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;
}