From 465dfcb4b534bd45f162f98663ac317d85d7e39c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Daniel=20Kn=C3=BCttel?= <daniel.knuettel@daknuett.eu>
Date: Wed, 7 Nov 2018 15:22:04 +0100
Subject: [PATCH] exercises for week 3

---
 ex_09.py | 18 +++++++++++
 ex_10.py | 96 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 ex_11.py | 28 +++++++++++++++++
 ex_12.py | 14 +++++++++
 4 files changed, 156 insertions(+)
 create mode 100644 ex_09.py
 create mode 100644 ex_10.py
 create mode 100644 ex_11.py
 create mode 100644 ex_12.py

diff --git a/ex_09.py b/ex_09.py
new file mode 100644
index 0000000..5013951
--- /dev/null
+++ b/ex_09.py
@@ -0,0 +1,18 @@
+#!/usr/bin/python3
+from math import gamma
+
+def factorial(n):
+	n = int(n)
+	result = 1
+	if(n < 0):
+		raise ValueError("n must be greater than 0")
+	if(n == 0):
+		return result
+	for i in range(1, n + 1):
+		result *= i
+	return result
+
+if( __name__ == "__main__"):
+	print("factorial(5) = ", factorial(5))
+
+	print("gamma(6) = ", gamma(6))
diff --git a/ex_10.py b/ex_10.py
new file mode 100644
index 0000000..3383d35
--- /dev/null
+++ b/ex_10.py
@@ -0,0 +1,96 @@
+#!/usr/bin/python3
+
+from collections import deque
+from itertools import count
+import decimal
+
+# Only for reference.
+def fibonacci(n):
+	a = 1
+	b = 0
+	swp = 0
+
+	for i in range(n):
+		swp = a
+		a += b
+		b = swp
+	return a
+
+_fibonacci_series_context_stack = deque()
+
+class FibonacciSeriesContext(object):
+	def __init__(self):
+		self._pre_calculated = {0: 1, 1: 1}
+		self._biggest = 1
+
+	def __contains__(self, other):
+		return other in self._pre_calculated
+	
+	def __getitem__(self, n):
+		return self._pre_calculated[n]
+	def __setitem__(self, n, v):
+		self._pre_calculated[n] = v
+
+	def get_biggest_pair(self):
+		return ((self._biggest - 1, self._pre_calculated[self._biggest - 1])
+			, (self._biggest, self._pre_calculated[self._biggest]))
+	def __enter__(self):
+		_fibonacci_series_context_stack.append(self)
+		return self
+	def __exit__(self, *exc):
+		_fibonacci_series_context_stack.pop()
+		return False
+
+_fibonacci_series_context_stack.append(FibonacciSeriesContext())
+
+
+def getfibonacciseriescontext():
+	return _fibonacci_series_context_stack[-1]
+
+def fast_ctx_fibonacci(n, context = getfibonacciseriescontext()):
+	if(n in context):
+		return context[n]
+
+	(n_start_minus_one, b), (n_start, a) = context.get_biggest_pair()
+
+	for i in range(n_start, n):
+		swp = a
+		a += b
+		b = swp
+		context[n] = a
+
+	return a
+	
+
+
+if( __name__ == "__main__"):
+
+	decimal.getcontext().prec = 5
+	golden_ratio = decimal.Decimal((1 + decimal.Decimal(5).sqrt()) / 2)
+	print("Seeking n, such that F(n + 1) / F(n) = ", golden_ratio)
+	print("Precision is 1e-5.")
+
+	# Try to approximate the result faster using big steps first.
+
+	# At first try steps of 100. This way we can approximate an interval
+	# with width 100 where we do the fine approximation.
+	
+	for i in count(1, 100):
+		if(fast_ctx_fibonacci(i) / decimal.Decimal(fast_ctx_fibonacci(i - 1)) == golden_ratio):
+			break
+
+	n_stop = i
+	n_start = n_stop - 101
+
+	print("Found that n is in range({}, {})".format(n_start, n_stop))
+
+	for i in range(n_start, n_stop):
+		if(fast_ctx_fibonacci(i) / decimal.Decimal(fast_ctx_fibonacci(i - 1)) == golden_ratio):
+			break
+	n = i + 1
+
+	print("n = ", n)
+
+	print("F(n + 1) / F(n) = %0.6g" % (fast_ctx_fibonacci(n + 1) / fast_ctx_fibonacci(n)))
+
+
diff --git a/ex_11.py b/ex_11.py
new file mode 100644
index 0000000..f11d04b
--- /dev/null
+++ b/ex_11.py
@@ -0,0 +1,28 @@
+#!/usr/bin/python3
+
+import pprint
+
+from util.io import readvalue
+
+
+def divisors(n):
+	return [i for i in range(2, n) if not n % i]
+
+def is_prime(n):
+	return not divisors(n)
+
+if( __name__ == "__main__"):
+	
+	def positive_int(s):
+		v = int(s)
+		if(v > 0):
+			return v
+
+	number = readvalue("n > ", positive_int)
+	print("Divisors:")
+	pprint.pprint(divisors(number))
+
+	if(is_prime(number)):
+		print("Also", number, "is a prime.")
+	else:
+		print(number, "is not a prime.")
diff --git a/ex_12.py b/ex_12.py
new file mode 100644
index 0000000..0a4cb2e
--- /dev/null
+++ b/ex_12.py
@@ -0,0 +1,14 @@
+#!/usr/bin/python3
+
+def numerical_shitty_integration(func, n, a, b):
+	epsilon = (b - a) / n
+	result = 0
+
+	for i in range(n):
+		result += epsilon * func( a + epsilon * i)
+	return result
+
+if( __name__ == "__main__"):
+	f = lambda x: (1 - x**2)**0.5
+
+	print(numerical_shitty_integration(f, 5000, -1, 1))