ZOJ 267601点数計画最小割

#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 5555
#define INF 100000007
using namespace std;
typedef double type;
struct node
{
    int v;
    type c, f;
    int next, r;
}edge[MAXM];
int dist[MAXN], nm[MAXN], src, des, n;
int head[MAXN], e;
void add(int x, int y, type 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));
}
type maxflow()
{
    rev_BFS();
    int u;
    type 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
        {
            type 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, m;
int xx[MAXM], yy[MAXM], vis[MAXN], out[MAXM];
type cc[MAXM];
bool ok(double mid)
{
    init();
    double flow = 0;
    for(int i = 1; i <= m; i++)
    {
        if(cc[i] > mid)
            add(xx[i], yy[i], cc[i] - mid), add(yy[i], xx[i], cc[i] - mid);
        else flow += cc[i] - mid;
    }
    flow += maxflow();
    if(flow < eps) return true;
    else return false;
}
void dfs(int u)
{
    vis[u] = 1;
    for(int i = head[u]; i != -1; i = edge[i].next)
        if(edge[i].c > 0 && !vis[edge[i].v])
            dfs(edge[i].v);
}
int main()
{
    int cas = 0;
    while(scanf("%d%d", &nt, &m) != EOF)
    {
        if(cas++) printf("
");
        src = 1;
        des = nt;
        n = nt;
        double low = INF, high = 0;
        for(int i = 1; i <= m; i++)
        {
            scanf("%d%d%lf", &xx[i], &yy[i], &cc[i]);
            low = min(low, cc[i]);
            high = max(high, cc[i]);
        }
        while(high - low > eps)
        {
            double mid = (low + high) / 2;
            if(ok(mid)) high = mid;
            else low = mid;
        }
        ok(low);
        memset(vis, 0, sizeof(vis));
        dfs(src);
        int cnt = 0;
        for(int i = 1; i <= m; i++)
            if(vis[xx[i]] + vis[yy[i]] == 1 || cc[i] <= low)
                out[cnt++] = i;
        printf("%d
", cnt);
        for(int i = 0; i < cnt; i++)
        {
            printf("%d", out[i]);
            if(i < cnt - 1) putchar(' ');
            else putchar('
');
        }
    }
    return 0;
}