Frogger POJ - 2253 (max in reachable path)

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

The meaning of the question: Given the coordinates of frogs A, B and several stones, now frog A thinks of frog B, A can reach B through any stone, ask the shortest distance among the longest sides of the multiple paths from A to B

Analysis: This problem is the deformation of the shortest path. The minimum value of the total length of the path was previously obtained, and this problem is the minimum value of the longest side in the path. The weight of each side can be calculated by the coordinates, because it is a single source starting point, You can use the SPFA algorithm or the dijkstra algorithm directly.

#include<cstdio>
#include<cstring>
#include<cmath>
#include<queue>
#define Inf 0x3f3f3f3f
using namespace std;
const int N = 205;
double mp[N][N],dis[N];
double x[N],y[N];
int force[N];
int n;
double getdis(int a,int b){
	double X=(x[a]-x[b]) * (x[a]-x[b]);
	double Y=(y[a]-y[b]) * (y[a]-y[b]);
	return sqrt(X+Y);
}
double SPFA(int s){
	for(int i=0;i<=n;i++){
		dis[i]=Inf;
		show [i] = 0;
	}
	queue<int>p;
	dis[s]=0;
	vis [s] = 1;
	p.push(s);
	while(!p.empty()){
		int i=p.front();
		p.pop();
		show [i] = 0;
		for(int j=1;j<=n;j++){
			if(dis[j]>max(dis[i],mp[i][j])){
				dis[j]=max(dis[i],mp[i][j]);
				if(!vis[j]){
					vis[j]=1;
					p.push(j);
				}
			}
		}
	}
	return dis[2];
}
int main(){
	int Case=0;
	while(scanf("%d",&n)!=EOF&&n){
		memset(mp,0,sizeof(mp));
		for(int i=1;i<=n;i++){
			scanf("%lf%lf",&x[i],&y[i]);
			for(int j=1;j<i;j++)
			   mp[i][j]=mp[j][i]=getdis(i,j);
		}
		printf("Scenario #%d\n",++Cas);
		printf("Frog Distance = %.3f\n",SPFA(1));
		puts("");
	}
	return 0;
}