Range Minimum Query

For range minimum queries, precompute $blockMin[k]$ instead of $blockSum[k]$. The query logic is similar:

$1.$ Left tail: find min from $l$ to end of $l$'s block

$2.$ Complete blocks: find min of $blockMin[b]$ values

$3.$ Right tail: find min from start of $r$'s block to $r$ Time: still $O(\sqrt{n})$ per query. Updates are trickier. If you update $arr[i]$ to a smaller value, $blockMin$ might decrease. If you update to a larger value, you might need to recompute the entire block's minimum.