In Python, a list of lists is a common data structure used to represent a collection of elements, where each element is also a list. Sometimes, we may need to sum up all the elements of all the lists in this structure. In this article, we will discuss different ways to do this in Python.

## Using a For Loop

The most basic way to sum up the elements of a list of lists is to use a for loop to iterate through each list and add up the elements. Here is an example:

```
list_of_lists = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
total = 0
for sublist in list_of_lists:
for element in sublist:
total += element
print(total)
```

Code language: PHP (php)

This will output the sum of all the elements in the list of lists, which is 45.

The time complexity of this method is O(n^2) where n is the total number of elements in the list of lists. This is because we are iterating through each list and then iterating through each element in that list.

## Using a List Comprehension

We can also use a list comprehension to accomplish the same task. Here is an example:

```
list_of_lists = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
total = sum([element for sublist in list_of_lists for element in sublist])
print(total)
```

Code language: PHP (php)

This will also output the sum of all the elements in the list of lists, which is 45.

The time complexity of this method is also O(n^2). This is because we are iterating through each list and then iterating through each element in that list, similar to the for loop method.

## Using the Built-in sum() Function

Python has a built-in function called `sum()`

that can be used to add up the elements of a list. We can use this function to sum up the elements of a list of lists by using it in combination with the `*`

operator. Here is an example:

```
list_of_lists = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
total = sum(*list_of_lists)
print(total)
```

Code language: PHP (php)

This will also output the sum of all the elements in the list of lists, which is 45.

The time complexity of this method is O(n) where n is the total number of elements in the list of lists. This is because the built-in `sum()`

function has a time complexity of O(n).

## Using numpy

Another way to sum up the elements of a list of lists is to use the `numpy`

library. Here is an example:

```
import numpy as np
list_of_lists = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
total = np.sum(list_of_lists)
print(total)
```

Code language: JavaScript (javascript)

This will also output the sum of all the elements in the list of lists, which is 45.

The time complexity of this method is O(n) where n is the total number of elements in the list of lists. This is because NumPy uses a more efficient algorithm to sum up the elements of a list.

## Conclusion

In this article, we have discussed different ways to sum up the elements of a list of lists in Python. We have seen that we can use a for loop, a list comprehension, the built-in `sum()`

function and numpy to accomplish this task.

The time complexity of each method varies depending on the specific implementation. The for loop and list comprehension methods have a time complexity of O(n^2), while the built-in `sum()`

function and numpy have a time complexity of O(n).

When deciding which method to use, it is important to consider the specific requirements of your use case. If performance is a concern and the list of lists is large, using the built-in `sum()`

function or numpy may be more efficient. If you are working with small lists or if readability is more important, using a for loop or list comprehension may be more suitable.

Overall, Python provides many ways to sum up the elements of a list of lists, and the best approach will depend on your specific use case.