uva 10816 - Travel in Desert（最小瓶颈生成树+最短路）

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题目连接：10816 - Travel in Desert

求出最小生成树，瓶颈值为n-1条边中最大那条，将所有权值大于瓶颈值的边舍去，剩下一张无向图，做一遍最短路。

#include <cstdio>#include <cstring>#include <cmath>#include <vector>#include <queue>#include <algorithm>using namespace std;typedef pair<int, double> pii;const int maxn = 105;const int maxm = 10005;const double inf = 1e20;const double eps = 1e-8;struct Edge {int u, v;double t, d;Edge(int u = 0, int v = 0, double t = 0, double d = 0): u(u), v(v), t(t), d(d) {}bool operator < (const Edge& a) const { return t < a.t || (fabs(t-a.t) < eps && d < a.d); }}E[maxm];struct State {int u;double d;State(int u = 0, double d = 0): u(u), d(d) {}bool operator < (const State& a) const { return d > a.d; }};int N, M, S, T, F[maxn], P[maxn], done[maxn];double D[maxn];vector<int> ans;vector<pii> G[maxn];int find(int x) { return x == F[x] ? x : F[x] = find(F[x]); }void init () {scanf("%d%d", &S, &T);for (int i = 1; i <= N; i++)G[i].clear(), F[i] = i;for (int i = 0; i < M; i++)scanf("%d%d%lf%lf", &E[i].u, &E[i].v, &E[i].t, &E[i].d);sort(E, E + M);}void put(int u) {if (u == 0) return;put(P[u]);ans.push_back(u);}double dijkstra(int s, int e) {memset(done, 0, sizeof(done));for (int i = 0; i <= N; i++) D[i] = inf;P[s] = D[s] = 0;priority_queue<State> Q;Q.push(State(s, D[s]));while (!Q.empty()) {int u = Q.top().u;Q.pop();if (done[u]) continue;done[u] = 1;for (int i = 0; i < G[u].size(); i++) {int v = G[u][i].first;if (D[v] > D[u] + G[u][i].second) {P[v] = u;D[v] = D[u] + G[u][i].second;Q.push(State(v, D[v]));}}}ans.clear();put(e);for (int i = 0; i < ans.size(); i++)printf("%d%c", ans[i], i == ans.size()-1 ? '\n' : ' ');return D[e];}void solve () {double temp;bool flag = false;for (int i = 0; i < M; i++) {int u = E[i].u, v = E[i].v;if (flag && fabs(E[i-1].t - E[i].t) > eps) break;if (find(u) != find(v))F[find(u)] = find(v);G[u].push_back(make_pair(v, E[i].d));G[v].push_back(make_pair(u, E[i].d));if (find(S) == find(T)) {temp = E[i].t;flag = true;}}double dis = dijkstra(S, T);printf("%.1lf %.1lf\n", dis, temp);}int main () {while (scanf("%d%d", &N, &M) == 2) {init();solve();}return 0;}

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