Search a rotated sorted array in O(log n) by identifying which half is always sorted at each step and checking whether the target falls inside it. A top FAANG interview problem.
Find the length of the longest strictly increasing subsequence in O(n log n) using patience sorting — a binary search on a maintained tails array that is simpler and faster than classic DP.
Place C cows in N stalls to maximise the minimum distance between any two cows. Learn the canonical binary-search-on-answer pattern — the template behind Magnetic Force Between Two Balls, Split Array, and dozens of other hard problems.
Find the secret number between 1 and n using the guess() API in O(log n) calls. Master the exact binary search template used in all interactive/guessing problems and understand why the API return values map directly to the lo/hi update rules.
Solve the Knight's Tour with backtracking and Warnsdorff's heuristic. Visit every square exactly once on an n by n board with O(8^(n^2)) brute force tamed by smart move ordering.
M-coloring, bipartite check, and Hamiltonian path/cycle: backtracking on graphs with constraint propagation, ordering heuristics, and FAANG interview prep.