = 0;
    for(int i = 1; i <= n; ++i)
    {
        dist[i] = MAXN;
        nm[i] = 0;
    }
    Q[t++] = des;
    dist[des] = 0;
    nm[0] = 1;
    while(h != t)
    {
        int v = Q[h++];
        for(int i = head[v]; i != -1; i = edge[i].next)
        {
            if(edge[edge[i].r].c == 0 || dist[edge[i].v] < MAXN)continue;
            dist[edge[i].v] = dist[v] + 1;
            ++nm[dist[edge[i].v]];
            Q[t++] = edge[i].v;
        }
    }
}
void init()
{
    e = 0;
    memset(head, -1, sizeof(head));
}
int maxflow()
{
    rev_BFS();
    int u;
    int total = 0;
    int cur[MAXN], rpath[MAXN];
    for(int i = 1; i <= n; ++i)cur[i] = head[i];
    u = src;
    while(dist[src] < n)
    {
        if(u == des)     // find an augmenting path
        {
            int tf = INF;
            for(int i = src; i != des; i = edge[cur[i]].v)
                tf = min(tf, edge[cur[i]].c);
            for(int i = src; i != des; i = edge[cur[i]].v)
            {
                edge[cur[i]].c -= tf;
                edge[edge[cur[i]].r].c += tf;
                edge[cur[i]].f += tf;
                edge[edge[cur[i]].r].f -= tf;
            }
            total += tf;
            u = src;
        }
        int i;
        for(i = cur[u]; i != -1; i = edge[i].next)
            if(edge[i].c > 0 && dist[u] == dist[edge[i].v] + 1)break;
        if(i != -1)     // find an admissible arc, then Advance
        {
            cur[u] = i;
            rpath[edge[i].v] = edge[i].r;
            u = edge[i].v;
        }
        else        // no admissible arc, then relabel this vtex
        {
            if(0 == (--nm[dist[u]]))break;    // GAP cut, Important!
            cur[u] = head[u];
            int mindist = n;
            for(int j = head[u]; j != -1; j = edge[j].next)
                if(edge[j].c > 0)mindist = min(mindist, dist[edge[j].v]);
            dist[u] = mindist + 1;
            ++nm[dist[u]];
            if(u != src)
                u = edge[rpath[u]].v;    // Backtrack
        }
    }
    return total;
}
int nt, v[MAXN], f[MAXN], out[MAXN];
double D, x[MAXN], y[MAXN];
double dis(int i, int j)
{
    return sqrt((x[i] - x[j]) * (x[i]- x[j]) + (y[i] - y[j]) * (y[i] - y[j]));
}
int main()
{
    int T;
    scanf("%d", &T);
    while(T--)
    {
        scanf("%d%lf", &nt, &D);
        int sum = 0;
        for(int i = 1; i <= nt; i++)
        {
            scanf("%lf%lf%d%d", &x[i], &y[i], &v[i], &f[i]);
            sum += v[i];
        }
        src = 2 * nt + 1;
        n = 2 * nt + 1;
        int cnt = 0;
        for(int k = 1; k <= nt; k++)
        {
            init();
            for(int i = 1; i <= nt; i++)
                for(int j = i + 1; j <= nt; j++)
                {
                    if(dis(i, j) <= D) add(i + nt, j, INF), add(j + nt, i, INF);
                }
            for(int i = 1; i <= nt; i++) add(src, i, v[i]), add(i, i + nt, f[i]);
            des = k;
            int flow = maxflow();
            //printf("%d\n", flow);
            if(flow == sum) out[cnt++] = k - 1;
        }
        if(!cnt) printf("-1\n");
        else
        {
            for(int i = 0; i < cnt - 1; i++) printf("%d ", out[i]);
            printf("%d\n", out[cnt - 1]);
        }
    }
    return 0;
}

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