Frequently Asked Questions(FAQ’s) on Logarithmic Time Complexity
1) Why does logarithmic complexity need no base?
Logarithms from any base i.e. 2, 10, e can be transformed to any other base with an addition of a constant, So the base of log doesn’t matter.
2) How are logarithms used in real life?
In Real Life scenario like measuring the acidic, basic or neutral behavior of a substance that describes a chemical property in terms of pH value logarithm is used.
3) Is logarithm repeated division?
Logarithm is repeated division by the base b until 1 is reached. The logarithm is the number of divisions by b. Repeated division doesn’t always result in exactly 1.
4) What is the difference between logarithm and algorithm?
Algorithm is a step by step process to solve a certain problem whereas logarithm is an exponent.
5) Why is binary search logarithmic?
Binary search is a Divide and Conquer method of searching, its key idea is to reduce the search space to half after each comparison to find the key. Thus the search space repeatedly drops by half and the complexity is logarithmic.
6) What is faster N or log N?
log N is faster than N as the value of log N is smaller than N.
7) What is faster O(1) or O(log N)?
O(1) is faster than O(log N), as O(1) constant time complexity and fastest possible .
8) What is best case time complexity?
In the best case constant number of operations need to be performed irrespective of value of N. So time complexity in the best case would be O(1) i.e. Most optimal time complexity.
What is Logarithmic Time Complexity? A Complete Tutorial
Logarithmic time complexity is denoted as O(log n). It is a measure of how the runtime of an algorithm scales as the input size increases. In this comprehensive tutorial. In this article, we will look in-depth into the Logarithmic Complexity. We will also do various comparisons between different logarithmic complexities, when and where such logarithmic complexities are used, several examples of logarithmic complexities, and much more. So let’s get started.
Table of Content
- What is a Logarithm?
- What is Complexity Analysis?
- What is Space Complexity?
- What is Time Complexity?
- How to measure complexities?
- What is a Logarithm?
- Different Types of Logarithmic Complexities
- Simple Log Complexity (Log a)
- Double Logarithm (log log N)
- N logarithm N (N * log N)
- logarithm^2 N (log^2 N)
- N^2 logarithm N (N^2 * log N)
- N^3 logarithm N (N^3 log N)
- logarithm √N (log √N)
- Examples To Demonstrate Logarithmic Time Complexity
- Practice Problems for Logarithmic Time Complexity
- Comparison of various Logarithmic Time Complexities
- Frequently Asked Questions(FAQ’s) on Logarithmic Time Complexity
- Conclusion