zoj 2676 Network Wars 【0-1分数规划 + 最小割】 【吃一堑长一智】

Input

Output

Example

6 8
1 2 3
1 3 3
2 4 2
2 5 2
3 4 2
3 5 2
5 6 3
4 6 3

4
3 4 5 6

4 5
1 2 2
1 3 2
2 3 1
2 4 2
3 4 2

3
1 2 3

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <queue>
#include <cmath>
#include <algorithm>
#define MAXN 110
#define MAXM 2000
#define INF 0x3f3f3f3f
#define eps 1e-8
using namespace std;
struct Edge
{
    int from, to;
    double cap, flow;
    int ID, next;
};
Edge edge[MAXM];
int head[MAXN], edgenum;
int dist[MAXN], cur[MAXN];
bool vis[MAXN];
int N, M;
struct rec
{
    int from, to;
    double val;
};
rec num[MAXM];
double Max;
void input()
{
    Max = 0;
    for(int i = 1; i <= M; i++)
        scanf("%d%d%lf", &num[i].from, &num[i].to, &num[i].val), Max = max(Max, num[i].val);
}
void init()
{
    edgenum = 0;
    memset(head, -1, sizeof(head));
}
void addEdge(int u, int v, double w, int id)
{
    Edge E1 = {u, v, w, 0, id, head[u]};
    edge[edgenum] = E1;
    head[u] = edgenum++;
    Edge E2 = {v, u, 0, 0, id, head[v]};
    edge[edgenum] = E2;
    head[v] = edgenum++;
}
double ans;//记录总值
void getMap(double o)
{
    ans = 0;//初始化
    for(int i = 1; i <= M; i++)
    {
        double t = num[i].val - o;
        if(t > eps)
            addEdge(num[i].from, num[i].to, t, i), addEdge(num[i].to, num[i].from, t, i);
        else
            ans += t;//该边就是割边
    }
}
bool BFS(int s, int t)
{
    queue<int> Q;
    memset(dist, -1, sizeof(dist));
    memset(vis, false, sizeof(vis));
    dist[s] = 0;
    vis[s] = true;
    Q.push(s);
    while(!Q.empty())
    {
        int u = Q.front();
        Q.pop();
        for(int i = head[u]; i != -1; i = edge[i].next)
        {
            Edge E = edge[i];
            if(!vis[E.to] && E.cap - E.flow > eps)
            {
                dist[E.to] = dist[u] + 1;
                if(E.to == t) return true;
                vis[E.to] = true;
                Q.push(E.to);
            }
        }
    }
    return false;
}
double DFS(int x, double a, int t)
{
    if(x == t || fabs(a) < eps) return a;//精度
    double flow = 0, f;
    for(int &i = cur[x]; i != -1; i = edge[i].next)
    {
        Edge &E = edge[i];
        if(dist[E.to] == dist[x] + 1 && (f = DFS(E.to, min(a, E.cap-E.flow), t)) > eps)
        {
            edge[i].flow += f;
            edge[i^1].flow -= f;
            flow += f;
            a -= f;
            if(fabs(a) < eps) break;//精度
        }
    }
    return flow;
}
double Maxflow(int s, int t)
{
    double flow = 0;
    while(BFS(s, t))
    {
        memcpy(cur, head, sizeof(head));
        flow += DFS(s, Max, t);
    }
    return flow;
}
void find_S(int u)//找源点能到的点集 S
{
    vis[u] = true;
    for(int i = head[u]; i != -1; i = edge[i].next)
    {
        Edge E = edge[i];
        if(vis[E.to]) continue;
        if(E.cap - E.flow > eps)
            find_S(E.to);
    }
}
bool mark[MAXM];//标记该边是否是 选中最小割的边
int sum;//记录最小割里面 的边数
void solve()
{
    double l = 0, r = Max, mid;
    while(r - l >= eps)
    {
        mid = (l + r) / 2;
        init();
        getMap(mid);//每次根据mid值 重建图 
        ans += Maxflow(1, N);//求一次最小割
        if(ans > eps)
            l = mid;
        else
            r = mid;
    }
    memset(vis, false, sizeof(vis));
    find_S(1);//找源点能到 的点集S集
    sum = 0;//总边数
    memset(mark, false, sizeof(mark));
    for(int i = 1; i <= M; i++)
    {
        if((vis[num[i].from] && !vis[num[i].to]) || (!vis[num[i].from] && vis[num[i].to]) || num[i].val <= mid)
            sum++, mark[i] = true;
    }
    printf("%d\n", sum);
    int used = 0;
    for(int i = 1; i <= M; i++)
    {
        if(mark[i])
        {
            if(used) printf(" ");
            printf("%d", i);
            used++;
        }
    }
    printf("\n");
}
int main()
{
    int k = 0;
    while(scanf("%d%d", &N, &M) != EOF)
    {
        if(k)
            printf("\n");
        k++;
        input();
        solve();
    }
    return 0;
}