LC 51 N-Queens is the gold standard for testing backtracking, constraint propagation, and bit-mask elegance. Master row-by-row placement, three diagonal-tracking sets, and the bitmask trick that runs N=15 in milliseconds.
LC 37 Sudoku Solver is the most-asked constraint-satisfaction problem in tech interviews. Master row, column, and box bitsets, MRV heuristic ordering, and the cell-by-cell decision tree that solves any 9x9 grid in milliseconds.
LC 22 Generate Parentheses is the backtracking warm-up every FAANG interviewer reaches for. Master the open and close counter invariant, the Catalan number trail, and why a string-builder beats array joins for clean recursion.
LC 79 Word Search and LC 212 Word Search II ship in nearly every FAANG onsite. Master DFS with in-place visited marking, four-directional exploration, and the trie trick that turns multi-word search into a single traversal.
LC 17 Letter Combinations of a Phone Number is the cleanest cartesian-product backtracking template ever written. Master the digit-to-letter mapping, the per-position branching, and why the iterative BFS variant is asked at Amazon.