uva 1494 - Qin Shi Huang's National Road System（最小生成树）

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题目链接：uva 1494 - Qin Shi Huang's National Road System

建成最小生成树之后，枚举两节点，然后删除路径上权值上最大的边。

#include <cstdio>#include <cstring>#include <cmath>#include <vector>#include <algorithm>using namespace std;const int maxn = 1005;struct Edge {int u, v, l;Edge(int u = 0, int v = 0, int l = 0): u(u), v(v), l(l) {}bool operator < (const Edge& u) const { return l < u.l; }};int N, F[maxn], X[maxn], Y[maxn], P[maxn], D[maxn][maxn];vector<Edge> edges, G[maxn];int find (int x) { return x == F[x] ? x : F[x] = find(F[x]); }int distance(int x, int y) { return x * x + y * y; }void init () {scanf("%d", &N);edges.clear();memset(D, 0, sizeof(D));for (int i = 1; i <= N; i++) {F[i] = i;G[i].clear();}for (int i = 1; i <= N; i++) {scanf("%d%d%d", &X[i], &Y[i], &P[i]);for (int j = 1; j < i; j++)edges.push_back(Edge(i, j, distance(X[i]-X[j], Y[i]-Y[j])));}sort(edges.begin(), edges.end());}void dfs (int u, int f, int d, int* p) {p[u] = d;for (int i = 0; i < G[u].size(); i++) {int v = G[u][i].v, td = G[u][i].l;if (v == f) continue;dfs(v, u, max(d, td), p);}}int main () {int cas;scanf("%d", &cas);while (cas--) {init();double S = 0;for (int i = 0; i < edges.size(); i++) {int u = edges[i].u, v = edges[i].v;if (find(u) != find(v)) {F[find(u)] = find(v);G[u].push_back(Edge(u, v, edges[i].l));G[v].push_back(Edge(v, u, edges[i].l));S += sqrt(edges[i].l);}}double ans = 0;for (int i = 1; i <= N; i++) dfs(i, -1, 0, D[i]);for (int i = 1; i <= N; i++)for (int j = i+1; j <= N; j++)ans = max(ans, (P[i] + P[j]) * 1.0 / (S - sqrt(D[i][j])));printf("%.2lf\n", ans);}return 0;}

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