Frogger （弗洛伊德）

Problem Description

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

20 03 4317 419 418 50

 

Sample Output

Scenario #1Frog Distance = 5.000Scenario #2Frog Distance = 1.414

弗洛伊德思想：思想：从i--->j 的距离大于从i-->k加k-->j 的和，那么就用这个更短的来更新i-->j的距离

这个题稍有带动，要求的是，在路径里的最大距离，在所有的路径的这种距离比一比，最小的是多少？

//弗洛伊德 算法 求最短路径问题 这里的问题问的是 i----->j ，路径里的最大距离，在所有的路径里，最小是多少？ // Frogger#if 0#include<iostream>#include<cmath>#include<iomanip>#include<cstring>using namespace std;int main(){int n,ans=0;while(cin>>n&&n){double point[201][2]={0},mapp[201][201]={0};for(int i=0; i<n; i++)cin>>point[i][0]>>point[i][1];for(int i=0; i<n; i++){for(int j=0; j<n; j++){mapp[i][j]=mapp[j][i]=sqrt((point[i][0]-point[j][0])*(point[i][0]-point[j][0])+(point[i][1]-point[j][1])*(point[i][1]-point[j][1]));}}for(int k=0; k<n; k++){for(int i=0; i<n; i++){for(int j=0; j<n; j++){if(i!=j&&i!=k&&j!=k){mapp[i][j]=min(mapp[i][j],max(mapp[i][k],mapp[k][j]));}}}}cout<<"Scenario #"<<++ans<<endl<<"Frog Distance"<<" = "<<fixed<<setprecision(3)<<mapp[0][1]<<endl<<endl; }}#endif