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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;

}

}