92 lines
2.2 KiB
Java
92 lines
2.2 KiB
Java
package DynamicProgramming;
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import java.util.HashMap;
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import java.util.Map;
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import java.util.Scanner;
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/** @author Varun Upadhyay (https://github.com/varunu28) */
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public class Fibonacci {
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private static Map<Integer, Integer> map = new HashMap<>();
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public static void main(String[] args) {
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// Methods all returning [0, 1, 1, 2, 3, 5, ...] for n = [0, 1, 2, 3, 4, 5, ...]
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Scanner sc = new Scanner(System.in);
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int n = sc.nextInt();
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System.out.println(fibMemo(n));
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System.out.println(fibBotUp(n));
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System.out.println(fibOptimized(n));
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sc.close();
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}
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/**
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* This method finds the nth fibonacci number using memoization technique
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*
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* @param n The input n for which we have to determine the fibonacci number Outputs the nth
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* fibonacci number
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*/
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public static int fibMemo(int n) {
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if (map.containsKey(n)) {
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return map.get(n);
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}
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int f;
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if (n <= 1) {
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f = n;
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} else {
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f = fibMemo(n - 1) + fibMemo(n - 2);
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map.put(n, f);
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}
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return f;
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}
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/**
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* This method finds the nth fibonacci number using bottom up
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*
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* @param n The input n for which we have to determine the fibonacci number Outputs the nth
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* fibonacci number
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*/
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public static int fibBotUp(int n) {
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Map<Integer, Integer> fib = new HashMap<>();
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for (int i = 0; i <= n; i++) {
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int f;
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if (i <= 1) {
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f = i;
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} else {
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f = fib.get(i - 1) + fib.get(i - 2);
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}
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fib.put(i, f);
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}
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return fib.get(n);
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}
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/**
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* This method finds the nth fibonacci number using bottom up
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*
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* @param n The input n for which we have to determine the fibonacci number Outputs the nth
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* fibonacci number
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* <p>This is optimized version of Fibonacci Program. Without using Hashmap and recursion. It
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* saves both memory and time. Space Complexity will be O(1) Time Complexity will be O(n)
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* <p>Whereas , the above functions will take O(n) Space.
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* @author Shoaib Rayeen (https://github.com/shoaibrayeen)
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*/
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public static int fibOptimized(int n) {
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if (n == 0) {
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return 0;
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}
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int prev = 0, res = 1, next;
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for (int i = 2; i <= n; i++) {
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next = prev + res;
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prev = res;
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res = next;
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}
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return res;
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}
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}
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