Question: What is the time complexity of the Fibonacci sequence using dynamic programming?
Options:
O(2^n)
O(n)
O(n log n)
O(n^2)
Correct Answer: O(n)
Solution:
Using dynamic programming, the Fibonacci sequence can be computed in O(n) time by storing previously computed values.
What is the time complexity of the Fibonacci sequence using dynamic programming?
Practice Questions
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)
Questions & Step-by-Step Solutions
What is the time complexity of the Fibonacci sequence using dynamic programming?
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).
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