Practice: Binary Search Variants

I'll give you problems requiring bounds. Find the number of elements in range $[L, R]$ in a sorted vector using the difference between upper and lower bounds. You'll use: upper_bound(v.begin(), v.end(), R) - lower_bound(v.begin(), v.end(), L) to count elements where $L \leq x \leq R$.

This runs in $O(\log n)$ time. Try variants: count elements less than $x$, greater than $y$, or exactly equal to $z$. Each uses different combinations of lower_bound and upper_bound.