# Iterative Function To Find X to the power N

Discussion in 'Perl' started by pradeep, Mar 14, 2008.

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In rashida.par's Recursive function to find X to the power n (http://www.go4expert.com/showthread.php?t=9307) I see that she intelligently used recursion to find the power of x to n. So, I was wondering whether we can do this iteratively also, I always do that - trying to find a iterative solution to a recursive one.

Being more of a Perl programmer than C, I wrote my code in Perl - can be understood by any programmer. I also benchmarked the recursive function to the iterative version.

### The Iterative Solution

Code:
sub power_iterative
{
my (\$x,\$n) = @_; ## take in parameters
my \$result = 1;

while(\$n--)
{
\$result *= \$x;
}

return \$result;
}

Test run of the code:
Code:
printf("\n %.4f to the power of % d is %.4f",\$x,\$n,power_iterative(\$x,\$n));

Code:

4.0000 to the power of  10 is 1048576.0000

### Benchmarking

I also benchmarked the recursive function to the iterative version to see which one performs better.

Code:
use Benchmark;

sub power_iterative
{
my (\$x,\$n) = @_; ## take in parameters
my \$result = 1;

while(\$n--)
{
\$result *= \$x;
}

return \$result;
}

sub power_recursive
{
my (\$x,\$n) = @_; ## take in parameters

if (\$x==0)
{
return 0;
}
elsif(\$n==0)
{
return 1;
}
elsif (\$n>0)
{
return( \$x* power_recursive(\$x,\$n-1));
}
else
{
return ((1/\$x)*power_recursive(\$x,\$n+1));
}
}

my (\$x,\$n) = (4,10);

timethese(400000,{
'iterative'=> sub{my \$power = power_iterative(\$x,\$n);},
'recursive'=> sub{my \$power = power_recursive(\$x,\$n);}});

Result:
Code:
Benchmark: timing 400000 iterations of iterative, recursive...
iterative:  2 wallclock secs ( 1.28 usr +  0.00 sys =  1.28 CPU) @ 312500.00/s (n=400000)
recursive:  6 wallclock secs ( 5.90 usr +  0.00 sys =  5.90 CPU) @ 67796.61/s (n=400000)

As we see here, the iterative version performs much better than the recursive one, the reason being the recursive version need more memory for function call stacks etc.

I hope this was helpful to you all.

2. ### rai_gandalfNew Member

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As was evident from the Recursive implementation, there was tail recursion, which is both redundant & inefficient. Tail recursion must always be replaced with a more efficient, easier to comprehend iterative counter-part, as you have done here.

Only, you have done it in Perl - a language which I do not know much about - so I got to learn the basics of a new language as well!

Regards,
Rajiv