C++ Program to Find Fibonacci Numbers using Dynamic Programming

The Fibonacci sequence is like this,

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,……

In this sequence the nth term is the sum of (n-1)^th and (n-2)^th terms.

To generate we can use the recursive approach, but in dynamic programming the procedure is simpler. It can store all Fibonacci numbers in a table, by using that table it can easily generate the next terms in this sequence.

Input − Take the term number as an input. Say it is 10

Output − The 10^th fibinacci term is 55

Algorithm

genFiboSeries(n)

Input

max number of terms.

Output

The nth Fibonacci term.

Begin
define array named fibo of size n+2
fibo[0] := 0
fibo[1] := 1
for i := 2 to n, do
fibo[i] := fibo[i-1] + fibo[i-2]
done
return fibo[n]
End

Example Code

#include<iostream>
using namespace std;
int genFibonacci(int n) {
   int fibo[n+2]; //array to store fibonacci values
   // 0th and 1st number of the series are 0 and 1
   fibo[0] = 0;
   fibo[1] = 1;
   for (int i = 2; i <= n; i++) {
      fibo[i] = fibo[i-1] + fibo[i-2]; //generate ith term using previous
      two terms
   }
   return fibo[n];
}
int main () {
   int n;
   cout << "Enter number of terms: "; cin >>n;
   cout << n<<" th Fibonacci Terms: "<<genFibonacci(n)<<endl;
}

Output

Enter number of terms: 10
10th Fibonacci Terms: 55