JavaAlgorithms/DynamicProgramming/Fibonacci.java

package DynamicProgramming;

import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

/** @author Varun Upadhyay (https://github.com/varunu28) */
public class Fibonacci {

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

  public static void main(String[] args) {

    // Methods all returning [0, 1, 1, 2, 3, 5, ...] for n = [0, 1, 2, 3, 4, 5, ...]
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();

    System.out.println(fibMemo(n));
    System.out.println(fibBotUp(n));
    System.out.println(fibOptimized(n));
    sc.close();
  }

  /**
   * 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
   */
  public static int fibMemo(int n) {
    if (map.containsKey(n)) {
      return map.get(n);
    }

    int f;

    if (n <= 1) {
      f = n;
    } 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
   */
  public static int fibBotUp(int n) {

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

    for (int i = 0; i <= n; i++) {
      int f;
      if (i <= 1) {
        f = i;
      } 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
   *
   * @param n The input n for which we have to determine the fibonacci number Outputs the nth
   *     fibonacci number
   *     <p>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)
   *     <p>Whereas , the above functions will take O(n) Space.
   * @author Shoaib Rayeen (https://github.com/shoaibrayeen)
   */
  public 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;
  }
}