Lab 2: while

Comp 150, Dordal
In this lab we will write two functions, each using a while loop.

1. Factorial loop

Here is a definition of the factorial function using a for loop: 

def fact(n):
    prod = 1
    for factor in range(1,n):
        prod = prod * factor
    return prod
Recall that the for loop runs the variable factor through each member of the list [1,2,3....,n-1], which is created by the range(1,n) call. While the creation of simple lists is pretty fast, it is fundamentally unnecessary here and in some cases can degrade performance.

You are to rewrite this using a while loop; that is, without using for or range.

2. Base-2 conversion

You are to write a function binary(n) containing a loop to convert a base-10 number to base 2. The output should be either printed or else returned as a list of digits.

Start with n. To get one binary digit, use n % 2 (this is the remainder upon dividing n by 2). Then set n = n/2, and continue (this is where the while comes in). Stop when n=0 (that is, the while loop will be while n > 0:)

Alas, if you print the digits n%2 as you go, you get them in the reverse order; the digit you get with n%2 is the last digit. A fix is to put the digits into a list or string as you go. If the list is to be called digits, then you start with digits = '' (the empty string) or digits = [] (the empty list), and then add each successive digit to the front:
    digits = num2dig(n%2) + digits   # string version; see below for num2dig
    digits = [n%2] + digits            # list version

If you use the list version, then at the end you have to convert to a string: "".join(digits) (this joins all the characters of digits to the end of the empty string ""). If you use the string version, you need to write num2dig, which takes the number 0 or 1 and returns the character (string) '0' or '1'. Here's one approach:
    def num2dig(num):
       if num = 0:
          return '0'
       else:
          return '1'
An even simpler method is to use indexing on the string "01": "01"[0] is '0' and "01"[1] is '1'. You can use this as the body of num2dig, or you can just put it "in-line" in the body of binary(). Another simple method is chr(48+n%2): chr(x) is the ascii character with numeric value x, n%2 is either 0 or 1, and chr(48) == '0', chr(49)=='1'.

You will need a separate case to handle n==0; you can test for this with an if statement. Do not worry about negative n.

Examples

Here are a few examples of numeric while loops. Do not forget the i=i+1 increment!

To find the sum of the numbers from 1 to N: 

	N = 100
	i= 1
	sum = 0
	while i<=N:
	    sum = sum + i
	    i = i+1
The value of 1+2+...+N is now in variable sum.

To find the sum of the numbers in a list L: 

    L=[2,3,5,7,11,13,17,19]
    i=0
    sum = 0
    while i<len(L):
        sum = sum + L[i]
        i = i+1

To reverse a string S. The reversed string will be in the variable revS, at the end of the loop. 

    S = "hello, world"
    i = len(S)-1;		# last position of S
    revS = ""
    while i>=0:
        revS = revS + S[i]
        i = i-1			# this time i is DECREMENTED