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$ curl repovive.com/roadmaps/data-structures/wavelet-trees/coordinate-compression

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$ curl repovive.com/roadmaps/data-structures/wavelet-trees/coordinate-compression

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Coordinate Compression - Wavelet Trees | Data Structures | Repovive

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Data Structures19 sections · 729 units49h total

Open in Course

Coordinate Compression

Shrinking the alphabet

When values range up to $10^9$ but there are only $n$ distinct values, compress:

function compress(arr)
    sorted := sort(unique(arr))
    mapping := map from value to compressed index
    for i from 0 to length(sorted) - 1
        mapping[sorted[i]] := i

    for i from 0 to length(arr) - 1
        arr[i] := mapping[arr[i]]

Now alphabet size $\sigma = n$ instead of $10^9$ .

This reduces wavelet tree depth from 30 to $\log n \approx 17$ .

Always compress when values are sparse. The queries work the same; just remember to translate results back if needed.