What is the time complexity of the Fibonacci sequence using dynamic programming?
Practice Questions
1 question
Q1
What is the time complexity of the Fibonacci sequence using dynamic programming?
O(2^n)
O(n)
O(n log n)
O(n^2)
Using dynamic programming, the Fibonacci sequence can be computed in O(n) time by storing previously computed values.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the time complexity of the Fibonacci sequence using dynamic programming?
Solution: Using dynamic programming, the Fibonacci sequence can be computed in O(n) time by storing previously computed values.
Steps: 6
Step 1: Understand the Fibonacci sequence. 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 approach to calculate Fibonacci numbers can be very slow because it recalculates the same values multiple times.
Step 3: Learn about dynamic programming. It is a method that stores previously computed values to avoid redundant calculations.
Step 4: Implement a dynamic programming approach by creating an array (or list) to store Fibonacci numbers as you calculate them.
Step 5: Fill the array iteratively. Start with the first two Fibonacci numbers (0 and 1) and use a loop to calculate the next numbers up to n.
Step 6: Since you only loop through the numbers once, the time it takes to compute the Fibonacci sequence using this method is O(n).
