On Fri Jul 10 2009 @ 9:26, Dermot wrote:
> The algorithm works perfectly but my understanding of it's workings is amiss.
>
> When I look at this I see $E initialised and then concatenate with the
> the modulus of
> 37 % 2 =1
> 18 % 2 = 0
> 9 % 2 = 1
> 4 % 2 = 0
> 2 % 2 = 0
>
> That by my reckoning is 10100. Almost the reverse of the answer but I
> am obviously wrong and I can't see how the final expressions:
>
> my $E = binary($k);
> return $E . $b;
>
> work to give the answer.
It helps for me to walk through it visually, indenting once each time the
script needs to call the binary sub-routine. Notice that it keeps going down
and inward, until it "bottoms out" on the base case. At that point, the answers
ripple back up to fit into the calls to binary($E) that were left hanging
(because in those cases $E wasn't 1 or 0). Maybe this will help you as well.
Does 37 == 0 || 1? No; continue...
$k = 18; $b = 1; $E = binary(18) -> go do that...
Does 18 == 0 || 1? No; continue...
$k = 9; $b = 0; $E = binary(9) -> go do that...
Does 9 == 0 || 1? No; continue...
$k = 4; $b = 1; $E = binary(4) -> go do that...
Does 4 == 0 || 1? No; continue...
$k = 2; $b = 0; $E = binary(2) -> go do that...
Does 2 == 0 || 1? No; continue...
$k = 1; $b = 0; $E = binary(1) -> go do that...
Does 1 == 0 || 1? Yes; return 1
$E = 1; return 1 . 0
$E = 10; return 10 . 0
$E = 100; return 100 . 1
$E = 1001; return 1001 . 0
$E = 10010; return 10010 . 1
Hope this helps, T
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