ANARC08F - Einbahnstrasse


Einbahnstrasse (German for a one-way street) is a street on which vehicles should only move in one direction. One reason for having one-way streets is to facilitate a smoother flow of traffic through crowded areas. This is useful in city centers, especially old cities like Cairo and Damascus. Careful planning guarantees that you can get to any location starting from any point. Nevertheless, drivers must carefully plan their route in order to avoid prolonging their trip due to one-way streets. Experienced drivers know that there are multiple paths to travel between any two locations. Not only that, there might be multiple roads between the same two locations. Knowing the shortest way between any two locations is a must! This is even more important when driving vehicles that are hard to maneuver (garbage trucks, towing trucks, etc.)

You just started a new job at a car-towing company. The company has a number of towing trucks parked at the company's garage. A tow-truck lifts the front or back wheels of a broken car in order to pull it straight back to the company's garage. You receive calls from various parts of the city about broken cars that need to be towed. The cars have to be towed in the same order as you receive the calls. Your job is to advise the tow-truck drivers regarding the shortest way in order to collect all broken cars back in to the company's garage. At the end of the day, you have to report to the management the total distance traveled by the trucks.

Input

Your program will be tested on one or more test cases. The first line of each test case specifies three numbers (N , C , and R ) separated by one or more spaces. The city has N locations with distinct names, including the company's garage. C is the number of broken cars. R is the number of roads in the city. Note that 0 < N < 100 , 0 <= C < 1000 , and R < 10000 . The second line is made of C + 1 words, the first being the location of the company's garage, and the rest being the locations of the broken cars. A location is a word made of 10 letters or less. Letter case is significant. After the second line, there will be exactly R lines, each describing a road. A road is described using one of these three formats:

A --v-> B
A <-v-- B
A <-v-> B

A and B are names of two different locations, while v is a positive integer (not exceeding 1000) denoting the length of the road. The first format specifies a one-way street from location A to B , the second specifies a one-way street from B to A , while the last specifies a two-way street between them. A , "the arrow", and B are separated by one or more spaces. The end of the test cases is specified with a line having three zeros (for N , C , and R .)

The test case in the example below is the same as the one in the figure.

Output

For each test case, print the total distance traveled using the following format:

k. V

Where k is test case number (starting at 1,) is a space, and V is the result.

Example

Input:
4 2 5
NewTroy Midvale Metrodale
NewTroy   <-20-> Midvale
Midvale   --50-> Bakerline
NewTroy    <-5-- Bakerline
Metrodale <-30-> NewTroy
Metrodale  --5-> Bakerline
0 0 0

Output:
1. 80

hide comments
yogesh0201: 2018-09-18 09:18:38

If a road doesn't exist between two cities then distance between them should be taken as 1000000000 otherwise some test cases might fail in which a broken car is in a city with no connectivity.

amulyagaur: 2017-10-23 09:19:30

simple floyd-warshall :)

Ishaan: 2015-06-30 23:00:41

I am getting wrong answer. Have tried every possible case. does anyone have any idea y??

parijat bhatt: 2015-06-17 16:24:39

places for broken cars are duplicates

GAURAV CHANDEL: 2015-05-01 12:45:52

AC with floyd-warshall...

vishal: 2015-01-24 12:35:36

a must solve prob of
dijkstra algorithm
apply it on garage reverse the graph and apply it back and add the value
try MICEMAZE.

Jens Stimpfle: 2014-02-11 03:16:35

At first I thought there were actually up to 180 distinct names (found that out via "binary search" and assertions), but then I noticed that the input has DOS line endings (so my program created more names than there actually are). I think this is normally not the case with other problems, at least it was totally unexpected for me.

Last edit: 2014-02-11 03:16:57
laith: 2012-06-28 19:02:52

am getting wrong answer but am sure my answer is correct i try the input that was used in the contests and compare my output with the output file they where matched !!!!?any idea

:D: 2011-06-12 18:47:29

I don't know, but I guess you can assume the driving cost to be 0 then.

Egor: 2011-02-13 11:18:39

whether the broken car is in town with the station?


Added by:Ahmed Aly
Date:2009-07-04
Time limit:0.174s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ANARC 2008