docs: update the whole repository

* fix some bugs
* delete duplicate files
* format code

DynamicProgramming/Fibonacci.java

@@ -0,0 +1,98 @@
+package DynamicProgramming;
+
+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<>();
+
+    public static void main(String[] args) throws Exception {
+
+        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
+        int n = Integer.parseInt(br.readLine());
+
+        // Methods all returning [0, 1, 1, 2, 3, 5, ...] for n = [0, 1, 2, 3, 4, 5, ...]
+        System.out.println(fibMemo(n));
+        System.out.println(fibBotUp(n));
+    }
+
+    /**
+     * 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 <= 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
+     **/
+    private 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)
+     **/
+    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;
+    }
+}