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  • UVA

    题目大意:有n个城市m条航线。给出每条航线的出发地,目的地,座位数,起飞时间和到达时间(所给形式为HHMM。记得转化),再给出城市A和B。和到达城市B的最晚时间。如今问一天内最多有多少人能从A飞到B,能够在其它城市中转

    解题思路:将飞机票拆点,拆成i–>i + m,容量为座位数。
    接着推断一下。航线之间的连线
    假设航线的起点是A的话,那么就和超级源点相连,容量为INF
    假设航线的终点是B且到达时间小于等于最晚时间。那么连线,容量为INF
    假设航线i的终点和航线j的起点同样。且航线i的到达时间+30<=航线j的起始时间,那么连线。容量为INF

    #include <cstdio>
    #include <cstring>
    #include <algorithm>
    #include <vector>
    #include <queue>
    #include <map>
    #include <iostream>
    using namespace std;
    #define N 10010
    #define INF 0x3f3f3f3f
    
    struct Edge{
        int from, to, cap, flow;
        Edge() {}
        Edge(int from, int to, int cap, int flow) : from(from), to(to), cap(cap), flow(flow) {}
    };
    
    struct Dinic{
        int n, m, s, t;
        vector<Edge> edges;
        vector<int> G[N];
        bool vis[N];
        int d[N], cur[N];
    
        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));
            int 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);
            vis[s] = 1;
            d[s] = 0;
    
            while (!Q.empty()) {
                int u = Q.front();
                Q.pop();
                for (int i = 0; i < G[u].size(); i++) {
                    Edge &e = edges[G[u][i]];
                    if (!vis[e.to] && e.cap > e.flow) {
                        vis[e.to] = true;
                        d[e.to] = d[u] + 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) {
            this->s = s; this->t = t;
            int flow = 0;
            while (BFS()) {
                memset(cur, 0, sizeof(cur));
                flow += DFS(s, INF);
            }
            return flow;
        }
    };
    
    
    Dinic dinic;
    #define M 5100
    #define S 160
    int n, m, source, sink, Time;
    int num[S];
    map<string, int> Map;
    struct Node {
        int u, v, c, s, t;
    }node[M];
    
    int getTime(string T) {
        int a = (T[0] - '0') * 10 + (T[1] - '0');
        int b = (T[2] - '0') * 10 + (T[3] - '0');
        return a * 60 + b;
    }
    
    void solve() {
        Map.clear();
        int cnt = 3;
        string a, b, s, t;
    
        cin >> a >> b >> s >> m;
        Map[a] = 1; Map[b] = 2;
        Time = getTime(s);
    
        memset(num, 0, sizeof(num));
        source = 0; sink = 2 * m + 1;
        dinic.init(sink);
    
        for (int i = 1; i <= m; i++) {
            cin >> a >> b >> node[i].c >> s >> t;
    
            if (!Map[a]) Map[a] = cnt++;
            if (!Map[b]) Map[b] = cnt++;
    
            node[i].u = Map[a]; 
            node[i].v = Map[b];
            node[i].s = getTime(s);
            node[i].t = getTime(t);
    
            num[node[i].u]++; num[node[i].v]++;
            dinic.AddEdge(i, i + m, node[i].c);
        }
    
        if (!num[1] || !num[2]) {
            printf("0
    ");
            return ;
        }
    
        for (int i = 1; i <= m; i++) {
            int u = node[i].u, v = node[i].v;
            if (u == 1) dinic.AddEdge(source, i, INF);
            if (v == 2 && node[i].t <= Time) dinic.AddEdge(i + m, sink, INF);
    
            for (int j = 1; j <= m; j++) {
                if (i == j) continue;
                if (v != node[j].u) continue;
                if (node[i].t + 30 <= node[j].s) dinic.AddEdge(i + m, j, INF);
    
            }
        }
        int ans = dinic.Maxflow(source, sink);
        printf("%d
    ", ans);
    }
    
    int main() {
        while (scanf("%d
    ", &n) != EOF)  solve();
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/yjbjingcha/p/7068247.html
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