Update fibonacci.rb

dynamic_programming/fibonacci.rb

@@ -1,53 +1,16 @@
-# 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,
-#
-# F(0) = 0, F(1) = 1
-# F(n) = F(n - 1) + F(n - 2), for n > 1
-#
-# Given n, calculate F(n).
+def fibonacci(n)
+  # Create an array to store Fibonacci numbers
+  fib = [0, 1]
 
-#
-# Approach: Top-Down Approach using Memoization
-#
+  # Calculate Fibonacci numbers from the bottom up
+  (2..n).each do |i|
+    fib[i] = fib[i - 1] + fib[i - 2]
+  end
 
-# Complexity Analysis:
-#
-# Time complexity: O(n). Each number, starting at 2 up to and
-# including N, is visited, computed and then stored for O(1) access
-# later on.
-#
-# Space complexity: O(n). The size of the stack in memory is
-# proportionate to N.
-#
-def fibonacci(number, memo_hash = {})
-  return number if number <= 1
-
-  memo_hash[0] = 0
-  memo_hash[1] = 1
-
-  memoize(number, memo_hash)
-end
-
-def memoize(number, memo_hash)
-  return memo_hash[number] if memo_hash.key? number
-
-  memo_hash[number] = memoize(number - 1, memo_hash) + memoize(number - 2, memo_hash)
-
-  memoize(number, memo_hash)
+  return fib[n]
 end
 
-n = 2
-fibonacci(n)
-# Output: 1
-# Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.
-
-n = 3
-fibonacci(n)
-# Output: 2
-# Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.
-
-n = 4
-fibonacci(n)
-# Output: 3
-# Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.
+# Example usage:
+n = 10
+result = fibonacci(n)
+puts "The #{n}-th Fibonacci number is #{result}"