subtree(users/wpcarro): docking briefcase at '24f5a642'

git-subtree-dir: users/wpcarro
git-subtree-mainline: 464bbcb15c
git-subtree-split: 24f5a642af
Change-Id: I6105b3762b79126b3488359c95978cadb3efa789

users/wpcarro/scratch/facebook/hard/random-choice.py

@@ -0,0 +1,50 @@
+import random
+
+# This class of problems is known as "resevoir sampling".
+def choose_a(m, xs):
+    """
+    Randomly choose `m` elements from `xs`.
+    This algorithm runs in linear time with respect to the size of `xs`.
+    """
+    result = [None] * m
+    for i in range(len(xs)):
+        j = random.randint(0, i)
+        if j < m:
+            result[j] = xs[i]
+    return result
+
+def choose_b(m, xs):
+    """
+    This algorithm, which copies `xs`, which runs in linear time, and then
+    shuffles the copies, which also runs in linear time, achieves the same
+    result as `choose_a` and both run in linear time.
+
+    `choose_a` is still preferable since it has a coefficient of one, while this
+    version has a coefficient of two because it copies + shuffles.
+    """
+    ys = xs[:]
+    random.shuffle(ys)
+    return ys[:m]
+
+def choose_c(m, xs):
+    """
+    This is one, possibly inefficient, way to randomly sample `m` elements from
+    `xs`.
+    """
+    choices = set()
+    while len(choices) < m:
+        choices.add(random.randint(0, len(xs) - 1))
+    return [xs[i] for i in choices]
+
+# ROYGBIV
+xs = [
+    'red',
+    'orange',
+    'yellow',
+    'green',
+    'blue',
+    'indigo',
+    'violet',
+]
+print(choose_b(3, xs))
+print(choose_c(3, xs))