Common Sparse Table Mistakes

Common mistakes when implementing Sparse Tables:

$1.$ Wrong power-of-2 calculation: Use $k = \lfloor \log_2(r - l + 1) \rfloor$, not $\lceil \log_2(...) \rceil$.

$2.$ Off-by-one in second range: The second range starts at $r - 2^k + 1$, not $r - 2^k$.

$3.$ Forgetting to precompute LOG array: Using built-in log functions is slow. Precompute.

$4.$ Array bounds: The range $[i, i + 2^j - 1]$ must fit in the array. Check $i + 2^j - 1 < n$.

$5.$ Using for non-idempotent operations: Remember, the overlap trick only works for idempotent ops. Debug by testing against brute force for small inputs.