019f8fd211
git-subtree-dir: users/wpcarro git-subtree-mainline:464bbcb15cgit-subtree-split:24f5a642afChange-Id: I6105b3762b79126b3488359c95978cadb3efa789
49 lines
1.8 KiB
Python
49 lines
1.8 KiB
Python
from random import choice
|
|
from math import floor
|
|
|
|
# Applying Chapter 1 from "Algorithms to Live By", which describes optimal
|
|
# stopping problems. Technically this simulation is invalid because the
|
|
# `candidates` function takes a lower bound and an upper bound, which allows us
|
|
# to know the cardinal number of an individual candidates. The "look then leap"
|
|
# algorithm is ideal for no-information games - i.e. games when upper and lower
|
|
# bounds aren't known. The `look_then_leap/1` function is ignorant of this
|
|
# information, so it behaves as if in a no-information game. Strangely enough,
|
|
# this algorithm will pick the best candidate 37% of the time.
|
|
#
|
|
# Chapter 1 describes two algorithms:
|
|
# 1. Look-then-leap: ordinal numbers - i.e. no-information games. Look-then-leap
|
|
# finds the best candidate 37% of the time.
|
|
# 2. Threshold: cardinal numbers - i.e. where upper and lower bounds are
|
|
# known. The Threshold algorithm finds the best candidate ~55% of the time.
|
|
#
|
|
# All of this and more can be studied as "optimal stopping theory". This applies
|
|
# to finding a spouse, parking a car, picking an apartment in a city, and more.
|
|
|
|
|
|
# candidates :: Int -> Int -> Int -> [Int]
|
|
def candidates(lb, ub, ct):
|
|
xs = list(range(lb, ub + 1))
|
|
return [choice(xs) for _ in range(ct)]
|
|
|
|
|
|
# look_then_leap :: [Integer] -> Integer
|
|
def look_then_leap(candidates):
|
|
best = candidates[0]
|
|
seen_ct = 1
|
|
ignore_ct = floor(len(candidates) * 0.37)
|
|
for x in candidates[1:]:
|
|
if ignore_ct > 0:
|
|
ignore_ct -= 1
|
|
best = max(best, x)
|
|
else:
|
|
if x > best:
|
|
print('Choosing the {} candidate.'.format(seen_ct))
|
|
return x
|
|
seen_ct += 1
|
|
print('You may have waited too long.')
|
|
return candidates[-1]
|
|
|
|
|
|
candidates = candidates(1, 100, 100)
|
|
print(candidates)
|
|
print(look_then_leap(candidates))
|