poj 2253

/*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. 




Input


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. 


Output


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. 


Sample Input
2
0 0
3 4


3
17 4
19 4
18 5


0




Sample Output
Scenario #1
Frog Distance = 5.000


Scenario #2
Frog Distance = 1.414
这是图论，最短路类的题型

*/
#include<iostream>
#include<cmath>
#include <cstring> 
using namespace std;
const int Max = 205;
const int inf = 99999999;
 
struct{
    int x, y;
}sto[Max];
int n;
float edge[Max][Max], dict[Max];
bool vis[Max];
 
float find_edge(int u, int v){   //  计算两石头之间的距离，即边长。
     float dx = sto[u].x - sto[v].x;
     float dy = sto[u].y - sto[v].y;
     return sqrt(dx * dx + dy * dy);
}
 
float max(float a, float b){
    return a > b ? a : b;
}
 
void dijkstra(){   //  dij的变形。
    int now = 0, count = n - 1;
    while(count --){
        int k;
        float min_dis = inf;
        for(int i = 1; i < n; i ++)
            if(!vis[i]){
                if(dict[i] > max(dict[now], edge[i][now]))  //  取路程中最长的值。
                    dict[i] = max(dict[now], edge[i][now]);
                if(min_dis > dict[i]){
                    min_dis = dict[i];
                    k = i;
                }
            }
        if(k == 1)  return;  //  若sto[1]已被访问，则说明已得到sto[0]到sto[1]的最短路径。跳出。
        now = k;
        vis[k] = true;
    }
}
 
int main(){
    int t = 0;
    while(cin >> n && n != 0){
        memset(vis, false, sizeof(vis));
        vis[0] = true;
    for(int i = 1; i < n; i ++)
        dict[i] = inf;
        for(int i = 0; i < n; i ++){
            cin >> sto[i].x >> sto[i].y;  //  这样Freddy的点默认为sto[0]，Fiona的点默认为sto[1]。
            for(int j = i - 1; j >= 0; j --){
                float val = find_edge(i, j);
                edge[i][j] = edge[j][i] = val;
            }
        }
        dijkstra();
        printf("Scenario #%d\nFrog Distance = %.3f\n\n", ++t, dict[1]);
    }
    return 0;
}