0005-no-div-1-20.py

"""
Problem 5
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20

Note: For this particular problem, I am satisfied that it is a better and optimized approach than the one
provided in the overview pdf
"""

def traditional():
    # Taking the entire list
    l = range(2, 21)

    # Doing this the old C++ style
    # Initializing the pointer to first element
    i = 0

    # Traversing the entire list
    while i < len(l):
        # Starting the next element in the list
        j = i + 1
        while j < len(l):
            # Checking if L[j] is completely divisible by L[i] 
            if l[j] % l[i] == 0:
                # If yes, replace L[j] by L[j]/L[i]
                # This is just normal reduction
                l[j] = l[j] / l[i]

            j = j + 1

        i = i + 1

    # Finding the product of the list
    ans = reduce(lambda x, y: x * y, l)
    return ans

print "Answer by traditional method:", traditional()