POJ 2253 Frogger Floyd

原题链接：http://poj.org/problem?id=2253

Frogger

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 30637		Accepted: 9883

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

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

Source

Ulm Local 1997

题意

有个青蛙要从某个石头跳到另外一个石头，告诉你石头的坐标，求最小的跳跃范围。跳跃范围的定义是：对于任意一条可行路径中最长的跳跃。

题解

改造floyd，floyd是dp的思想，那么我们可以定义，dp[i][j]表示从i到j的最小跳跃范围，那么dp[i][j]=min(dp[i][j],max(dp[i][k],dp[k][j]))

代码

#include<iostream>
#include<queue>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<cmath>
#define INF 1008611
#define MAX_N 234
using namespace std;

double f[MAX_N][MAX_N];

double x[MAX_N],y[MAX_N];
int n;
int cas=;
int main() {
    while (true) {
        scanf("%d", &n);
        if (n == )break;
        for (int i = ; i < n; i++)cin >> x[i] >> y[i];
        for (int i = ; i < n; i++) {
            f[i][i]=;
            for (int j = ; j < n; j++)
                f[i][j] = f[j][i] = sqrt(pow(x[i] - x[j], 2.0) + pow(y[i] - y[j], 2.0));
        }
        for (int k = ; k < n; k++)
            for (int j = ; j < n; j++)
                for (int i = ; i < n; i++)
                    f[i][j] = min(f[i][j], max(f[i][k], f[k][j]));
        printf("Scenario #%d\nFrog Distance = %.3lf\n\n", ++cas, f[][]);
    }
    return ;
}