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# [Google Foobar Challenge](https://foobar.withgoogle.com/)
## Level3
### doomsday-fuel
* Completed in: 2 days, 19 hrs, 36 mins, 16 secs.
* Reference
* [L26.6 Absorption Probabilities, MIT OpenCourseWare](https://www.youtube.com/watch?v=vEsUsaK1HBk)
### the-grandest-staircase-of-them-all
* Completed in: 16 hrs, 38 mins, 52 secs.
* DP
### bomb-baby
* Completed in: 1 hr, 46 mins, 55 secs.
* GCD
## Level4
### running-with-bunnies
* Completed in: 1 day, 4 hrs, 40 mins, 40 secs.
* Shortest Paths
### escape-pods
* Completed in: 1 day, 2 hrs, 16 mins, 11 secs.
* Minimum cut
## Level5
### expanding-nebula
* Completed in: 6 hrs, 49 mins, 26 secs.
* DP & Optimization
## Encrypted message
CFcSBwgCCBoHRhkKU1cGAA4AGU5YQR5THBwNFwoGGAxTQQMQVBUSBg4EAAwQRhUQVBUHFAQTGRpT QQMQVBkPERkECQAWDVwXX1BGEwgJBAwCBFRVHQRGUlFBShwaDVZTGBUFVUdBShsVA1tZBwNGUlFB ShoVB1wXX1BGFAQOSklOQR5HGh5AVRY=
## Extra
* Requested problems after level 5 clear
### dodge-the-laser
* Completed in: 2 days, 20 hrs, 22 mins, 39 secs.
* References
* [Beatty sequence, Wikipedia](https://en.wikipedia.org/wiki/Beatty_sequence)
* [How to find A001951 A Beatty sequence: a(n)=floor(n\*sqrt(2)), StackExchange](https://math.stackexchange.com/questions/2052179/how-to-find-sum-i-1n-left-lfloor-i-sqrt2-right-rfloor-a001951-a-beatty-s)
* [Beatty Sequence와 Rayleigh's theorem, blog](https://tamref.com/36)
* Feedback
> [level5/dodge-the-lasers] (1) Some of the text readme.txt are duplicated. (2) Though the input type is string, Java input example uses quotes for string instead of double quotation marks. (3) While expected output type is string, in the output example does not use quotes. So the readers can confuse the return type.
### disorderly-escape
* Completed in: 9 days, 17 hrs, 30 mins, 3 secs.
* Reference
* [Burnside's lemma: counting up to symmetries, Youtube](https://www.youtube.com/watch?v=D0d9bYZ_qDY)
### bringing-a-gun-to-a-trainer-fight
* Completed in: 1 day, 23 hrs, 49 mins, 54 secs.
### free-the-bunny-workers
* Completed in: 3 hrs, 6 mins, 8 secs.
### distract-the-trainers
* Completed in: 1 day, 23 hrs, 21 secs.
* Check Loop Proof
1. (ac, bc) => (2ac, bc-ac) = (a, b) => (2a, b-a)
* a < b
1. (ac, bc+d) => (2ac, bc+d-ac) = (2ac, (b-a)c+d)
* a < b and 0 < d < c
1. (a, 2n-a) => (2a, 2n-2a) = (a, n-a)
* a < n
1. (x, y) will loop iff (x + y) % 2 == 1
* x and y are relatively prime
* Reference
* [Maximum Matching in General Graph](https://www.secmem.org/blog/2020/04/18/Blossom/)
### extra/prepare-the-bunnies-escape
* Completed in: 3 hrs, 17 mins, 20 secs.