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 and Output
Input: Take the term number as an input. Say it is 10 Output: Enter number of terms: 10 10th fibinacci Terms: 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
#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