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Task 1: "FUSC Sequence
Write a script to generate first 50 members of FUSC Sequence. Please
refer to http://oeis.org/A002487 for more information.
The sequence defined as below:
fusc(0) = 0
fusc(1) = 1
for n > 1:
when n is even: fusc(n) = fusc(n / 2),
when n is odd: fusc(n) = fusc((n-1)/2) + fusc((n+1)/2)
"
My notes: looks like a case for Memoize to make this highly recursive
function efficient. No, turns out it's quite efficient, so we don't
even need Memoize!
Task 2: "NIM Game
Write a script to simulate the NIM Game.
It is played between 2 players. For the purpose of this task, let assume
you play against the machine.
There are 3 simple rules to follow:
a) You have 12 tokens
b) Each player can pick 1, 2 or 3 tokens at a time
c) The player who picks the last token wins the game
"
My notes: damn! I was really looking forward to this, but THAT'S NOT
NIM! That's a similar "simple take away game" as described here:
https://www.cs.cmu.edu/afs/cs/academic/class/15859-f01/www/notes/comb.pdf
(although that starts with 21 tokens, not 12).
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