poj2253 求生成树的最大边最小值

描述 Freddy Frog is sitting on a stone in the middle of a lake. Suddenly he notices Fiona Frog who is sitting on another stone. He plans to visit her, but since the water is dirty and full of tourists' sunscreen, he wants to avoid swimming and instead reach her by jumping. Unfortunately Fiona's stone is out of his jump range. Therefore Freddy considers to use other stones as intermediate stops and reach her by a sequence of several small jumps. To execute a given sequence of jumps, a frog's jump range obviously must be at least as long as the longest jump occuring in the sequence. The frog distance (humans also call it minimax distance) between two stones therefore is defined as the minimum necessary jump range over all possible paths between the two stones. You are given the coordinates of Freddy's stone, Fiona's stone and all other stones in the lake. Your job is to compute the frog distance between Freddy's and Fiona's stone. 输入 The input will contain one or more test cases. The first line of each test case will contain the number of stones n (2<=n<=200). The next n lines each contain two integers xi,yi (0 <= xi,yi <= 1000) representing the coordinates of stone #i. Stone #1 is Freddy's stone, stone #2 is Fiona's stone, the other n-2 stones are unoccupied. There's a blank line following each test case. Input is terminated by a value of zero (0) for n. 输出 For each test case, print a line saying "Scenario #x" and a line saying "Frog Distance = y" where x is replaced by the test case number (they are numbered from 1) and y is replaced by the appropriate real number, printed to three decimals. Put a blank line after each test case, even after the last one. 样例输入 2 0 0 3 4 3 17 4 19 4 18 5 0 样例输出 Scenario #1 Frog Distance = 5.000 Scenario #2 Frog Distance = 1.414

思路：建图后，本题求的是在所有从顶点1到顶点2的路径中，使得路径上最大边的权值，最小，求出该权值 容易想多用kurscal算法

注意输出：c++交时，输出用%lf。g++则用%f

#include <cstdio> #include <cstring> #include <algorithm> #include <cstdlib> #include <cmath> #define N 205 using namespace std; const double inf = 999999999.0; typedef struct note { int x; int y; }point; typedef struct node { int u; int v; double w; }edge; int n,f[N]; point a[N]; edge e[N*N]; double minjump; void init() { for (int i = 1; i <= n; i++) f[i] = i; } int find(int x)//找父节点 { if (f[x] == x) return x; else return f[x] = find(f[x]); } int merge(int x, int y) { int t1, t2; t1 = find(x); t2 = find(y); if (t1 != t2)//根不一样 { f[t2] = t1; return 1; } return 0; } int same(int x, int y) { return find(x) == find(y); } int cmp(edge a, edge b) { return a.w < b.w; } int main() { int cas = 0, vis[N]; while (scanf("%d", &n) != EOF && n) { int cnt = 0; minjump = 0; memset(vis, 0, sizeof(vis)); for (int i = 1; i <= n; i++) scanf("%d%d", &a[i].x, &a[i].y); //存储边 for (int i = 1; i <= n; i++) { for (int j = i + 1; j <= n; j++) { e[cnt].u = i; e[cnt].v = j; e[cnt].w = sqrt(pow(a[i].x - a[j].x, 2) + pow(a[i].y - a[j].y, 2)); cnt++; } } int m = cnt;//m条边 sort(e, e + m, cmp); init();//初始化集合 cnt = 0; for (int i = 0; i < m; i++) { if (merge(e[i].u, e[i].v)) { if (minjump < e[i].w) minjump = e[i].w; } if (same(1,2)) break;//当1,2位于同一集合时，说明已找到生成树 } if (cas) printf("\n"); printf("Scenario #%d\n", ++cas); printf("Frog Distance = %.3lf\n", minjump); } return 0; }

方法2：迪杰斯特拉变式，或者floyd也行

把松弛的方程改为dis[i] = min(dis[i], max(dis[k], map[k][i]));

#include <cstdio> #include <cstring> #include <cstdlib> #include <algorithm> #include <cmath> #define N 205 #define INF 99999999 using namespace std; typedef struct node { int x; int y; }point; point note[N]; int n; double map[N][N]; double dis[N]; int vis[N]; double distance(point a, point b) { return sqrt(pow(a.x - b.x, 2) + pow(a.y - b.y, 2)); } void dijkstra() { memset(vis, 0, sizeof(vis)); vis[1] = 1;//标记第一个点 dis[1] = 0; for (int i = 2; i <= n; i++) dis[i] = INF; for (int i = 1; i <= n; i++) dis[i] = map[1][i]; for (int i = 1; i <= n-1; i++)//循环n-1次 { /*找出离起点最近的点*/ double minn = INF; int k = -1; for (int j = 1; j <= n; j++) { if (!vis[j] && dis[j] < minn) { minn = dis[j]; k = j; } } vis[k] = 1; for (int i = 1; i <= n; i++)//松弛操作 { if (!vis[i]) dis[i] = min(dis[i], max(dis[k], map[k][i])); //dis的含义为起点到顶点i所有路径中最长边的最小值。 } } } int main() { int cnt = 0; while (scanf("%d", &n) != EOF && n) { //建图,起点为1，终点为2 for (int i = 1; i <= n; i++) scanf("%d%d", ¬e[i].x, ¬e[i].y); for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) { map[i][j] = map[j][i] = distance(note[i], note[j]); } } //迪杰斯特拉算法 dijkstra(); //输出 if (cnt) printf("\n"); printf("Scenario #%d\nFrog Distance = %.3lf\n",++cnt,dis[2]); } return 0; }