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?

Here's an implementation.  It actually does a little more, as it loops through and shows the results for several values of N.

CLS
FOR n = 1 TO 40
 s = n: d = n
 DO
   d = INT(d / 2)
   s = s - d
 LOOP UNTIL d = 0
 PRINT USING "##  ## "; n; s
NEXT

 

 

Resulting in:

 1   1
 2   1
 3   2
 4   1
 5   2
 6   2
 7   3
 8   1
 9   2
10   2
11   3
12   2
13   3
14   3
15   4
16   1
17   2
18   2
19   3
20   2
21   3
22   3
23   4
24   2
25   3
26   3
27   4
28   3
29   4
30   4
31   5
32   1
33   2
34   2
35   3
36   2
37   3
38   3
39   4
40   2

Posted by Charlie on 2005-01-14 15:16:49