509 Fibonacci Number ✅¶

Leetcode

The Fibonacci numbers, commonly denoted F(n) form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,

::: tip 💡 Use fibCache = new Dictionary<int, int>() to improve performance :::

F(0) = 0, F(1) = 1
F(n) = F(n - 1) + F(n - 2), for n > 1.

Given n, calculate F(n).

Example 1:

Input: n = 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.

Example 2:

Input: n = 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.

Example 3:

Input: n = 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.

C# Solution¶

using System;
using System.Collections.Generic;

namespace Algorithms.Simple
{
  public class FibonacciNumber
  {
    public static int Recursive(int v)
    {
      if (v <= 1) return v;

      return Recursive(v - 1) + Recursive(v - 2);
    }

    public static int Dynamic(int v)
    {
      var fibCache = new Dictionary<int, int>();

      if (v <= 1) return v;

      if (fibCache.ContainsKey(v))
      {
        return fibCache[v];
      }
      else
      {
        fibCache.Add(v, Dynamic(v - 1) + Dynamic(v - 2));

      }

      return fibCache[v];
    }

    public static int Cache01Space(int v)
    {

      if (v <= 1) return v;

      var fb0 = 0;
      var fb1 = 1;

      for (var i = 2; i <= v; i++)
      {
        var fb = fb0 + fb1;
        fb0 = fb1;
        fb1 = fb;
      }

      return fb1;
    }
  }


}

C# Tests¶

using System;
using Algorithms.Simple;
using Xunit;

namespace AlgorithmTests.Simple
{
  public class FibonacciNumberTests
  {
    [Fact]
    public void RecursiveTest1()
    {
      Assert.Equal(3, FibonacciNumber.Recursive(4));
    }

    [Fact]
    public void DynamicTest1()
    {
      Assert.Equal(3, FibonacciNumber.Dynamic(4));
    }

    [Fact]
    public void FibCacheO1Space()
    {
      Assert.Equal(3, FibonacciNumber.Cache01Space(4));
    }
  }
}