DMPG '15 S6 - Apples to Oranges

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

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:

  • 1 orange → 0.5 apples
  • 1 apple → 2 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:

  • 1 orange → 2 apples
  • 1 apple → 0.5 oranges
  • 1 apple → 1 grape
  • 1 grape → 1 orange

Then Sun can exchange his original apple for a grape, a grape for an orange, and an orange for 2 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 N (2 \le N \le 500), the number of different types of fruit, and M (2 \le M \le 4\,000), the number of exchange rates.

The next N lines will each contain the name of a fruit, no longer than 25 alphanumeric characters long. Note that Sun starts with one apple, so APPLES will always be a type of fruit given.

Finally, the last M lines will contain an exchange in the space-separated form of a, b, c, indicating that fruit a may be exchanged for c (0.0 < c \le 10\,000.0) units of fruit b.

Output Specification

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

Sample Input

3 4

Sample Output



  • 0
    juho  commented on March 17, 2018, 10:59 p.m.


    Can anyone please check my code and see what I am doing wrong? Thanks in advance.

  • 2
    Evan_Yu123  commented on Sept. 5, 2017, 8:50 p.m.

    Is double accurate enough for this question?

    • 0
      Pleedoh  commented on Sept. 6, 2017, 11:13 a.m.


  • 0
    TheZombieCloud  commented on June 25, 2017, 5:07 p.m.

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

    • 0
      eric574  commented on June 25, 2017, 8:30 p.m.

      Have you considered decimals?

      • 0
        TheZombieCloud  commented on June 25, 2017, 10:27 p.m.

        I think so. I've used double to for the decimals. Idk if the decimals would be long enough for some precision errors though.

        • 2
          eric574  commented on June 25, 2017, 11:12 p.m. edit 3

          I checked your code and the problem doesn't seem to be decimals. In fact, some parts of your code seem to be unnecessary. The problem involves performing a BFS (or a similar SSSP algorithm), which means that you don't have to check for the indegree or outdegree. Also, optimize your code a bit and you will AC. (Try using a HashMap)

  • -2
    cranberrysauce26  commented on June 20, 2017, 7:22 a.m.

    Decimals are a pain in the ass

  • 0
    root  commented on June 18, 2017, 7:10 p.m. 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.

    • 1
      wleung_bvg  commented on June 18, 2017, 7:52 p.m.

      The exchange rates are decimals

      • 0
        root  commented on June 18, 2017, 8:14 p.m.

        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.

  • 0
    Ninjaclasher  commented on June 18, 2017, 5:27 p.m.

    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.

    • 1
      wleung_bvg  commented on June 18, 2017, 7:57 p.m.

      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).

      • 3
        Ninjaclasher  commented on June 18, 2017, 9:14 p.m.

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

  • -1
    root  commented on June 18, 2017, 1:51 p.m. 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.

  • 2
    atarw  commented on March 27, 2016, 3:30 p.m.
    trading partial fruits

    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?

    • 1
      arock  commented on March 27, 2016, 4:31 p.m.


  • 6
    bruce  commented on June 23, 2015, 3:21 p.m.
    Description conflicts with test case

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

    • 2
      Xyene  commented on June 25, 2015, 10:27 p.m.

      Thanks for noticing: the upper bound for M is 4000. I've updated the problem statement.

  • 0
    BMP  commented on May 30, 2015, 2:36 p.m.
    Trading Back

    Can you trade back?

    1 Grape = 3 Oranges.

    Is this equivalent to:

    3 Oranges = 1 Grape?

    • 9
      jimgao  commented on Dec. 28, 2015, 9:12 p.m.


    • 1
      Xyene  commented on May 30, 2015, 3:20 p.m.


  • -1
    ThorhillTeam3_15  commented on May 28, 2015, 11:30 a.m.
    partial fruits

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

    • 2
      Xyene  commented on May 28, 2015, 11:32 a.m.