Recursion and Dynamic Programming

Author: Turingfly

src/chapter08RecursionAndDynamicProgramming/Fibonacci.java

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+package chapter08RecursionAndDynamicProgramming;
+
+/**
+ * 
+ * Problem: Compute the Nth Fibonacci number.
+ *
+ */
+public class Fibonacci {
+	/**
+	 * Method 1: Recursive
+	 * 
+	 * Time Complexity: O(2N), where N is the number of nodes.
+	 */
+	public int fibonacci1(int n) {
+		if (n == 0 || n == 1) {
+			return n;
+		}
+		return fibonacci1(n - 1) + fibonacci1(n - 2);
+	}
+
+	/**
+	 * Method 2: Top-Down Dynamic Programming (or Memorization)
+	 * 
+	 * Time Complexity: O(N)
+	 */
+	public int fibonacci2(int n) {
+		return helper(n, new int[n + 1]);
+	}
+
+	private int helper(int n, int[] memo) {
+		if (n == 0 || n == 1) {
+			return n;
+		}
+		if (memo[n] == 0) {
+			memo[n] = helper(n - 1, memo) + helper(n - 2, memo);
+		}
+		return memo[n];
+	}
+
+	/**
+	 * Method 3: Bottom-Up Dynamic Programming
+	 */
+	public int fibonacci3(int n) {
+		if (n == 0 || n == 1) {
+			return n;
+		}
+		int[] memo = new int[n];
+		memo[0] = 0;
+		memo[1] = 1;
+		for (int i = 2; i < n; i++) {
+			memo[i] = memo[i - 1] + memo[i - 2];
+		}
+		return memo[n - 1] + memo[n - 2];
+	}
+
+	/**
+	 * Method 4: Optimize Method3
+	 */
+	public int fibonacci4(int n) {
+		if (n == 0 || n == 1) {
+			return n;
+		}
+		int a = 0;
+		int b = 1;
+		for (int i = 2; i < n; i++) {
+			int c = a + b;
+			a = b;
+			b = c;
+		}
+		return a + b;
+	}
+}