add problem 2 file, add efficiency check in prime_factorization

0002-even-fibonacci-numbers/even_fibonacci.py

@@ -0,0 +1,88 @@
+"""Even Fibonacci numbers
+Problem 2
+Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
+
+1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
+
+By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms."""
+
+def fib_recursive(n):
+    """
+    Returns the nth Fibonacci number using the naive recursive solution.
+    This takes exponential time and space (BAD!).
+    """
+    if n<=1:
+        return n
+    return fib_recursive(n-1) + fib_recursive(n-2)
+
+def fib_memoized(n, memo={}):
+    """
+    Returns the nth Fibonacci number using a memoized recursive solution.
+    The memo is a dictionary (hashtable).
+    This takes linear time and space.
+    """
+    if n <=1:
+        return n
+
+    if n not in memo:
+        memo[n] = fib_memoized(n-1, memo) + fib_memoized(n-2, memo)
+
+    return memo[n]
+
+def fibonacci(n):
+    """
+    Returns the nth Fibonacci number using a for loop.
+    This takes linear time and constant space.
+    """
+    if n==0:
+        return 0
+
+    f_previous = 0
+    f_current = 1
+    for i in range(1, n):
+        f_next = f_current + f_previous
+        f_previous = f_current
+        f_current = f_next
+
+    return f_current
+
+def fibonacci_generator(upper_bound):
+    """
+    Generates all Fibonacci numbers less than upper_bound.
+    """
+    yield 0
+
+    f_previous = 0
+    f_current = 1
+    while(f_current < upper_bound):
+        yield f_current
+        f_next = f_current + f_previous
+        f_previous = f_current
+        f_current = f_next
+
+def even_fibonacci(n, upper_bound=float('inf')):
+    """
+    Generates all even Fibonacci numbers up to (and including) the n^th one.
+    Indexing starts at 0, so n+1 numbers will be generated.
+    """
+    if n>=0:
+        yield 0
+
+    f_previous = 0
+    f_current = 1
+    #Every 3^rd Fibonacci number is even, so we need 3n Fibonacci numbers
+    #to get n even ones:
+    #0 1 2 3 4 5 6 7  8  9  10 11 12  13  14  15  16  17
+    #0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1579
+    #0     1     2       3        4           5
+    # counter = 1
+    # while(counter <= 3*n and f_current <= upper_bound)
+    for i in range(3*n):
+        if f_current % 2 == 0:
+            yield f_current
+        f_next = f_current + f_previous
+        f_previous = f_current
+        f_current = f_next
+
+if __name__=="__main__":
+    pass

project_euler.py

@@ -193,7 +193,7 @@ def prime_factorization(n):
     #it is a product of smaller primes, so we know that
     #if d divides n, then d must be prime.
     d = 3
-    while d*d <= n:
+    while dividend > 1 and d*d <= n:
         while dividend%d == 0:
             dividend //= d
             factors[d] += 1