test(euler): add doctests to p1-4, 6 and refactored code.

ISSUE: p5 and p7 solutions incomplete.

Author: Jessica Yung

mathematics/project-euler/1_multiples_of_three_and_five.py

@@ -3,25 +3,30 @@
 
 Find the sum of all multiples of 3 or 5 below a positive integer n
 
+Examples:
+>>> sum_multiples_3_5(10)
+23
+
+>>> sum_multiples_3_5(-1)
+0
+
+Author: Jessica Yung
+Refactored October 2016
 """
 
-# Function calculates sum of multiples of k less than n
-def sum_multiples(n,k):
+
+def sum_multiples(n, k):
+    """Calculates sum of multiples of k less than n."""
     sum = 0
     if n >= k:
-        for i in range(1,int(n/k)):
+        for i in range(1, int(n/k)):
             sum += k*i
         # It should be range(1,int(n/k)+1) for k such that n % k != 0, so
         if n % k != 0:
             sum += int(n/k)*k
     return sum
 
-# Function calculates sum of all multiples of 3 or 5 below n
-def sum_multiples_3_5(n):
-    return sum_multiples(n,3) + sum_multiples(n,5) - sum_multiples(n,15)
 
-# Read input and solve
-t = int(input().strip())
-for j in range(t):
-    n = int(input().strip())
-    print(sum_multiples_3_5(n))
+def sum_multiples_3_5(n):
+    """Calculates sum of all multiples of 3 or 5 below n."""
+    return sum_multiples(n, 3) + sum_multiples(n, 5) - sum_multiples(n, 15)

mathematics/project-euler/2_even_fibonacci_numbers.py

@@ -3,8 +3,25 @@
 
 Calculate the sum of all even Fibonacci numbers below positive integer n
 
+Example:
+>>> sum_even_fibs_under_n(10)
+10
+
+This file also includes a function that returns the nth Fibonacci number:
+>>> fib(0)
+1
+
+>>> fib(1)
+1
+
+>>> fib(10)
+89
+
+
+Author: Jessica Yung
+Refactored October 2016
 """
-import unittest
+
 
 def fib(n):
     """Function to calculate nth Fibonacci number, n being a non-negative integer.
@@ -38,37 +55,3 @@ def sum_even_fibs_under_n(n):
         return sum
     else:
         return "Null"
-
-# Tests
-
-class Tests(unittest.TestCase):
-    """Tests fib(n)."""
-
-    def __init__(self):
-        super(Tests, self).__init__()
-        self.nth_fibonacci_test()
-        self.sum_even_fibs_under_n_test()
-
-
-    def nth_fibonacci_test(self):
-        # type: () -> Error or not?
-        self.assertEqual(fib(0), 1)
-        self.assertEqual(fib(1), 1)
-        self.assertEqual(fib(4), 5)
-
-    def sum_even_fibs_under_n_test(self):
-        self.assertEqual(sum_even_fibs_under_n(10), 10)
-        self.assertEqual(1, 0)
-
-if __name__ == '__main__':
-    unittest.main()
-#    Tests.nth_fibonacci_test()
-#    Tests.sum_even_fibs_under_n_test()
-
-"""
-# Read input and solve
-t = int(input().strip())
-for i in range(t):
-    n = int(input().strip())
-    print(sum_even_fibs_under_n(n))
-"""

mathematics/project-euler/3_largest_prime_factor.py

@@ -1,45 +1,60 @@
 """
-Problem 3: 
+Problem 3:
 
-Find the largest prime factor of a positive integer n
+Find the largest prime factor of a positive integer n.
 
+Example:
+>>> largest_prime_factor(10)
+5
+
+Author: Jessica Yung
+Refactored October 2016
 """
 import math
+import unittest
+
 
-# Function to find all factors
 def factors(n):
-	factors = set()
-	for i in range(1, int(math.sqrt(n))+1):
-		if n % i == 0:
-			factors.add(i)
-			factors.add(int(n/i))
-	return factors
-
-# Function that tests if integers are prime
-def isprime(n):
-	isprime = True
-	if n < 2:
-		isprime = False
-	elif n > 3:
-		for i in range(2, int(math.sqrt(n))+1):
-			if n % i == 0:
-				isprime = False
-				break
-	return isprime
-
-# Function that finds largest prime factor
+    """Find all factors of a positive integer n."""
+    factors_of_n = set()
+    for i in range(1, int(math.sqrt(n))+1):
+        if n % i == 0:
+            factors_of_n.add(i)
+            factors_of_n.add(int(n / i))
+    return factors_of_n
+
+
+def is_prime(n):
+    """Tests if a positive integer n is prime."""
+    is_n_prime = True
+    if n < 2:
+        is_n_prime = False
+    elif n > 3:
+        for i in range(2, int(math.sqrt(n))+1):
+            if n % i == 0:
+                is_n_prime = False
+                break
+    return is_n_prime
+
+
 def largest_prime_factor(n):
-	primefactors = set()
-	for i in factors(n):
-		if isprime(i):
-			primefactors.add(i)
-	if len(primefactors) == 0:
-		return "Null"
-	else:
-		return max(primefactors)
-
-# Read input and solve
-t = int(input().strip())
-for i in range(t):
-    n = int(input().strip())
-    print(largest_prime_factor(n))
+    """Finds largest prime factor of a positive integer n."""
+    prime_factors = set()
+    for i in factors(n):
+        if is_prime(i):
+            prime_factors.add(i)
+    if len(prime_factors) == 0:
+        return "Null"
+    else:
+        return max(prime_factors)
+
+
+class Tests(unittest.TestCase):
+
+    def test_largest_prime_factor(self):
+        self.assertEqual(largest_prime_factor(10), 5)
+        self.assertEqual(largest_prime_factor(1), "Null")
+
+
+if __name__ == '__main__':
+    unittest.main()

mathematics/project-euler/4_largest_palindrome_product.py

@@ -3,48 +3,50 @@
 
 Find the largest palindrome made from the product of two 3-digit integers which is less than positive integer n.
 
-"""
+Examples:
+>>> greatest_palindromic_product_below_n(10000)
+0
 
-# Function to test if a number is a palindrome
-def is_palindrome(n):
-	is_palindrome = True
-	n = str(n)
-	for i in range(int(len(n)/2)):
-		if n[i] != n[len(n)-1-i]:
-			is_palindrome = False
-			break
-	return is_palindrome
-
-# Narrow range
-def largest_three_digit_to_consider(n):
-	k = 999
-	while k*100 > n:
-		k -= 1
-	return k
+>>> greatest_palindromic_product_below_n(111112)
+111111
 
+Author: Jessica Yung
+Refactored October 2016
 """
-Given the palindromic product must be a six-digit number, it must also be a multiple of 11. Thus at least one of the factors must be a multiple of 11.
 
-"""
+def is_palindrome(number):
+    """Test if a number is a palindrome."""
+    is_a_palindrome = True
+    number = str(number)
+    for i in range(int(len(number) / 2)):
+        if number[i] != number[len(number) - 1 - i]:
+            is_a_palindrome = False
+            break
+    return is_a_palindrome
+
+
+# Narrow down range
+def largest_three_digit_to_consider(n):
+    k = 999
+    while k * 100 > n:
+        k -= 1
+    return k
+
 
-# Systematically go through all relevant products and find the greatest palindrome product
 def greatest_palindromic_product_below_n(n):
-	k = largest_three_digit_to_consider(n)
-	l = int(k/11)
-	greatest = 0
-	# Let a be the factor that must be a multiple of 11
-	for i in range(10, l+1):
-		a = 11*i
-		for j in range(100,k):
-			product = a*j
-			if product < n:
-				if product > greatest:
-					if is_palindrome(product):
-						greatest = product
-	return greatest
-
-# Read input and solve
-t = int(input().strip())
-for i in range(t):
-    n = int(input().strip())
-    print(greatest_palindromic_product_below_n(n))
+    """# Systematically go through all relevant products and find the greatest palindrome product."""
+    k = largest_three_digit_to_consider(n)
+    # Given the palindromic product must be a six-digit number, it must also be a multiple of 11.
+    # Thus at least one of the factors must be a multiple of 11.
+    l = int(k / 11)
+    greatest = 0
+    # Let a be the factor that must be a multiple of 11
+    for i in range(10, l + 1):
+        a = 11 * i
+        for j in range(100, k):
+            product = a * j
+            if product < n:
+                if product > greatest:
+                    if is_palindrome(product):
+                        greatest = product
+    return greatest

mathematics/project-euler/6_sum_square_difference.py

@@ -1,27 +1,34 @@
 """
 Problem 6:
 
-Find the absolute difference between the sum of the squares of the first n natural numbers and the square of the sum.
+Find the absolute difference between the sum of the squares of
+the first n natural numbers and the square of the sum.
 
+>>> abs_diff(10)
+2640
+
+Author: Jessica Yung
+Refactored October 2016
 """
 
+
 # Need abs((1^2+2^2+...+N^2) - (1+2+...+N)^2)
 
-# Sum of the squares of the first n natural numbers
+
 def sum_of_squares(n):
-	sum = 0
-	for i in range(1,n+1):
-		sum += i**2
-	return sum
+    """Sum of the squares of the first n natural numbers."""
+    sum_of_sq = 0
+    for i in range(1, n + 1):
+        sum_of_sq += i ** 2
+    return sum_of_sq
+
 
 def square_of_sum(n):
-	sum = 0
-	for i in range(1, n+1):
-		sum += i
-	return sum**2
-
-# Read input and solve
-t = int(input().strip())
-for i in range(t):
-	n = int(input().strip())
-	print(abs(sum_of_squares(n) - square_of_sum(n)))
+    sum = 0
+    for i in range(1, n + 1):
+        sum += i
+    return sum ** 2
+
+
+def abs_diff(n):
+    return abs(sum_of_squares(n) - square_of_sum(n))

mathematics/project-euler/example_code_with_unittest.py

@@ -1,8 +1,11 @@
 """
 A simple function and a unit test to go with it.
+
 Have tested that this returns no errors with the uncommented tests and that
 it returns an AssertionError when the commented (deliberately false) test is included.
 
+Author: Jessica Yung
+October 2016
 """
 
 import unittest
@@ -20,4 +23,4 @@ def test_square_x(self):
 #        self.assertEqual(square_x(1), -1)
 
 if __name__ == '__main__':
-    unittest.main()
+    unittest.main()