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Fibonacci.java
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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;
}
}