Why the Time Complexity of This Function is O(n^3)

In computer science, the time complexity of an algorithm or a function is a measure of how long it takes to run as the input size increases. The time complexity is often expressed using Big O notation, which describes the asymptotic behavior of a function as the input size approaches infinity.

In this blog post, we will discuss the time complexity of the following function:

``` def calculate_sum(n): total = 0 for i in range(n): for j in range(n): for k in range(n): total += 1 return total ```

We will show that the time complexity of this function is O(n^3).

Analysis of the Function

To analyze the time complexity of the function, we need to count the number of operations that are performed as the input size increases. In this case, the input size is n, which is the value passed to the function.

The first loop in the function iterates n times. For each iteration of this loop, the second loop iterates n times. And for each iteration of the second loop, the third loop iterates n times.

Therefore, the total number of operations performed by the function is n * n * n = n^3.

Conclusion

Based on the analysis above, we can conclude that the time complexity of the function is O(n^3). This means that as the input size n increases, the running time of the function will increase by a factor of n^3.