No account? Create an account
 Factors and Factorials - Lindsey Kuper [entries|archive|friends|userinfo]
Lindsey Kuper

 [ website | composition.al ] [ userinfo | livejournal userinfo ] [ archive | journal archive ]

Factors and Factorials [Jan. 7th, 2009|01:49 pm]
Lindsey Kuper
 [ Tags | programming ]

At Streamtech, where I'm thinking about applying for an internship, they say, "When applying for a programming job, feel free to solve one of these problems in your language of choice and send along the code." You know I had to pick the one that was about factorials.

Here's what the output looks like for 2 through 100. Kind of pretty, don't you think?

```\$ petite --script factors.scm
2! =  1
3! =  1  1
4! =  3  1
5! =  3  1  1
6! =  4  2  1
7! =  4  2  1  1
8! =  7  2  1  1
9! =  7  4  1  1
10! =  8  4  2  1
11! =  8  4  2  1  1
12! = 10  5  2  1  1
13! = 10  5  2  1  1  1
14! = 11  5  2  2  1  1
15! = 11  6  3  2  1  1
16! = 15  6  3  2  1  1
17! = 15  6  3  2  1  1  1
18! = 16  8  3  2  1  1  1
19! = 16  8  3  2  1  1  1  1
20! = 18  8  4  2  1  1  1  1
21! = 18  9  4  3  1  1  1  1
22! = 19  9  4  3  2  1  1  1
23! = 19  9  4  3  2  1  1  1  1
24! = 22 10  4  3  2  1  1  1  1
25! = 22 10  6  3  2  1  1  1  1
26! = 23 10  6  3  2  2  1  1  1
27! = 23 13  6  3  2  2  1  1  1
28! = 25 13  6  4  2  2  1  1  1
29! = 25 13  6  4  2  2  1  1  1  1
30! = 26 14  7  4  2  2  1  1  1  1
31! = 26 14  7  4  2  2  1  1  1  1  1
32! = 31 14  7  4  2  2  1  1  1  1  1
33! = 31 15  7  4  3  2  1  1  1  1  1
34! = 32 15  7  4  3  2  2  1  1  1  1
35! = 32 15  8  5  3  2  2  1  1  1  1
36! = 34 17  8  5  3  2  2  1  1  1  1
37! = 34 17  8  5  3  2  2  1  1  1  1  1
38! = 35 17  8  5  3  2  2  2  1  1  1  1
39! = 35 18  8  5  3  3  2  2  1  1  1  1
40! = 38 18  9  5  3  3  2  2  1  1  1  1
41! = 38 18  9  5  3  3  2  2  1  1  1  1  1
42! = 39 19  9  6  3  3  2  2  1  1  1  1  1
43! = 39 19  9  6  3  3  2  2  1  1  1  1  1  1
44! = 41 19  9  6  4  3  2  2  1  1  1  1  1  1
45! = 41 21 10  6  4  3  2  2  1  1  1  1  1  1
46! = 42 21 10  6  4  3  2  2  2  1  1  1  1  1
47! = 42 21 10  6  4  3  2  2  2  1  1  1  1  1  1
48! = 46 22 10  6  4  3  2  2  2  1  1  1  1  1  1
49! = 46 22 10  8  4  3  2  2  2  1  1  1  1  1  1
50! = 47 22 12  8  4  3  2  2  2  1  1  1  1  1  1
51! = 47 23 12  8  4  3  3  2  2  1  1  1  1  1  1
52! = 49 23 12  8  4  4  3  2  2  1  1  1  1  1  1
53! = 49 23 12  8  4  4  3  2  2  1  1  1  1  1  1
1
54! = 50 26 12  8  4  4  3  2  2  1  1  1  1  1  1
1
55! = 50 26 13  8  5  4  3  2  2  1  1  1  1  1  1
1
56! = 53 26 13  9  5  4  3  2  2  1  1  1  1  1  1
1
57! = 53 27 13  9  5  4  3  3  2  1  1  1  1  1  1
1
58! = 54 27 13  9  5  4  3  3  2  2  1  1  1  1  1
1
59! = 54 27 13  9  5  4  3  3  2  2  1  1  1  1  1
1  1
60! = 56 28 14  9  5  4  3  3  2  2  1  1  1  1  1
1  1
61! = 56 28 14  9  5  4  3  3  2  2  1  1  1  1  1
1  1  1
62! = 57 28 14  9  5  4  3  3  2  2  2  1  1  1  1
1  1  1
63! = 57 30 14 10  5  4  3  3  2  2  2  1  1  1  1
1  1  1
64! = 63 30 14 10  5  4  3  3  2  2  2  1  1  1  1
1  1  1
65! = 63 30 15 10  5  5  3  3  2  2  2  1  1  1  1
1  1  1
66! = 64 31 15 10  6  5  3  3  2  2  2  1  1  1  1
1  1  1
67! = 64 31 15 10  6  5  3  3  2  2  2  1  1  1  1
1  1  1  1
68! = 66 31 15 10  6  5  4  3  2  2  2  1  1  1  1
1  1  1  1
69! = 66 32 15 10  6  5  4  3  3  2  2  1  1  1  1
1  1  1  1
70! = 67 32 16 11  6  5  4  3  3  2  2  1  1  1  1
1  1  1  1
71! = 67 32 16 11  6  5  4  3  3  2  2  1  1  1  1
1  1  1  1  1
72! = 70 34 16 11  6  5  4  3  3  2  2  1  1  1  1
1  1  1  1  1
73! = 70 34 16 11  6  5  4  3  3  2  2  1  1  1  1
1  1  1  1  1  1
74! = 71 34 16 11  6  5  4  3  3  2  2  2  1  1  1
1  1  1  1  1  1
75! = 71 35 18 11  6  5  4  3  3  2  2  2  1  1  1
1  1  1  1  1  1
76! = 73 35 18 11  6  5  4  4  3  2  2  2  1  1  1
1  1  1  1  1  1
77! = 73 35 18 12  7  5  4  4  3  2  2  2  1  1  1
1  1  1  1  1  1
78! = 74 36 18 12  7  6  4  4  3  2  2  2  1  1  1
1  1  1  1  1  1
79! = 74 36 18 12  7  6  4  4  3  2  2  2  1  1  1
1  1  1  1  1  1  1
80! = 78 36 19 12  7  6  4  4  3  2  2  2  1  1  1
1  1  1  1  1  1  1
81! = 78 40 19 12  7  6  4  4  3  2  2  2  1  1  1
1  1  1  1  1  1  1
82! = 79 40 19 12  7  6  4  4  3  2  2  2  2  1  1
1  1  1  1  1  1  1
83! = 79 40 19 12  7  6  4  4  3  2  2  2  2  1  1
1  1  1  1  1  1  1  1
84! = 81 41 19 13  7  6  4  4  3  2  2  2  2  1  1
1  1  1  1  1  1  1  1
85! = 81 41 20 13  7  6  5  4  3  2  2  2  2  1  1
1  1  1  1  1  1  1  1
86! = 82 41 20 13  7  6  5  4  3  2  2  2  2  2  1
1  1  1  1  1  1  1  1
87! = 82 42 20 13  7  6  5  4  3  3  2  2  2  2  1
1  1  1  1  1  1  1  1
88! = 85 42 20 13  8  6  5  4  3  3  2  2  2  2  1
1  1  1  1  1  1  1  1
89! = 85 42 20 13  8  6  5  4  3  3  2  2  2  2  1
1  1  1  1  1  1  1  1  1
90! = 86 44 21 13  8  6  5  4  3  3  2  2  2  2  1
1  1  1  1  1  1  1  1  1
91! = 86 44 21 14  8  7  5  4  3  3  2  2  2  2  1
1  1  1  1  1  1  1  1  1
92! = 88 44 21 14  8  7  5  4  4  3  2  2  2  2  1
1  1  1  1  1  1  1  1  1
93! = 88 45 21 14  8  7  5  4  4  3  3  2  2  2  1
1  1  1  1  1  1  1  1  1
94! = 89 45 21 14  8  7  5  4  4  3  3  2  2  2  2
1  1  1  1  1  1  1  1  1
95! = 89 45 22 14  8  7  5  5  4  3  3  2  2  2  2
1  1  1  1  1  1  1  1  1
96! = 94 46 22 14  8  7  5  5  4  3  3  2  2  2  2
1  1  1  1  1  1  1  1  1
97! = 94 46 22 14  8  7  5  5  4  3  3  2  2  2  2
1  1  1  1  1  1  1  1  1  1
98! = 95 46 22 16  8  7  5  5  4  3  3  2  2  2  2
1  1  1  1  1  1  1  1  1  1
99! = 95 48 22 16  9  7  5  5  4  3  3  2  2  2  2
1  1  1  1  1  1  1  1  1  1
100! = 97 48 24 16  9  7  5  5  4  3  3  2  2  2  2
1  1  1  1  1  1  1  1  1  1```

The code that does it is about 100 lines of Scheme, not including the comments. The most difficult part was figuring out how to do the formatting stuff.

Now, I really want to put this away and do some Python or something, but now that it's done, I realize that my algorithm isn't very smart: it calculates n! and then goes about finding the prime factors of that big number. But we could actually find the prime factors of n! just by finding the prime factors of each of the numbers up to n and then adding up their multiplicities. (For example, 5! is 5 x 4 x 3 x 2 = 5 x 22 x 3 x 2 = 5 x 3 x 23.) I'm not sure how big n has to get before that starts to be cheaper, but I imagine the answer is "not very big". Maybe I'll play with it more later.

From:
2009-01-07 09:50 pm (UTC)

Python in 37 lines at http://pastie.org/355066
From:
2009-01-08 12:18 am (UTC)

### Re: Your nerdsniping was successful

my output was a little longer, with a slightly different approach: http://pastie.org/355170
From:
2009-01-08 06:08 am (UTC)

### Re: Your nerdsniping was successful

Since I'm giving Haskell another try: 15 lines of code at http://pastie.org/355372 (4 to compute the multiplicities, 11 for the REPL).
From:
2009-01-08 03:15 pm (UTC)

### Re: Your nerdsniping was successful

Nice! I do like mine (and 's (and 's, I think)) for being able to handle arbitrarily large inputs, though.
From:
2009-01-08 03:42 pm (UTC)

### Re: Your nerdsniping was successful

44 lines python, different approach (can't read conform's approach to tell), arbitrarily large inputs, and a real sieve of eratosthenes

http://pastie.org/355725
From:
2009-01-08 11:16 pm (UTC)

### Re: Your nerdsniping was successful

first non-trivial program I've ever written in Scala.
http://pastie.org/356165

i got tired and cheated on the primes, but it reuses the values of the line above, so I only have to factor n instead of n!
From:
2009-01-08 11:19 pm (UTC)

### Re: Your nerdsniping was successful

scala is weird. It's like writing strictified haskell in ruby syntax with unsafePerformIO always on, plus the Java API