uva 11248 最小割

Dinic


  1 #include<iostream>
#include<string>
#include<algorithm>
#include<cstdlib>
#include<cstdio>
#include<set>
#include<map>
#include<vector>
#include<cstring>
#include<stack>
#include<cmath>
#include<queue>
using namespace std;
#define INF 0x3f3f3f3f
#define LL long long
#define MAXN 110
struct Edge{
    int from, to, cap, flow;
};
bool comp(const Edge& a, const Edge& b){
    return a.from < b.from || (a.from == b.from && a.to < b.to);
}
struct Dinic{
    int n, m, s, t;
    vector<Edge> edges;
    vector<int> G[MAXN];
    bool vis[MAXN];
    int d[MAXN];
    int cur[MAXN];
    void init(int n){
        this->n = n;
        for (int i = 0; i <= n; i++) 
            G[i].clear();
        edges.clear();
    }
    void AddEdge(int from, int to, int cap){
        edges.push_back(Edge{ from, to, cap, 0 });
        edges.push_back(Edge{ to, from, 0, 0 });
        m = edges.size();
        G[from].push_back(m - 2);
        G[to].push_back(m - 1);
    }
    bool BFS(){
        memset(vis, 0, sizeof(vis));
        queue<int> Q;
        Q.push(s);
        d[s] = 0;
        vis[s] = 1;
        while (!Q.empty()){
            int x = Q.front();
            Q.pop();
            for (int i = 0; i<G[x].size(); i++){
                Edge& e = edges[G[x][i]];
                if (!vis[e.to] && e.cap>e.flow){
                    vis[e.to] = 1;
                    d[e.to] = d[x] + 1;
                    Q.push(e.to);
                }
            }
        }
        return vis[t];
    }
    int DFS(int x, int a){
        if (x == t || a == 0)return a;
        int flow = 0, f;
        for (int& i = cur[x]; i<G[x].size(); i++){
            Edge& e = edges[G[x][i]];
            if (d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap - e.flow)))>0){
                e.flow += f;
                edges[G[x][i] ^ 1].flow -= f;
                flow += f;
                a -= f;
                if (a == 0)break;
            }
        }
        return flow;
    }
    int Maxflow(int s, int t, int need){
        this->s = s; this->t = t;
        int flow = 0;
        while (BFS()){
            memset(cur, 0, sizeof(cur));
            flow += DFS(s, INF);
            if (flow > need)return flow;
        }
        return flow;
    }
    //最小割割边
    vector<int> Mincut(){
        BFS();
        vector<int> ans;
        for (int i = 0; i<edges.size(); i++){
            Edge& e = edges[i];
            if (vis[e.from] && !vis[e.to] && e.cap>0)ans.push_back(i);
        }
        return ans;
    }
    void Reduce(){
        for (int i = 0; i < edges.size(); i++) edges[i].cap -= edges[i].flow;
    }
    void ClearFlow(){
        for (int i = 0; i < edges.size(); i++) edges[i].flow = 0;
    }
};
Dinic ex;
int main(){
    int N, E, C, cas = 0;
    while (~scanf("%d%d%d", &N, &E, &C))
    {
        if (!N)break;
        ex.init(N);
        int a, b, c;
        while (E--)
        {
            scanf("%d%d%d", &a, &b, &c);
            ex.AddEdge(a, b, c);
        }
        int flow = ex.Maxflow(1, N, INF);
        printf("Case %d: ", ++cas);
        if (flow > C)printf("possible
");
        else{
            vector<int> cut = ex.Mincut();
            ex.Reduce();
            vector<Edge>ans;
            for (int i = 0; i < cut.size(); i++){
                Edge& e = ex.edges[cut[i]];
                int temp = e.cap;
                e.cap = C;
                ex.ClearFlow();
                if (flow + ex.Maxflow(1, N, C - flow) >= C)ans.push_back(e);
                e.cap = temp;
            }
            if (ans.empty())printf("not possible
");
            else{
                sort(ans.begin(), ans.end(), comp);
                printf("possible option:(%d,%d)", ans[0].from, ans[0].to);
                for (int i = 1; i < ans.size(); i++)
                    printf(",(%d,%d)", ans[i].from, ans[i].to);
                printf("
");
            }
        }
    }
    return 0;
}