C[omp]ute

From: andrew cooke <andrew@...>

Date: Fri, 25 Feb 2011 09:07:26 -0300

Since other people have posted solutions and linked to them from HN I thought
I may as well post mine.


First question is based on summing "influences" defined in a matrix.  Given
the form of the input it's simplest to construct a set of delayed functions,
one per input line.  These can then be called, and call each other to
calculate the sum.  Memoization would help, but isn't needed for such a small
problem.

#!/usr/bin/python3

# see http://hyperpublic.com/challenge/question1

from itertools import count
from sys import argv

# read test file from command line
filename = argv[1] if len(argv) > 1 else 'challenge2input.txt'

# build tree of functions that terminate in users with no influence
# scorers array allows reference to functions not yet defined
def make_scorer(line):
    def scorer(scorers):
        return sum(1 + scorers[user](scorers)
                   for (user, char) in zip(count(), line)
                   if char == 'X')
    return scorer

scorers = [make_scorer(line) for line in open(filename)]
scores = [scorer(scorers) for scorer in scorers]
scores.sort(reverse=True)
print(scores)
print('result', ''.join(str(score) for score in scores[0:3]))


Second question involves plitting the score for a user into groups of points,
so that the minimum number of groups are used.  Apparently this is a ell known
problem called "coin change", which makes sense.  I didn't know that, but did
see that a dynamic solution is going to work (if you start with N points then
the best solution is going to be with group i if the solution with N-P(i) is
smallest; repeat...).

I am pretty sure you can write this directly as a recursive expression with
memoization, but it's easier to just build the anser from the bottom:

#!/usr/bin/python3

# see http://hyperpublic.com/challenge/question2

from operator import mul
from functools import reduce

scores = [2349, 2102, 2001, 1747]
points = [98, 42, 23, 17, 3, 2]

big = 1+max(*scores)
best = [None] * big # either None or (min number, history)

# simple dynamic solution, building from bottom up
for n in range(big):
    for p in points:
        if n == p:
            best[n] = (1, [p])
            break
        elif n > p and best[n-p]:
            (m, h) = best[n-p]
            if not best[n] or best[n][0] > m+1:
                best[n] = (m+1, h+[p])

assert best[20] == (2, [3,17])
assert best[34] == (2, [17,17]) # not greedy

for score in scores:
    (n, history) = best[score]
    print(score, n, history)

print('result', reduce(mul, map(lambda score: best[score][0], scores)))


Andrew