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C++ Program to Display Fibonacci Series
The fibonacci series contains numbers in which each term is the sum of the previous two terms. This creates the following integer sequence −
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377…….
The recurrence relation that defines the fibonacci numbers is as follows −
F(n) = F(n-1) + F(n-2) F(0)=0 F(1)=1
Programs to Display Fibonacci Series
There are two methods to display fibonacci series i.e. using dynamic programming and recursive programming. These are further explained as follows −
Dynamic Programming
Example
#include<iostream>
using namespace std;
void fib(int n) {
int f[n];
int i;
f[0] = 0;
f[1] = 1;
for (i = 2; i < n; i++) {
f[i] = f[i-1] + f[i-2];
}
for (i = 0; i < n; i++) {
cout<<f[i]<<" ";
}
}
int main () {
int n = 10;
fib(n);
getchar();
return 0;
}The output of the above program is as follows.
Output
0 1 1 2 3 5 8 13 21 34
In the program, main() is the driver function. The actual code for the creation of the fibonacci series is stored in the function fib() which is called from main.
An array f[n] is created which will store the first n terms of the fibonacci series. The first and second elements of this array are initialized to 0 and 1 respectively.
f[0] = 0; f[1] = 1;
Then for loop is used to store each element in the array as the sum of its previous two elements.
for (i = 2; i < n; i++) {
f[i] = f[i-1] + f[i-2];
}Finally the fibonacci series is displayed.
for (i = 0; i < n; i++) {
cout<<f[i]<<" ";
}Recursive Programming
Let us see how to display fibonacci series using recursion.
Example
#include<iostream>
using namespace std;
int fib(int n) {
if (n <= 1)
return n;
return fib(n-1) + fib(n-2);
}
int main () {
int n = 10, i;
for(i=0;i<n;i++)
cout<<fib(i)<<" ";
return 0;
}Output
0 1 1 2 3 5 8 13 21 34
In the above program, a for loop is set that creates each term of the fibonacci series using recursion. This is done by calling the function fib() for each term in the series.
for(i=0;i<n;i++) cout<<fib(i)<<" ";
The function fib() returns 0 or 1 if n is 0 or 1 respectively. If not, it calls itself recursively as the sum of the previous two terms until the correct value is returned.
if (n <= 1) return n; return fib(n-1) + fib(n-2);
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