Recursion.java

import java.io.*;

public class Recursion
{
	public static void main( String[] args )
	{

		// T R I S T A R S 
		int rows = 5;
		System.out.format("A tringle with %d rows contains %d stars\n", rows, triStars( rows ) );
		
		// S U M D I G I T S
		int number = 12345;
		System.out.format("The sum of the digits in the number %d = %d\n", number, sumDigits( number ) );
		
		// C O U N T 7 S
		number = 713274772;
		System.out.format("There are %d occurances of the digit 7 in the number %d\n", count7s(number), number );
		
		// C O U N T 8 S
		number = 82338828;
		System.out.format("There are %d occurances of the digit 8 in the number %d\n", count8s(number), number );	

		// P O W E R N
		int base=2,exponent=8;
		System.out.format("%d to the power %d = %d\n", base, exponent, powerN(base,exponent) );	
	

		// I S S O R T E D 
		// perturb values as needed to test on an unsorted array
		int[] array = { 7, 8, 12, 20, 21, 22, 37, 41, 55, 60, 65, 74, 83, 84, 87 };
		int startingAt=0;
		boolean isSorted = isSorted( array, startingAt, array.length );
		System.out.print( "array: ");
		for ( int i=0 ; i<array.length ; ++i ) System.out.print( array[i] + " " );
		if (isSorted)
			System.out.println(" is SORTED" );	
		else
			System.out.println(" is NOT SORTED" );	

 
		// P A L I N D R O M E
		String s = "stanleyyelnats"; // try with several differnt values that are or not palindromes	
		if ( isPalindrome( s, 0, s.length()-1 ) )
			System.out.format("%s IS a palindrome\n", s );	
		else
			System.out.format("\n%s NOT a palindrome\n", s ); 	
		
	
	
	} // END MAIN

	// count stars in a triangle using # of rows as input
	static int triStars(int rows)  
	{	
		if (rows==0) return 0;
		return rows + triStars(rows-1);
	}
	
	// given a number return the sum of the digits
	static int sumDigits(int n) 
	{	
		if (n==0) return 0;
		return n%10 + sumDigits(n/10);	
	}
	
	// given a number compute the number of 7's in that number 
	static int count7s(int n) 
	{	
		if (n==0) return 0;
		if (n%10==7) return 1 + count7s(n/10);
		return count7s(n/10);
	}
	
	// given a number count the number of 8 but if an 8 has another 8 to its immdiate left count it as 2 
	// the number 8802388 will return a count of 6
	static int count8s(int n) 
	{	
		if (n==0) return 0;
		if (n%10==8 && n%10==(n/10)%10) return 2 + count8s(n/10);
		if (n%10==8) return 1 + count8s(n/10);
		return count8s(n/10);
	}
	
	//compute base to the power n
	static int powerN(int base, int n) 
	{	
		if (n==0) return 1;
		return base * powerN(base,n-1);
	}
	
	// return true only if the array is sorted 
	static boolean isSorted(int array[], int i, int count ) 
	{	
		if (i==count-1) return true;
		if (array[i]>array[i+1]) return false;
		return isSorted(array, i+1, count);			                  //No [] after array
	}

	// return index of key or -1 
	static boolean isPalindrome(String s, int lo, int hi ) 
	{	
		if (lo==hi) return true;
		if (s.indexOf(lo)!=s.indexOf(hi)) return false;
		return isPalindrome(s, lo+1, hi+1);
	}
	
} // END CLASS Recursion