Exponents with Recursion
I'm trying to to do exponets with conversion somewhere i went wrong and cant seem to figure out why I keep getting errors
these were the formulas given
a^n = a^n/2(a^n/2) even
This formula only works for even exponents. To accommodate odd exponent values as well, we simply multiply one more time by a:
a^n = a^n/2(a^n/2) * a if a is odd
import java.util.*;
publicclass recursion3
{
publicstaticvoid main (String[] args)
{
int base;
int power;
Scanner sc =new Scanner(System.in);
System.out.println ("Please enter a non negative number");
base = sc.nextInt();
System.out.println ("Please enter a power");
power = sc.nextInt();
System.out.println(convert(base,power));
}
publicstaticdouble convert(int a,int n)
{
int ans;
ans = a^n/2*a^n/2;
if (n == 0)
{
return convert(a,n);
}
else
{
return (convert(a,n) * a);
}
}
}
Message was edited by:
jaydon34
[2008 byte] By [
jaydon34a] at [2007-11-26 19:52:58]
Are you expecting this to be Java syntax:ans = a^n/2*a^n/2;Java doesn't have an exponent operator. The operator ^ does bitwise exclusive or -- which is completely different.Also, isn't a^0 =1, for a>0? You seem to have an infinite recursion in this case.
In general, you just aren't implementing what you just described. Where is n/2 in your code, for example?
What about this formulation?a^n = 1when n is 0= b*bwhen n is even, > 0= b*b*a when n is oddwhere b is a^(n/2)
So how would I go about using formulating an exponent with out using the Math.pow(base,exponent)
try this
public static double convert(int a,int n) {
if (n % 2 == 1 && n > 1){
return convert(a, 0 ) * convert(a, 1);
}
if (n % 2 == 0){ //even
return Math.pow(a,n/2) * Math.pow(a,n/2);
} else {
return a;
}
}
somebody tell me he's kidding please
ejpa at 2007-7-9 22:44:15 >
>>So how would I go about using formulating an exponent with out using the >>Math.pow(base,exponent)
Algorithms my friend.
http://www.osix.net/modules/article/?id=696
Create your own method that calculates the number to a certain number (x^n)
Then just call this method to calculate the power...
Of course, the Math class has already created this method called "power" and all you have to do is use it (Instead of creating it by yourself ! Which would probably be less efficient than the method from the Math class)
imigod another one. All you need for the solution is to create your own method that implements the solution?
ejpa at 2007-7-9 22:44:15 >
Let this be over and done with:int power(int a, int n) {
if (n < 0) return 0; // just in case
if (n == 0) return 1; // the easy part
if (n == 1) return a; // also easy
//
int half= power(a, n/2);
if (n%2 == 0) return half*half;
return half*half*a;
}
kind regards,
Jos
isn't a^(-1) = 1/a?maybe my maths is rusty?
> isn't a^(-1) = 1/a?> maybe my maths is rusty?lol.
Darn mike you made me wiki it out. ok I was right, so
replace if (n < 0) return 0;
with if (n == -1) return 1/a;
I think it "should" work.
Edit: Sorry it won't work for odd negative power, but I won't solve it ;p
Message was edited by:
Icycool
> replace if (n < 0) return 0;
> with if (n == -1) return 1/a;
> I think it "should" work.
Both n and a are ints. btw, take n == -2 for an example: the results will
be turtles all the way down, that's why I used n < 0 as a sentinel value.
kind regards,
Jos
>replace
>if (n < 0) return 0;
>with
>if (n == -1) return 1/a;
You can catch negative powers by saying
if (n < 0) return 1/convert(a, -n);
This will actually result in 0 in any possible case, so Jos provided the most efficient way by simply returning 0 instead of executing useless recursions.
But it's a fact that negative powers do exist.
You should make the program produce correct result, but not ignoring a certain domain.
For instance power(2,-4) should produce 1/16, if you can't do it, at least print "sorry this program don't know negative" instead of 0.
I'm not understand why -2 wont work.
power(3,-2) will become power(3,-1)*power(3,-1), then become 1/3*1/3
Edit: oh i see it now, the result is not capable of floating type. Well, I got a silly workaround, if(n<0) print "1/"+result ;p
Message was edited by:
Icycool
<nevermind>Message was edited by: jsalonen
> Let this be over and done with:Jos, man, you caved! This chappie was fishing with an assignment and you did it for him!
> > Let this be over and done with:
>
> Jos, man, you caved! This chappie was fishing with an
> assignment and you did it for him!
Yeah I guess so, but this thread was also full of incorrect answers and
the entire thread sort of made me feel itchy ;-)
kind regards,
Jos
JosAHa at 2007-7-21 17:45:12 >
Yeah I was asking for help with an assignment but not the whole answer just some direction
