Add miscellaneous python code that I want to keep.

resources/python/birthday_problem.py

@@ -0,0 +1,73 @@
+import random
+import math
+
+class BirthdayProblem(object):
+
+    def __init__(self):
+        pass
+
+
+def birthday_problem(problem_size=365):
+    birthdays = set()
+    while True:
+        new_birthday = random.randint(1, problem_size)
+        if new_birthday in birthdays:
+            return len(birthdays) + 1
+        birthdays.add(new_birthday)
+
+
+def theoretical_average(problem_size):
+    probabilities = []
+    contributions = []
+    for n in range(1, problem_size):
+        probability = (float(n-1) / problem_size) * falling_factorial_over_exponentiation(problem_size, n-1)
+        contribution = n * probability
+        probabilities.append(probability)
+        contributions.append(contribution)
+    return sum(contributions)
+
+
+def falling_factorial(n, k):
+    product = 1
+    while k > 0:
+        product *= n
+        n -= 1
+        k -= 1
+    return product
+
+
+
+def falling_factorial_over_exponentiation(n, k):
+    orig = n
+    product = float(1)
+    while k > 0:
+        product *= n
+        product = product/orig
+        n -= 1
+        k -= 1
+    return product
+
+
+def run_birthday_problem_n_times(times_to_run, problem_size=365):
+    return [birthday_problem(problem_size) for i in range(int(times_to_run))]
+
+
+def number_of_people_to_times_occured(runs):
+    number_of_people_to_times_occured = {}
+    for run in runs:
+        number_of_people_to_times_occured[run] = number_of_people_to_times_occured.get(run, 0) + 1
+
+
+if __name__ == '__main__':
+    times_to_run = 131072
+    while times_to_run <= 131072:
+        for problem_size in range(4000, 5000, 100):
+            average = sum(run_birthday_problem_n_times(times_to_run, problem_size=problem_size))/float(times_to_run)
+            print "problem size {3} ran {0} times, average was {1}, theoretical average is {2}".format(
+                times_to_run,
+                average,
+                theoretical_average(problem_size),
+                problem_size
+            )
+            print math.fabs(average - theoretical_average(problem_size))
+        times_to_run *= 2