dsa1 min read
Range Sum Query Mutable — BIT / Segment Tree
Support point updates and range sum queries. BIT (Fenwick Tree) gives O(log n) both operations with elegant implementation.
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Count of Smaller Numbers After Self — BIT + Coordinate Compress
Count smaller elements to the right of each element. Process from right to left; BIT tracks seen elements. Coordinate compress values to BIT indices.
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Reverse Pairs — Merge Sort / BIT
Count pairs (i,j) where i<j and nums[i] > 2*nums[j]. Modified merge sort: during merge, count pairs across left/right halves.
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My Calendar I — Sorted Dict / Segment Tree
Book events without double-booking. Use sorted dictionary to find previous and next events; check overlap with both.
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Range Module — Segment Tree / SortedDict
Track coverage of half-open intervals. addRange, removeRange, queryRange. Sorted dictionary of disjoint intervals with merge/split logic.
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