POJ 2253 Frogger (deformation of the shortest path)

Frogger

Time Limit:1000 MS		Memory Limit:65536 K
Total Submissions:17842		Accepted:5818

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 login Ming 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 in 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

Source

When the Ulm Local 1997 shortest circuit is relaxed, the condition can be changed. DIjkstra Algorithm

/* POJ 2253 */# include <stdio. h> # include <algorithm> # include <string. h> # include <math. h ># include <iostream> using namespace std; const int MAXN = 220; const int INF = 0x3f3f3f3f; //************************************** * ********************** // Dijkstra-array implementation O (n ^ 2) // single-source shortest path // lowcost [] --- distance from beg to other points // No path is recorded // start with node number 1 //***** **************************************** * ***************** # define INF 0x3f3f3f // This infinity cannot be too Large, preventing backend Overflow # define typec doublebool vis [MAXN]; void Dijkstra (typec cost [] [MAXN], typec lowcost [MAXN], int n, int beg) {typec minc; int I, j, w; memset (vis, false, sizeof (vis); vis [beg] = true; for (I = 1; I <= n; I ++) lowcost [I] = cost [beg] [I]; lowcost [beg] = 0; for (I = 1; I <n; I ++) {minc = INF; for (j = 1; j <= n; j ++) if (! Vis [j] & lowcost [j] <minc) {minc = lowcost [j]; w = j;} if (minc> = INF) break; vis [w] = true; for (j = 1; j <= n; j ++) if (! Vis [j] & max (lowcost [w], cost [w] [j]) <lowcost [j]) lowcost [j] = max (lowcost [w], cost [w] [j]) ;}} //************************************** * ********************** double dist [MAXN]; double map [MAXN] [MAXN]; struct Node {int x, y;} node [MAXN]; double dis (Node a, Node B) {return sqrt (double) (. x-b.x) * (. x-b.x) +. y-b.y) * (. y-b.y);} int main () {// freopen ("in.txt", "r", stdin); // freopen ("out.txt", "w", stdout ); int n; int iCase = 0; while (scanf ("% d", & n), n) {iCase ++; for (int I = 1; I <= n; I ++) scanf ("% d", & node [I]. x, & node [I]. y); for (int I = 1; I <= n; I ++) for (int j = I; j <= n; j ++) {if (I = j) map [I] [j] = 0; else map [I] [j] = map [j] [I] = dis (node [I], node [j]);} Dijkstra (map, dist, n, 1); printf ("Scenario # % d \ nFrog Distance =", iCase); printf ("%. 3f \ n ", (dist [2]); // on POJ, G ++ can only use % f // C ++ and can % lf} return 0 ;}