/*PLEASE READ:
 *When you are executing the code
 *Please keep in mind that factorial
 *of integers grow explosively
 *so an integer variable is unable to
 *store factorial of a number larger
 *than 16, if you need to deal with larger
 *numbers change the function make it
 *double fact(double)
 *
 */

#include<iostream>
#include<cstring>
#include<iomanip>
using namespace std;
int fact(int);
//exp is same as pow, I change the name
//because pow is a library function
//available in math header file  
double exp(double,int);
double mult(double,double);
int gcd(int,int);
//The name is change to make a distinction
//from strlen which is already difined
//in <cstring>
int strlength(char*,int);
int palindrome(char*,int);
//A function with two base cases
//following function returns the 
//nth element in a fibonacci series 
int fibonacci(int);

int main(){
	int x,y;
	char s[50];
	cout<<"Enter two positive integers: ";
	cin>>x>>y;
	cout<<"Factorial of "<<x<<" is "<<fact(x)
		<<" and factorial of "<<y<<" is "<<fact(y)
		<<endl;
	if (x==0|| y==0){
		cout<<"Couldn't compute gcd 'cause one"
			<<"of them is 0"<<endl;
	}
	
	else {
		cout<<"GCD of the two numbers you've"
			<<" entered is "<<gcd(x>y?x:y,x>y?y:x)
			<<endl;
	}
	
	cout<<x<<" to the power of "<<y<<" is "
		<<setiosflags(ios::fixed|ios::showpoint)
		<<setprecision(2)<<exp(x,y)<<endl;

	cout<<"The "<<x<< "th element of fibonacci "
		<<"is "<<fibonacci(x)<<endl;
	
	cout<<"Now enter a string: ";
	cin>>s;
	cout<<"The length of the string is "
		<<strlength(s,0)<<endl;
	
	if(palindrome(s,0))cout<<s<<" is a palindrome\n";
	else cout<<s<<" is not aplindrome\n";

	return 0;
}

int fact(int x){
	if(x==0) return 1;
	else return x*fact(x-1);
}

double exp(double base, int pow){
	if(pow==0) return 1;
	else if(pow>0) return base*exp(base,pow-1);
	//Now let's take care of negative power
	else return (1/base)*exp(base,pow+1);
}

int gcd(int big, int small){
	if(big%small==0) return small;
	else return gcd(small,big%small);
}

int strlength(char *s,int index){
	if(s[index]=='\0') return 0;
	else return 1+strlength(s,index+1);
}

int palindrome(char* s, int index){
	if(index == (strlen(s)/2)) return 1;
	else if(s[index] != s[strlen(s)-1-index]) return 0;
	else return palindrome(s,index+1);
}

int fibonacci(int n){
	if(n==0) return 0;
	else if(n==1) return 1;
	else return fibonacci(n-2)+fibonacci(n-1);
}