test: add sample unit test and function, write test(buggy) for p2.

- chore: change file names to match Python style guide (change dashes to underscores)

ISSUE: p2 tests don't run.

Author: Jessica Yung

mathematics/project-euler/1_multiples_of_three_and_five.py

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+"""
+Problem 1:
+
+Find the sum of all multiples of 3 or 5 below a positive integer n
+
+"""
+
+# Function calculates sum of multiples of k less than n
+def sum_multiples(n,k):
+    sum = 0
+    if 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))

mathematics/project-euler/2_even_fibonacci_numbers.py

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+"""
+Problem 2:
+
+Calculate the sum of all even Fibonacci numbers below positive integer n
+
+"""
+import unittest
+
+def fib(n):
+    """Function to calculate nth Fibonacci number, n being a non-negative integer.
+    Def: 0th Fibonacci number is 1.
+    """
+    if n < 0:
+        return "Null"
+    elif n == 0 or n == 1:
+        return 1
+    else:
+        f_two_before = 1
+        f = 1
+        for i in range(2, n+1):
+            # Save the value of f for use later
+            f_save = f
+            f = f + f_two_before
+            # Additional print statement for clarity            
+            # print(i, "th Fib is ", f)
+            f_two_before = f_save
+        return f
+  
+
+def sum_even_fibs_under_n(n):
+    """Calculates sum of even Fibonacci numbers under n."""
+    if fib(2) < n:    
+        sum = 0    
+        i = 2    
+        while fib(i) < n:
+            sum += fib(i)
+            i += 3
+        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

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+"""
+Problem 3: 
+
+Find the largest prime factor of a positive integer n
+
+"""
+import math
+
+# 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
+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))

mathematics/project-euler/4_largest_palindrome_product.py

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+"""
+Problem 4:
+
+Find the largest palindrome made from the product of two 3-digit integers which is less than positive integer n.
+
+"""
+
+# 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
+
+"""
+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.
+
+"""
+
+# 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))

mathematics/project-euler/5_smallest_multiple.py

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+""" 
+Problem 5: 
+
+2520 is the smallest number that can be divided by each of the numbers from  to  without any remainder. 
+What is the smallest positive number that is evenly divisible(divisible with no remainder) by all of the numbers from 1 to N?
+
+"""
+
+# Find all the prime factors and their powers in that number
+# Idea: Recursive
+
+def blah():
+    pass

mathematics/project-euler/6_sum_square_difference.py

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+"""
+Problem 6:
+
+Find the absolute difference between the sum of the squares of the first n natural numbers and the square of the sum.
+
+"""
+
+# 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
+
+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)))

mathematics/project-euler/7_nth_prime.py

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+"""
+Problem 7:
+
+Find the nth prime number. 
+n=< 10**4
+
+"""
+
+primes=[]
+def all_primes_under_n(n):
+	primes_under_n = []
+	for i in range(n):
+		if isprime(i) == True:
+			primes_under_n.append(i)
+	return primes_under_n
+
+def nth_prime(n):
+	all_primes_under_n[n]
+
+	i = int(primes[n-2])
+	while 
+