dsa1 min read
Count Smaller Numbers After Self — Merge Sort or Binary Indexed Tree
Count smaller elements to the right of each element using merge sort with position tracking in O(n log n).
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Bit
6 articles
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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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Count of Range Sum — Merge Sort / BIT
Count subarray sums within [lower, upper]. Use prefix sums and merge sort: during merge count pairs of prefix sums with difference in range.
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Max Sum Rectangle No Larger than K — BIT + Prefix
Find max rectangle sum <= k in 2D matrix. Fix row boundaries, compress to 1D array, use prefix sums + BIT/sorted set to find best subarray sum <= k.
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