kyu_5.number_of_trailing_zeros_of_n package

Submodules

kyu_5.number_of_trailing_zeros_of_n.test_zeros module

class kyu_5.number_of_trailing_zeros_of_n.test_zeros.ZerosTestCase(methodName='runTest')

Bases: unittest.case.TestCase

Testing zeros function

test_zeros()

Testing ‘zeros’ program that should calculate the number of trailing zeros in a factorial of a given number. :return:

kyu_5.number_of_trailing_zeros_of_n.zeros module

kyu_5.number_of_trailing_zeros_of_n.zeros.zeros(n)

A program that will calculate the number of trailing zeros in a factorial of a given number.

N! = 1 * 2 * 3 * … * N

For more info, see: http://mathworld.wolfram.com/Factorial.html

A simple way is to calculate floor(n/5). For example, 7! has one 5, 10! has two 5s. It is done yet, there is one more thing to consider. Numbers like 25, 125, etc have more than one 5.

For example if we consider 28!, we get one extra 5 and number of 0s become 6. Handling this is simple, first divide n by 5 and remove all single 5s, then divide by 25 to remove extra 5s and so on.

Following is the summarized formula for counting trailing 0s.

Trailing 0s in n! = Count of 5s in prime factors of n!

= floor(n/5) + floor(n/25) + floor(n/125) + ….

Parameters

n –

Returns

Module contents