Add 509. Fibonacci Number bottom up solution

Author: Rion5

LeetCode/FibonacciNumber.cs

@@ -22,6 +22,7 @@ public FibonacciNumber(int n)
 
  private int fib(int n)
  {
+ /*
  // Base cases
  int result = 0;
  if (n == 0) return result;
@@ -35,12 +36,53 @@ private int fib(int n)
  result = fib(n - 1) + fib(n - 2);
  }
  return result;
+ */
+ int?[] memo = new int?[n+1];
+ return fibMemoization(n, memo);
+ }
+
+ // Using Memoization to cache Fibonacci results
+ // Improves Time Complexity from O(2^n) to O(n)
+ private int fibMemoization(int n, int?[] memo)
+ {
+ // If the result has already been calculated, it will exist in the memo array.
+ if (memo[n] != null) return (int) memo[n];
+ int result = 0;
+ if (n == 0) return result;
+ if (n == 1 || n == 2)
+ {
+ result = 1;
+ }
+ else
+ {
+ result = fib(n - 1) + fib(n - 2);
+ memo[n] = result;
+ }
+ return result;
+ }
+
+ private int fibBottomUp(int n)
+ {
+ // Time Complexity : O(n)
+ // Space Complexity: O(n), where n is the input number
+ // Base Cases
+ if (n == 0) return 0;
+ if (n == 1 || n == 2) return 1;
+ // Build the Fibonacci Sequence from left to right iteratively
+ int[] bottomUp = new int[n + 1];
+ bottomUp[1] = 1;
+ bottomUp[2] = 1;
+ for (int i = 3; i < bottomUp.Length; i++)
+ {
+ bottomUp[i] = bottomUp[i - 1] + bottomUp[i - 2];
+ }
+ return bottomUp[n];
  }
 
  public override void PrintExample()
  {
  var watch = System.Diagnostics.Stopwatch.StartNew();
- var results = fib(this.n);
+ var results = fibBottomUp(this.n);
  watch.Stop();
  Console.WriteLine($"509. Fibonacci Number\n" +
  $"Input Num = {this.n} \n" +