Thank you so much. I don’t know why I missed that, but now it makes sense.

MC

On Tue, Apr 7, 2020 at 4:58 PM 'Facundo Parra' via Google Code Jam <
google-code@googlegroups.com> wrote:

> Hi!
> I don't know if it was updated or maybe you missed it, but in the analysis
> section it mentions "We can greedily pick any perfect matching for each row 
> *starting
> with the rows with B and C on their diagonal*. ".
> So yeah, there is a condition.
> Hope it helps you.
> Cheers.
>
> El lunes, 6 de abril de 2020 a las 21:56:00 UTC-3, MC escribió:
>
>> Hi,
>>
>> I read the analysis of the '
>> https://codingcompetitions.withgoogle.com/codejam/round/000000000019fd27/0000000000209aa0',
>> and it said you can fill each row greedily, but it doesn't work for some
>> cases.
>>
>> Case 1)
>> N=4, K=10 and A=1, B=2, C=3,
>> I filled the first row like below,
>>   1   4   3   2
>>   0   1   0   0
>>   0   0   2   0
>>   0   0   0   3
>> (0 means an unfiled cell)
>> But it cannot be filled correctly because both colum 3 and 4 should have
>> filled with 4.
>>
>> Case 2)
>> N=5, K=7, and A=1, B=2, C=2,
>> If filled the trace like,
>>   1   5   2   4   3
>>   2   1   5   3   4
>>   0   0   1   0   0
>>   0   0   0   2   0
>>   0   0   0   0   2
>> It either cannot be filled correctly because both colum 4 and 5 should
>> have filled with 5.
>>
>> When I filled a trace reversely - like CBAA...A - it works well. Is there
>> any condition that I missed?
>> And also, I couldn't prove the last part of the solution which Hall's
>> Marriage is used for. If any hint or proof of it, I would appreciate.
>>
>> Thank you!
>> Myeongchan
>>
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