Program | FROGGER.C, FROGGER.CPP, FROGGER.PAS |
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.
The input file 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.
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