My code is supposed to calculate the 100th element of the sequence $x_0=1 ; x_i=\dfrac{x_{i-1} 1}{x_{i-1} 2}, i=1,2, \ldots$
I wrote iterative and recursive functions, but the results are not equal. Is it due to the lost of decimals?
Here is my driver code. The data from the file is i=100.
int main()
{
int i;
ifstream f ("data.txt");
f >> i;
double x_0= 1.00;
double x_100 = l(x_0, i);
ofstream g ("results.txt", ios::app);
g <<"\n100th element (by looping): " << x_100;
x_100 = r(x_0);
g <<"\n100th element (by recursion): " << x_100;
return 0;
}
l()
is iterative function,
r()
is recursive function
double l(double x, int i)
{
for (int j = 0; j<i ; j ){
x = (x 1)/(x 2);
}
return x;
}
double r(double x)
{
if (x == 0)
return 1;
else
return (r(x-1) 1) / (r(x-1) 2);
}
Here are the results
100th element (by looping): 0.618034
100th element (by recursion): 0.666667
CodePudding user response:
I the recursive function you do
(r(x-1) 1) / (r(x-1) 2)
With x == 1.0
that's equal to
(r(1-1) 1) / (r(1-1) 2)
That's of course equal to
(r(0) 1) / (r(0) 2)
And since r(0)
will return 1
that equation is
(1.0 1) / (1.0 2)
There's no further recursion. The result is 2.0 / 3.0
which is 0.66667
.
The iterative function l
on the other hand will do 100
iterations where each iteration will change the value of x
, making it even smaller and smaller.
The functions simply does different things, leading to different results.