Common BIT Mistakes

Common mistakes when implementing BIT:

$1.$ Off-by-one with 0-indexing: BIT uses 1-based indexing. Convert: position $i$ in 0-indexed array → position $i+1$ in BIT.

$2.$ Forgetting to update the original array: For "set value" operations, compute delta first: $\delta = \text{newVal} - \text{oldVal}$.

$3.$ Wrong loop bounds: Update loop goes up to $n$, query loop goes down to $1$.

$4.$ Empty prefix edge case: $\text{prefix}(0) = 0$. Handle $l = 0$ in range queries.

$5.$ Integer overflow: For large values, use 64-bit integers. Debugging: print prefix sums at each step, verify against brute force for small inputs.