Why it matters

Wavelet trees unlock powerful range queries.

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The architecture

Tree: divide by median at each level.

Query: navigate via range at each level.

Wavelet treeAlphabet splitmedian at levelRange navigationsequence-level ranksk-th + countin O(log σ)Also handles range median, range mode
Wavelet tree applications.
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How it works end to end

k-th smallest in range: navigate tree.

Rank/count in range.

Space: O(n log σ).