Given positive, integer N, what does this algorithm produce?

let S and D = N
repeat 
    let D = ⌊D/2⌋
    subtract D from S
until D=0
produce S as the result

Note: ⌊x⌋ represents the integer part of x.

For non-programmers: start with a positive, integer number (say, 19). Divide it by 2, discarding remainders, until you get to 0. (In this case, you'd get 9, 4, 2, and 1.) Sum all the quotients. (9+4+2+1=16.) Subtract the sum from the original number. (19-16=3.) What's the result?

Didn't read any of the other solutions yet, but it appears to be the number of "1"s in the binary representation of N.  In binary, dividing by 2 is just a shift to the right.  If the right most digit is a 1, lop it off and add 1 to the result. 

Posted by Larry on 2005-01-14 23:42:34