Examples on Recursion.
Sum of natural number using Recursion.
public class SumOfNaturalNumber {
public static int sum(int x){
if(x<=0)
return 0;
return sum(x-1)+x;
}
public static void main(String[] args) {
System.out.println(sum(20));
}
}
Factorial of given number.
public class FactorialOfNumber {
public static int factorial(int x){
if(x==0)
return 1;
return factorial(x-1)*x;
}
public static void main(String[] args) {
System.out.println(factorial(20));
}
}
Find the power of the given number.
public class PowerOfNumber {
/*First method*/
public static int Power(int base,int exponent){
if(exponent==0)
return 1;
return factorial(base,exponent-1)*base;
}
/*second method*/
public static int Power1(int base,int exponent){
if(exponent==0)
return 1;
if(exponent%2==0)
return Power1(base*base,exponent/2);
return
base*Power1(base*base,(exponent-1)/2);
}
public static void main(String[] args) {
//input
Power(base,exponent)
System.out.println(Power(4,2));
System.out.println(Power1(4,2));
}
}
Taylor Series using recursion.
public class Exponential {
static int power=1;
static int factorial=1;
public static double exponential(int x,int n){
double r;
if(n==0)
return 1;
r=exponential(x,n-1);
power=power*x;
factorial=factorial*n;
return r+power/factorial;
}
public static void main(String[] args) {
System.out.println(exponential(1,10));
}
}
Factorial Of Given Number.
public class FactorialOfNumber {
public static int factorial(int x){
if(x==0)
return 1;
return factorial(x-1)*x;
}
public static void main(String[] args) {
System.out.println(factorial(20));
}
}
Taylor Series using Horner's rules.
public class TaylorSeriesOnHornerRule {
static int s=1;
public static double exponential(int x,int n){
if(n==0)
return s;
s=1+x*s/n;
return exponential(x,n-1);
}
public static void main(String[] args) {
System.out.println(exponential(2,10));
}
}
Find the nth term from Fibonacci series.
public class FibonacciSeries {
public static int fibonacciTerm(int x){
if(x==0)
return 0;
if(x==1)
return 1;
return fibonacciTerm(x-1)+fibonacciTerm(x-2);
}
public static void main(String[] args) {
System.out.println(fibonacciTerm(20));
}
}
Find the Combination using nCr
public class Combinations {
public static int ncr(int n,int r){
if(n==r || r==0)
return 1;
return ncr(n-1,r-1)+ncr(n-1,r);
}
public static void main(String[] args) {
System.out.println(ncr(5,2));
}
}