# Learning from Examples » Fibonacci Number

We study the classic problem, Fibonacci Number, to demonstrate the use of recursive task parallelism.

## Problem Formulation

In mathematics, the Fibonacci numbers, commonly denoted `F(n)`, form a sequence such that each number is the sum of the two preceding ones, starting from 0 and 1.

`0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...`

A common solution for computing fibonacci numbers is recursion.

    int fib(int n) {
      if(n < 2) return n;
      return fib(n-1) + fib(n-2);
    }

## Recursive Fibonacci Parallelism

We use tf::Subflow to recursively compute fibonacci numbers in parallel.

    #include <taskflow/taskflow.hpp>

    int spawn(int n, tf::Subflow& sbf) {
      if (n < 2) return n;
      int res1, res2;
      sbf.emplace([&res1, n] (tf::Subflow& sbf) { res1 = spawn(n - 1, sbf); } )
         .name(std::to_string(n-1));
      sbf.emplace([&res2, n] (tf::Subflow& sbf) { res2 = spawn(n - 2, sbf); } )
         .name(std::to_string(n-2));
      sbf.join();
      return res1 + res2;
    }

    int main(int argc, char* argv[]) {

      int N = 5;
      int res;

      tf::Executor executor;
      tf::Taskflow taskflow("fibonacci");

      taskflow.emplace([&res, N] (tf::Subflow& sbf) { res = spawn(N, sbf); })
              .name(std::to_string(N));

      executor.run(taskflow).wait();

      taskflow.dump(std::cout);

      std::cout << "Fib[" << N << "]: " << res << std::endl;

      return 0;
    }

The spawned taskflow graph for computing up to the fifth fibonacci number is shown below:

Even if recursive dynamic tasking or subflows are possible, the recursion depth may not be too deep or it can cause stack overflow.

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