# A Time Complexity Question

What is the time complexity of following function fun()? Assume that log(x) returns log value in base 2.

`void` `fun() ` `{ ` ` ` `int` `i, j; ` ` ` `for` `(i=1; i<=n; i++) ` ` ` `for` `(j=1; j<=` `log` `(i); j++) ` ` ` `printf` `(` `"GeeksforGeeks"` `); ` `} ` |

*chevron_right*

*filter_none*

Time Complexity of the above function can be written as Θ(log 1) + Θ(log 2) + Θ(log 3) + . . . . + Θ(log n) which is Θ (log n!)

Order of growth of ‘log n!’ and ‘n log n’ is same for large values of n, i.e., Θ (log n!) = Θ(n log n). So time complexity of fun() is Θ(n log n).

The expression Θ(log n!) = Θ(n log n) can be easily derived from following Stirling’s approximation (or Stirling’s formula).

log n! = n log n - n + O(log(n))

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Sources:

http://en.wikipedia.org/wiki/Stirling%27s_approximation

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: **DSA Self Paced**. Become industry ready at a student-friendly price.

## Recommended Posts:

- What does 'Space Complexity' mean?
- Time Complexity of building a heap
- Algorithm Practice Question for Beginners | Set 1
- An interesting time complexity question
- Time Complexity of Loop with Powers
- Time Complexity where loop variable is incremented by 1, 2, 3, 4 ..
- Time Complexity of a Loop when Loop variable “Expands or Shrinks” exponentially
- Performance of loops (A caching question)
- Understanding Time Complexity with Simple Examples
- Time complexity of recursive Fibonacci program
- Practice Questions on Time Complexity Analysis
- Complexity of different operations in Binary tree, Binary Search Tree and AVL tree
- Time taken by Loop unrolling vs Normal loop
- Time Complexity Analysis | Tower Of Hanoi (Recursion)
- Knowing the complexity in competitive programming
- Cyclomatic Complexity
- Measure execution time with high precision in C/C++
- Python Code for time Complexity plot of Heap Sort
- Microsoft Interview experience for full time position of software engineer at Microsoft Ireland Research
- Algorithms Sample Questions | Set 3 | Time Order Analysis