Add 'universe/' from commit '8ad51b24dd'

git-subtree-dir: universe
git-subtree-mainline: 15110e6de9
git-subtree-split: 8ad51b24dd

universe/data_structures_and_algorithms/optimal-stopping.py

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+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))