Searching: Linear and Binary
std::find vs binary_search/lower_bound, the sorted-data requirement, and why hand-rolled binary search is a rite of passage.
Linear search is std::find — O(n), works on anything with equality.
Binary search is different: it requires sorted data and random access,
and pays back with O(log n).
#include <algorithm>
#include <vector>
std::vector<int> v{1, 3, 5, 7, 9, 11};
bool has = std::binary_search(v.begin(), v.end(), 7); // yes/no
auto lb = std::lower_bound(v.begin(), v.end(), 7); // first >= 7
auto ub = std::upper_bound(v.begin(), v.end(), 7); // first > 7
lower_bound/upper_bound are the workhorses: lower_bound gives the
first position where the value could be inserted keeping order;
upper_bound gives the last. The distance between them is the count of
equal elements. On std::map/std::set, the same-named members do this
in O(log n) without touching iterators.
The classic beginner bug: binary searching unsorted data. It silently returns wrong answers — no exception, no warning. Sort first, or use a structure that keeps itself sorted.
Implementing your own binary search is a rite of passage precisely because
the boundary arithmetic (lo + (hi - lo) / 2, lo <= hi vs lo < hi)
has consumed generations of programmers. The standard library versions
already survived that fight — prefer them.