What is the time complexity of following function fun()? Assume that log(x) returns log value in base 2.
Time Complexity of the above function can be written as ?(log 1) + ?(log 2) + ?(log 3) + . . . . + ?(log n) which is ? (log n!)
Order of growth of ‘log n!’ and ‘n log n’ is same for large values of n, i.e., ? (log n!) = ?(n log n). So time complexity of fun() is ?(n log n).
The expression ?(log n!) = ?(n log n) can be easily derived from following Stirling’s approximation (or Stirling’s formula).
log n! = n*log n - n = O(n*log(n))
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- An interesting time complexity question
- Time Complexity of building a heap
- Time Complexity where loop variable is incremented by 1, 2, 3, 4 ..
- Time Complexity of a Loop when Loop variable “Expands or Shrinks” exponentially
- Understanding Time Complexity with Simple Examples
- Time complexity of recursive Fibonacci program
- Practice Questions on Time Complexity Analysis
- Time Complexity Analysis | Tower Of Hanoi (Recursion)
- Python Code for time Complexity plot of Heap Sort
- C program for Time Complexity plot of Bubble, Insertion and Selection Sort using Gnuplot
- Time Complexity of Loop with Powers
- What does 'Space Complexity' mean?
- Complexity of different operations in Binary tree, Binary Search Tree and AVL tree
- Knowing the complexity in competitive programming
- Cyclomatic Complexity
- Complexity Analysis of Binary Search
- Complexity analysis of various operations of Binary Min Heap
- Time taken by Loop unrolling vs Normal loop
- Measure execution time with high precision in C/C++
- Microsoft Interview experience for full time position of software engineer at Microsoft Ireland Research
Improved By : vroghelia6