What is the time complexity of the dynamic programming solution for the Fibonacci sequence?
Practice Questions
1 question
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)
The time complexity of the dynamic programming solution for the Fibonacci sequence is O(n) because it computes each Fibonacci number only once and stores the results.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the time complexity of the dynamic programming solution for the Fibonacci sequence?
Solution: The time complexity of the dynamic programming solution for the Fibonacci sequence is O(n) because it computes each Fibonacci number only once and stores the results.
Steps: 7
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).
