Program a mathematical using recursive function

Question

I want to program the mathematical function f(x)=sqrt(1^1+sqrt(2^2+sqrt(3^3)+...+sqrt(x^x))), where x should be 1 <= x <= 10. I tried to programm the function like this:

double f1Rek(int x)
{ 
   if( x < 1 ) return sqrt(power(x,x));
   return sqrt(power(x,x) + f1Rek(x-1));
}

The function power is also a self created recursive function:

double power(int x, int n)
{
   if( n == 0 ) return 1.0;
   if( x == 0 ) return 0.0;
   if( exp > 0 )
   {
       return n * power(n, exp - 1);
   }
   if( exp < 0 )
   {
       return 1 / ( n * power(n, -(exp-1));
   }
}

The problem is the f1Rek(int x) function, because it starts with the sqrt(x^x + sqrt( x-1^x-1... . How can I solve the problem in a very elegant way?

Update:

With the answer of Jim Balter, i created a function with 2 Arguments:

double f2Rek(int i, int x)
{
   if( i <= x )
   {
      return sqrt(power(i,i) + f2Rek(i+1, x));
   }
   else return 0.0;
}

Is there a possibility to define a recursive function with only one argument.

What do you mean with the ten? 1 <= x <= 10, do you mean the ten here? — Oni1
– Oni1, Commented Mar 26, 2013 at 19:47

Jim Balter · Accepted Answer · 2013-03-26 23:51:31Z

2

f(x)=sqrt(1^1+sqrt(2^2+ ( sqrt(3^3)+...+ ( sqrt(x^x))) )...

(Assuming what's in bold)

Equivalently,

f(x) = g(1, x)

where

g(i, n) = sqrt(i^i + g(i+1, n)) if i <= n, else 0

You should be able to elegantly code your recursive function from that.

In regard to a function with one argument:

f is a function with one argument. It calls a recursive helper function that takes two arguments. It's clear that the recursive inner function needs two arguments, one of which is the termination value, x. In a language with local functions that argument can be hoisted out of the function, e.g.,

double f(int x)
{
   double g(int i)
   {
       return (i <= x)? sqrt(pow(i, i) + g(i+1)) : 0.0;
   }

   return g(1);
}

GCC supports local functions, but they aren't in standard C.

edited Mar 26, 2013 at 23:51

answered Mar 26, 2013 at 19:49

Jim Balter

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7 Comments

Oni1 Over a year ago

The first argument of g(1,x) should always the one?

Jim Balter Over a year ago

Look again ... g(i+1, n) ... that's not 1. The initial first argument is 1, because that's how the series starts. The second argument is always n (the x argument of f) because that's the termination value.

WhozCraig Over a year ago

@T.C. "The first argument of g(1,x) should always the one" Presented like that, how could it be anything else? I think you meant g(i,x), and Jim answered that.

Oni1 Over a year ago

Okay i get it.. it's another solution, but i tried it with only one argument.

Oni1 Over a year ago

Jim Balter, is the function not possible with only one argument?

|

FKaria · Accepted Answer · 2013-03-26 19:55:48Z

1

double f1Rek(int x)
{  
   double res = 0.0;
   for(int i=x; i > 0; i--) {
     res = sqrt(power(i,i) + res));
   }
   return res;
}

answered Mar 26, 2013 at 19:55

FKaria

1,08213 silver badges16 bronze badges

2 Comments

Jim Balter Over a year ago

If all you need is the right results, then it's useful ... and you should change your question. But if you're doing homework that is supposed to help you understand how to write recursive functions then it isn't useful.

Oni1 Over a year ago

It has nothing to do with homework.. i just try to programm mathematical in C, nothing else.

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