## DMPG '15 S6 - Apples to Oranges

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Points:17 (partial)
Time limit:3.0s
Memory limit:256M
Authors:

Problem type

They say you cannot compare apples to oranges, but you actually can! In fact, by using money as a medium of exchange, we can compare anything in terms of value. Sun has a single apple. Being the incredibly talented person he is, he's visit a variety of markets with different rates of exchange for his apple. His goal is to obtain infinite apples, and therefore total control of the fruit market.

Suppose the rates of exchange are:

• orange → apples
• apple → oranges

Then it is easy to see that it is in fact impossible to obtain more than one apple through exchanges.

However, if the exchange is:

• orange → apples
• apple → oranges
• apple → grape
• grape → orange

Then Sun can exchange his original apple for a grape, a grape for an orange, and an orange for apples! He can then repeat this to get infinite apples.

The next trivial step is to note that he can now dominate and control the entire apple market.

Your goal is to find out if Sun's fruit market domination scheme is feasible.

#### Input Specification

The first line of input will contain two space-separated integers , the number of different types of fruit, and , the number of exchange rates.

The next lines will each contain the name of a fruit, no longer than alphanumeric characters long. Note that Sun starts with one apple, so APPLES will always be a type of fruit given.

Finally, the last lines will contain an exchange in the space-separated form of , , , indicating that fruit may be exchanged for units of fruit .

#### Output Specification

Output YA on a single line if Sun can get infinite apples, or NAW if he can not.

#### Sample Input

3 4
APPLES
ORANGE
GRAPE
ORANGE APPLES 2.0
APPLES ORANGE 0.5
APPLES GRAPE 1.0
GRAPE ORANGE 0.5

#### Sample Output

NAW

• TheZombieCloud
commented on June 25, 2017

I've been stuck on this problem for a few hours now. Is my idea wrong or is it something else?

• cranberrysauce26
commented on June 20, 2017

Decimals are a pain in the ass

• root
commented on June 18, 2017 edited

What exactly is the format of the input? The sample case seems to imply that ".0" will be included in the case that it is an integer. However, experimentation says otherwise.

• wleung_bvg
commented on June 18, 2017

The exchange rates are decimals

• root
commented on June 18, 2017

Thanks, I know that they are decimals, the issue seems to be with the format string, in theory, it should work with integers and decimals.

• Ninjaclasher
commented on June 18, 2017

Am I missing something really big here? I have no clue what's wrong......and the fact that there's no output doesn't help it the slightest.

• wleung_bvg
commented on June 18, 2017

I just ran your submission. It's essentially correct, except that you need to deal with floating point precision when exiting BFS (something like 1e-6 should work).

• Ninjaclasher
commented on June 18, 2017

Thanks so much! Such an easy fix that I would have never found....but now comes the real question....how does a few extra decimal places affect the final result?

• root
commented on June 18, 2017 edit 2

Hint: If you're like me, and tried to scan the input as two integers separated by a dot, be aware that the input contains input like "1e-6". And a note to future problem setters, please, if only for my sanity alone, mention it in the problem statement if you have numbers like that. I wasted eight hours today on this one problem.

• atarw
commented on March 27, 2016

if I have 0.5 of fruit A, and the exchange rate between fruit A and fruit B is 1:2, does that mean that I can trade 0.5 of fruit A for 1 of fruit B?

• arock
commented on March 27, 2016

Yes

• XIAOAGE
commented on Dec. 27, 2015 edited
No judge ?

So sad....................should check it b4 code this......

oh, i guess every problem doesn't have judge at the moment LOL nvm

• bruce
commented on June 23, 2015
Description conflicts with test case

In description, M <= 1000. But there are at least 3 cases M > 1000.

• Xyene
commented on June 25, 2015

Thanks for noticing: the upper bound for is . I've updated the problem statement.

• BMP
commented on May 30, 2015

1 Grape = 3 Oranges.

Is this equivalent to:

3 Oranges = 1 Grape?

• jimgao
commented on Dec. 28, 2015

NAW

• Xyene
commented on May 30, 2015

No.

• ThorhillTeam3_15
commented on May 28, 2015
partial fruits

is it possible for him to exchange a single apple for half an orange for example?

• Xyene
commented on May 28, 2015

Yes.