The Leonardo numbers are a sequence of integers defined by the following recurre

Question

The Leonardo numbers are a sequence of integers defined by the following recurrence:

L (0) = 1

L (1) = 1
L (n ) = L (n 1 ) + L ( n 2 ) + 1

The first few Leonardo numbers are 1, 1, 3, 5, 9, 15, 25.

The Leonardo number problem is:

input: a non-negative integer n

output: Leonardo number L(n )

1) Design an algorithm for this problem using the dynamic programming pattern. Write pseudocode for your algorithm below. If you write multiple drafts, circle your final draft.

2) then, Prove the efficiency class of your algorithm using any method you wish.

Explanation / Answer

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class LeonardoNumbers {

    
    public static void main(String[] args) throws NumberFormatException, IOException{
        
        InputStreamReader isr = new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(isr);
        
        System.out.println("Enter the range to which leonard numbers should be printed");
        int n = Integer.parseInt(br.readLine());
        
        LeonardoNumbers lnd = new LeonardoNumbers();
        System.out.println("Leonardo Series is as follows ");
        int result = 0;
        for(int i = 1;i<=n; i++){
            result = lnd.leonardo(i);
            System.out.print(" "+result);
        }
    }

    private int leonardo(int n) {
            
        if(n == 1)
            return 1;
        if(n == 2)
            return 1;
        else
            return leonardo(n-1)+leonardo(n-2) + 1;
        
    }
}

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