waveletTree is a Go package for myriad array operations using wavelet trees.
waveletTree stores a non-negative intger array V[0...n), 0 <= V[i] < s and support almost all operations in O(log s) time (not depends on num) using at most (n * log_2 s) bits plus small overheads for storing auxiually indices.
import "github.com/hillbig/waveletTree"
builder := NewBuilder()
for i := uint64(0); i < N; i++ {
builder.PushBack(uint64(rand.Int63())) // set values by PushBck
}
wt := builder.Build() // Build returns WaveletTree
// WaveletTree conceptually stores a non-negative integer array V[0...num)
// where 0 <= V[i] < s
// WaveletTree supports all operations in O(log s) time (not depend on num)
x := wt.Lookup(ind) // Lookup returns V[x]
rank := wt.Rank(ind, x) // Rank returns the number of xs in V[0...in)
sel := wt.Select(rank, x) // Select returns the position of (rank+1)-th x in V
v := wt.Quantile(Range{beg, end}, k) // Quantile returns k-th largest value in V[beg, end)The results shows that RSDic operations require always (almost) constant time with regard to the length and one's ratio.
go test -bench=.
// Build a waveletTree for an integer array of length 10^6 with s = 2^64
BenchmarkWTBuild1M 1 1455321650 ns/op
// 1.455 micro sec per an interger
// A waveletTree for an integer array of length 10M (10^7) with s = 2^64
BenchmarkWTBuild10M 1 1467061166 ns/op
BenchmarkWTLookup10M 100000 29319 ns/op
BenchmarkWTRank10M 100000 28278 ns/op
BenchmarkWTSelect10M 50000 50250 ns/op
BenchmarkWTQuantile10M 100000 28852 ns/op
// An array []uint64 of length 10M (10^7) for comparison
BenchmarkRawLookup10M 20000000 109 ns/op
BenchmarkRawRank10M 500 4683822 ns/op
BenchmarkRawSelect10M 500 6085992 ns/op
BenchmarkRawQuantile10M 100 44362885 ns/op