What is the time complexity of the dynamic programming solution for the Fibonacc
Practice Questions
Q1
What is the time complexity of the dynamic programming solution for the Fibonacci sequence?
O(n)
O(n^2)
O(2^n)
O(log n)
Questions & Step-by-Step Solutions
What is the time complexity of the dynamic programming solution for the Fibonacci sequence?
Step 1: Understand what the Fibonacci sequence is. It is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1.
Step 2: Recognize that a naive recursive solution to find Fibonacci numbers can be very slow because it recalculates the same Fibonacci numbers multiple times.
Step 3: Learn about dynamic programming, which is a method that solves problems by breaking them down into simpler subproblems and storing the results of these subproblems.
Step 4: In the dynamic programming approach for Fibonacci, we create an array (or list) to store the Fibonacci numbers we have already calculated.
Step 5: We calculate each Fibonacci number from the bottom up, starting from the base cases (F(0) and F(1)) and using the stored results to compute the next numbers.
Step 6: Since we only calculate each Fibonacci number once and store it, the total number of calculations is proportional to n, where n is the position in the Fibonacci sequence we want to find.
Step 7: Therefore, the time complexity of this dynamic programming solution is O(n).
