I have to count sum 1/1+1/2+1/3+1/4+1/n series using recursion. I have tried this but it does not work. how should I solve it?
#include<iostream>
using namespace std;
double sum(int n)
{
if(n==1){return 1;}
if(n==0){return 0;}
return 1+1/sum(n-1);
}
int main(){
cout<<sum(2);
}
As others already pointed out in the comments, the formula in your function results in another series than the intended harmonic series. Here, a possible solution:
#include <iostream>
using namespace std;
double sum_recursive(int n)
{
if (n <= 0) {
return 0.0;
} else {
cout << "1/" << n << (n!=1 ? " + " : " = "); // just for debugging
return (1.0 / double(n)) + sum_recursive(n-1);
}
}
double sum_iterative(int n)
{
double v = 0.0;
if (n <= 0) {
return 0.0;
}
for (int i=n; i>0; --i) {
v += 1.0 / double(i);
cout << "1/" << i << (i!=1 ? " + " : " = "); // just for debugging
}
return v;
}
int main()
{
const int x = 4;
cout << sum_iterative(x) << " (iterative)" << endl;
cout << sum_recursive(x) << " (recursive)" << endl;
return 0;
}
Console:
$ g++ test_seq.c && ./a.out
1/4 + 1/3 + 1/2 + 1/1 = 2.08333 (iterative)
1/4 + 1/3 + 1/2 + 1/1 = 2.08333 (recursive)
Assuming this is just used as an exercise, it should be noted, that a recursive solution doesn't have any apparent advantages over a simple loop...
There are several ways you can approach this. While recursive functions can provide elegant solutions for some problem where a non-recursive approach is difficult, recursion in general should not be your first choice. Why? Each recursive call is a separate function call that requires the setup and resources of a complete function stack. If you recurse too many times, you will actually learn about StackOverflow...
That said, learning recursive functions are a necessary part of learning to program. Here the number of recursive calls is limited to n so you are safe. Every recursive function has two things:
You want to preserve a sum over your recursive calls. A static variable initialized on its first declaration will do. So in this case, you can do something like:
double sum (int n)
{
static double val = 0.;
if (n) {
val += 1. / n;
sum (n - 1);
}
return val;
}
The scheme above is relatively simple. You use a check for a positive value for n as your exit condition, and each time you make a recursive call you reduce the value of n by 1. If you want to see how your recursion is progressing, you can add debug output between the update of val and the recursive call to sum (n - 1) such as:
std::cout << "n:" << n << " frac: 1/" << n << " val: " << val << '\n';
A short example that takes the first argument to the program as n could be:
#include <iostream>
#include <string>
double sum (int n)
{
static double val = 0.;
if (n) {
val += 1. / n;
sum (n - 1);
}
return val;
}
int main (int argc, char **argv) {
/* initialize with 1st argument to program (default: 2) */
std::string s { argc > 1 ? argv[1] : "2" };
int n;
try { /* stoi must have exception handler */
n = stoi (s); /* attempt conversion */
std::cout << sum (n) << '\n'; /* output result */
}
catch (const std::exception & e) { /* catch exception return error */
return 1;
}
}
Example Use/Output
The resulting values for n from 0 to 20 would be:
$ for i in {0..20}; do printf "%2d " $i; ./bin/frac_sum_recurse $i; done
0 0
1 1
2 1.5
3 1.83333
4 2.08333
5 2.28333
6 2.45
7 2.59286
8 2.71786
9 2.82897
10 2.92897
11 3.01988
12 3.10321
13 3.18013
14 3.25156
15 3.31823
16 3.38073
17 3.43955
18 3.49511
19 3.54774
20 3.59774
While you are building good habits learning C++, have a look at: Why is “using namespace std;” considered bad practice?. Here it would save no more than three std::.
Look things over and let me know if you have further questions.
