Recursive Staircase: Counting Every Step to the Top
In the Recursive Staircase problem, you’re faced with a staircase of n steps. How many unique paths can you take to the top, given you can ascend 1 or 2 steps at once? This age-old problem showcases the versatility of algorithms. Let’s navigate through four distinct solutions: a simple recursion, memoization, dynamic programming, and the...
Fibonacci Number: Classic and Closed-Form Explorations
Introduction to Fibonacci Number The Fibonacci sequence is one of the most iconic sequences in mathematics and computer science. Starting with 0 and 1, each subsequent number in the sequence is the sum of the two preceding ones. The sequence begins: 0, 1, 1, 2, 3, 5, 8, 13... and so on. Classic Recursive Approach...