Recursive Fibonacci memoization

Question

I need some help with a program I'm writing for my Programming II class at universtiy. The question asks that one calculates the Fibonacci sequence using recursion. One must store the calculated Fibonacci numbers in an array to stop unnecessary repeated calculations and to cut down to the calculation time.

I managed to get the program working without the array and memorization, now I'm trying to implement that and I'm stuck. I'm not sure how to structure it. I've Googled and skimmed through some books but haven't found much to help me solve how to implement a solution.

import javax.swing.JOptionPane;
public class question2
{
static int count = 0;
static int [] dictionary;

public static void main(String[] args)
{

int answer;
int num = Integer.parseInt(javax.swing.JOptionPane.showInputDialog("Enter n:"));

javax.swing.JOptionPane.showMessageDialog(null, 
        "About to calculate fibonacci(" + num + ")");

//giving the array "n" elements
dictionary= new int [num];

if (dictionary.length>=0)
dictionary[0]= 0;

if (dictionary.length>=1)
dictionary[0]= 0;
dictionary[1]= 1;


//method call
answer = fibonacci(num);

//output
JOptionPane.showMessageDialog(null,"Fibonacci("+num+") is "+answer+" (took "+count+" calls)");
}



  static int fibonacci(int n)
  {
count++;

// Only defined for n >= 0
if (n < 0) {
  System.out.println("ERROR: fibonacci sequence not defined for negative numbers.");
  System.exit(1);
}

// Base cases: f(0) is 0, f(1) is 1
// Other cases: f(n) = f(n-1) + f(n-2)/
if (n == 0) 
{
  return dictionary[0];
}

else if (n == 1) 
{
  return dictionary[1];
}

else
return dictionary[n] = fibonacci(n-1) + fibonacci(n-2);



}

}

The above is incorrect, the end of my fib method is the main problem. I've no idea how to get it to add the numbers recursively to the correctly parts of the array.

Answer 1

Here is my implementation of recursive fibonacci memoization. Using BigInteger and ArrayList allows to calculate 100th or even larger term. I tried 1000th terms, and result is returned in a matter of milliseconds, here is the code:

    private static List<BigInteger> dict = new ArrayList<BigInteger>();
    public static void printFebonachiRecursion (int num){
    if (num==1){
        printFebonachiRecursion(num-1);
        System.out.printf("Term %d: %d%n",num,1);
        dict.add(BigInteger.ONE);
    }
    else if (num==0){
        System.out.printf("Term %d: %d%n",num,0);
        dict.add(BigInteger.ZERO);
    }
    else {
    printFebonachiRecursion(num-1);
    dict.add(dict.get(num-2).add(dict.get(num-1)));
    System.out.printf("Term %d: %d%n",num,dict.get(num));
    }
}

Output example

printFebonachiRecursion(100);

Term 0: 0
Term 1: 1
Term 2: 1
Term 3: 2
...
Term 98: 135301852344706746049
Term 99: 218922995834555169026
Term 100: 354224848179261915075

Answer 2

Program to print first n fibonacci numbers using Memoization.

int[] dictionary; 
// Get Fibonacci with Memoization
public int getFibWithMem(int n) {
    if (dictionary == null) {
        dictionary = new int[n];
    }

    if (dictionary[n - 1] == 0) {
        if (n <= 2) {
            dictionary[n - 1] = n - 1;
        } else {
            dictionary[n - 1] = getFibWithMem(n - 1) + getFibWithMem(n - 2);
        }
    }

    return dictionary[n - 1];
}

public void printFibonacci()
{
    for (int curr : dictionary) {
        System.out.print("F[" + i++ + "]:" + curr + ", ");
    }
}

Answer 3

This is another way to approach memoization for recursive fibonacci() method using a static array of values -

public static long fibArray[]=new long[50];\\Keep it as large as you need

public static long fibonacci(long n){
long fibValue=0;
if(n==0 ){
    return 0;
}else if(n==1){
    return 1;
}else if(fibArray[(int)n]!=0){
    return fibArray[(int)n];    
}
else{
    fibValue=fibonacci(n-1)+fibonacci(n-2);
    fibArray[(int) n]=fibValue;
    return fibValue;
}
}

Note that this method uses a global(class level) static array fibArray[]. To have a look at the whole code with explanation you can also see the following - http://www.javabrahman.com/gen-java-programs/recursive-fibonacci-in-java-with-memoization/

Answer 4

#include <stdio.h>
long int A[100]={1,1};
long int fib(int n){
    if (A[n])
    {
        return A[n];
    }
    else
    {
         return A[n]=fib(n-1)+fib(n-2);
    }
}
int main(){
    printf("%ld",fib(30));
}