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

题目大意:
有N块石头,1—N。每块石头都有x,y坐标,青蛙一号站在第一块石头上,青蛙二号站在第二块石头上,
青蛙一号想要通过这N块石头去找青蛙二号,因为青蛙一号可以踩在任何一块石头上,所以从第一块石头到第二块石头有很多条路径,
假设为X,在每一条路径中,都有跳跃范围(即在这条路径中,两块石头之间的最大距离),那么一共有X个跳跃范围,
我们要求的就是这X个跳跃范围的最小值,就是the frog distance。 解题思路:
先求出所有的坐标之间的距离放入二维数组内,在判断那个是最小的。
#include<stdio.h>
#include<math.h>
#include<string.h>
const double inf=0x3f3f3f3;
int x[201],y[201];
double g[201][201],d[201],max;
int n;
void distence()
{
int i,r;
double minc;
bool used[201];
for(i=0; i<n; i++)
{
d[i]=g[0][i];
used[i]=false;
}
d[0]=0;
used[0]=true;
r=0;
while(r!=1)
{
minc=inf;
for(i=0; i<n; i++)
if(!used[i]&&d[i]<minc)
{
minc=d[i];
r=i;
}
if(minc>max) max=minc;
for(i=0; i<n; i++)
{
if(!used[i]&&g[r][i]<inf&&d[i]>g[r][i])
d[i]=g[r][i];
used[r]=true;
}
}
}
int main()
{
int cas=1;
while((scanf("%d",&n),n)!=0)
{
max=0;
for(int i=0; i<n; i++)
scanf("%d%d",&x[i],&y[i]);
memset(g,inf,sizeof(g));
for(int i=0;i<n;i++)
for(int j=0;j<n;j++)
{
g[i][j]=sqrt((1.0*x[i]-1.0*x[j])*(1.0*x[i]-1.0*x[j])+
(1.0*y[i]-1.0*y[j])*(1.0*y[i]-1.0*y[j]));
} distence();
printf("Scenario #%d\n",cas++);
printf("Frog Distance = %0.3lf\n",max);
printf("\n");
}
return 0;
}

  


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