JavaAlgorithms/Dynamic Programming/Fibonacci.java

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.Map;

/**
 *
 * @author Varun Upadhyay (https://github.com/varunu28)
 *
 */

public class Fibonacci {

    private static Map<Integer,Integer> map = new HashMap<Integer,Integer>();

    public static void main(String[] args) throws Exception {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());

        System.out.println(fibMemo(n)); // Returns 8 for n = 6
        System.out.println(fibBotUp(n)); // Returns 8 for n = 6
    }

    /**
     * This method finds the nth fibonacci number using memoization technique
     *
     * @param n The input n for which we have to determine the fibonacci number
     * Outputs the nth fibonacci number
     **/

    
   
    
    
    private static int fibMemo(int n) {
        if (map.containsKey(n)) {
            return map.get(n);
        }

        int f;

        if (n <= 2) {
            f = 1;
        }
        else {
            f = fibMemo(n-1) + fibMemo(n-2);
            map.put(n,f);
        }

        return f;
    }

    /**
     * This method finds the nth fibonacci number using bottom up
     *
     * @param n The input n for which we have to determine the fibonacci number
     * Outputs the nth fibonacci number
     **/

    private static int fibBotUp(int n) {

        Map<Integer,Integer> fib = new HashMap<Integer,Integer>();

        for (int i=1;i<n+1;i++) {
            int f = 1;
            if (i<=2) {
                f = 1;
            }
            else {
                f = fib.get(i-1) + fib.get(i-2);
            }
            fib.put(i, f);
        }

        return fib.get(n);
    }
    
    
    
    /**
     * This method finds the nth fibonacci number using bottom up
     *
     * @author Shoaib Rayeen (https://github.com/shoaibrayeen)
     * @param n The input n for which we have to determine the fibonacci number
     * Outputs the nth fibonacci number
     * 
     * This is optimized version of Fibonacci Program. Without using Hashmap and recursion.
     * It saves both memory and time.
     *  Space Complexity will be O(1)
     *  Time Complexity will be O(n)
     *
     *  Whereas , the above functions will take O(n) Space.
     **/
    private static int fibOptimized(int n) {
 
        if (n == 0) {
            return 0;
        }
        int prev = 0 , res = 1 , next;
        for ( int i = 2; i < n; i++) {
              next = prev + res;
              prev = res;
              res = next;
        }
        return res;
    }
}