How do different C++ algorithms compare in terms of performance?

What are the main differences between std::sort and std::stable_sort in C++?

std::sort is faster but not stable, while std::stable_sort maintains the relative order of equivalent elements but is slower.

Can you explain when to use std::lower_bound versus std::binary_search?

Use std::lower_bound to find the first position where an element can be inserted, while std::binary_search checks if an element exists.

How do the performance characteristics of quicksort compare to mergesort?

Quicksort is generally faster on average due to better cache performance, but mergesort is stable and has a guaranteed O(n log n) time complexity.

What about the performance of std::for_each compared to a traditional for loop?

std::for_each can be more readable and may allow for optimizations, but a traditional for loop can be more efficient in some cases.