### Andy Bohn

Cornell physics graduate student, studying merging black holes, board games, and barrel strength whiskey.

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# Almost always use std::vector

Common wisdom is you should use structures like linked lists instead of vectors when you expect to perform many insertions and deletions. Insertion in a list is $\mathcal{O}(1)$ operation, just allocate memory for the new element, and update a handful of pointers. Vector insertion on the other hand is $\mathcal{O}(n)$, since we must move all elements beyond the insertion point by 1 spot in the vector. However, we usually need to find the insertion location first, and this operation renders list insertions to be slower than vector insertions!

I recently watched a talk by Bjarne Stroustrup called Why you should avoid Linked Lists, where he talks about this exact issue. Unfortunately, his plot did not display properly during the talk, so I tried to recreate the results for myself.

### Benchmarking

For the timings, I start wit a sorted list and sorted vector with $N$ elements each. I generate $1,000$ random elements, and insert these elements both into the list and vector. This should give us a uniform distribution of insertion points for a fair speed test. The insertion procedure is to find the iterator to the correct location in the sorted container as to keep it sorted, then use .insert on the container. The std::vector will have to move all elements beyond the insertion spot, which on average is $n/2$ elements.

How do we find the insertion point? For std::list, since we do not have random access, we must step through the list one element at a time. Here is how I do that:

auto it = c.begin();
const auto kEnd = c.end();
while (it != kEnd && *it < insertElement) {
++it;
}


An alternative is to use std::lower_bound, but I think this will try to do a binary search with the non-RandomAccessIterator for some reason, as my timings suggest.

For std::vector, we can simply use std::lower_bound to do a binary search for the insertion point with our RandomAccessIterator. Since this was so fast, I also tried to handicap std::vector by forcing it to step through the vector using the code block above.

Here are the results, showing the total time in milliseconds to insert $1,000$ elements into a vector and list using the different find methods:

I ran the code with clang 3.6 and gcc 4.8, and the results were similar. The red squares show the std::list using std::lower_bound, and the blue stars use the linear search. The green triangles show std::vector using the linear search and the purple circles use the binary search with std::lower_bound.

This shows that the vector find and insert operation is about an order of magnitude faster than the list find and insert on my machine! As expected, the binary search and insert with vector is the fastest, and the linear search and insert with vector is not far behind. Iterating manually through the linked list and inserting was always faster than using the binary search, which also makes sense. What does not make sense to me is why std::lower_bound is trying the binary search without a RandomAccessIterator, but maybe someone can help me out in the comments.

The vector speed seems to slow down right where the dashed blue vertical line is shown, whereas the list speed does not seem to be affected. This dashed line corresponds exactly to the size of my L3 cache, so the increased runtime for vector is most likely just due to increased cache misses for the vector. When iterating through the list, we may have just as good a chance to cache miss with a small or large list due to the list elements not being contiguous in memory. This would explain why the speed is unaffected by the list size.

### Discussion

Bjarne Stroustrup has three suggestions regarding this topic:

1. “don’t store data unnecessarily”
2. “keep data compact”
3. “access memory in a predictable manner”

Point 1: The linked list has to store at least a forward pointer for each element, and if it is a doubly linked list, a back pointer. Thus, if the containers are storing doubles, then we are using 3x as much memory as we really need!

Point 2: The vector allows for random access, which speeds up the find, but remember that we did not need to use the random access property of the vector to beat list. Keeping the vector compact allows more data to be stored in cache, resulting in reduces cache misses.

Point 3: Even though we need to do $\mathcal{O}(n)$ operations to do the vector insertion, we are being nice to our CPUs and accessing memory in a predictable way. What does that even mean? Traversing contiguous data forwards or backwards constitutes predictable behavior, and allows the CPU to accurately prefetch data while other instructions are being carried out. Points 2 and 3 allow the $\mathcal{O}(n)$ vector insertion to be much faster than the list’s $\mathcal{O}(n)$ find operation.

When choosing vector versus list, the advice seems to be default to vector unless you have a good reason to use a list. This does not mean to always use vector, but at the very least, when using a data structure that doesn’t follow the points listed above, you should benchmark your choice.