import java.util.Arrays;

class Recursion {

	public static void main(String[] args) {
		Recursion r = new Recursion();
		System.out.println("2 to the power 5 = "+r.power(2,5));
		
		int [] array = {1,2,2,2,3,4,5,5,5,6};
		System.out.println("Mean of array {1,2,2,2,3,4,5,5,5,6} is: "+r.mean(array));
		System.out.println("Mode of array {1,2,2,2,3,4,5,5,5,6} is: "+r.mode(array));
	}

	public int power(int a, int b){
		if(b == 0)
			return 1;
		
		else
			return power(a, b, 0, 1);
	}
	
	public int power(int a, int b, int counter, int pow){
		if(b == counter)
			return pow;
		
		return power(a, b, counter+1, pow * a);
	}
	
	public int mean(int list[]){
		if(list == null)
			return 0;
		
		else return mean(list, 0, 0);
	}
	
	public int mean(int list[], int index, int sum){
		if(index == list.length)
			return (sum / list.length);
		else 
			return mean(list, index+1, sum+list[index]);
	}
	
	
	// if more than 1 element has the same number of duplications, the first one is returned
	public int mode(int list[]){
		Arrays.sort(list);
		return mode(list, list[0], 1, 1, 1);
	}
	
	public int mode(int list[], int maxMode, int maxOccurrence, int currentOccurrence, int index){
		if(index == list.length)
			return maxMode;
		
		// the new occurrence is more than the previous maximum occurrence
		else if (list[index] == list[index-1] && currentOccurrence == maxOccurrence)
			return mode(list, list[index], currentOccurrence+1, currentOccurrence+1, index+1);
		
		// the new occurrence is not more than the previous maximum occurrence
		else if(list[index] == list[index-1])
			return mode(list, maxMode, maxOccurrence, currentOccurrence+1, index+1);
		
		// the new element has a different number
		else
			return mode(list, maxMode, maxOccurrence, 1, index+1);
			
	}
}