wavelet-matrix crate for the Rust language

The Wavelet Matrix is a space-efficient variant of Wavelet Tree data structure. - https://en.wikipedia.org/wiki/Wavelet_Tree

Usage

After adding to Cargo.toml, add this line to lib.rs or main.rs. extern crate wavelet_matrix;

Example

Add to main.rs: ``` use wavelet_matrix::*;

fn main() { let vec: Vec = vec![1, 2, 4, 5, 1, 0, 4, 6, 2, 9, 2, 0]; // 0 1 2 3 4 5 6 7 8 9 10 11 let wm = WaveletMatrix::new(&vec); asserteq!(wm.len(), 12); asserteq!(wm.lookup(7), 6); asserteq!(wm.rank(5, 1), 2); asserteq!(wm.select(2, 2), 10);

println!("Worked as expected!");

} ```

Features

Given unsigned integer sequence A, it provides the following queries.

Basic operations

• .len(): returns the length of A.
• .lookup(pos): returns the value at the position pos of A, A[pos].

Counting

• .count(pos_range, value): returns the number of the element which satisfies e == value included in A[pos_range]
• .count_prefix(pos_range, value, ignore_bit): returns the number of the element which satisfies e >> ignore_bit == value >> ignore_bit included in A[pos_range]
  • This will be useful for counting the number of IPv4 prefix such as 172.22.0.0/16
• .count_lt(pos_range, value): returns the number of the element which satisfies e < value included in A[pos_range]
• .count_gt(pos_range, value): returns the number of the element which satisfies e > value included in A[pos_range]
• .count_range(pos_range, val_range): returns the number of the element which satisfies val_range.start <= e < val_range.end included in A[pos_range]

Classical WaveletMatrix operations

• .rank(pos, value): counts value included in A[0..pos].
  • Note: pos is exclusive. When pos is 0, .rank() always returns 0.
• .select(rank, value): return the position of the (rank+1)-th value
  • Note: When found nothing, it returns .len() instead of None.

Advanced queries

• to be added

Releases

v0.4.0

• Add .count(), .count_prefix(), .count_lt(), .count_gt() and .count_range().
• [INCOMPATIBLE] WaveletMatrix::new() takes &Vec, instead of Vec

v0.3.0

• [INCOMPATIBLE] .select() now returns .len() instead of None.

TODO

• Implement .top_n for WaveletMatrix
• Add Benchmark.
  • Implement same queries using trivial algorithm
  • Compare wm's queries against trivial one.
  • Make a nice plot.
• Profiling
• Optimize underlying rsdic structure.
• Add travis CI.

• Add u128 support or arbitrary-length integer support

• The fastest implementation on the planet

Credits

• A Go package for myriad array operations using wavelet trees

  • https://github.com/hillbig/waveletTree
  • Basically, the algorithm is deeply derived from the above Go implementation.

• excellent slides in Japanese

  • https://www.slideshare.net/pfi/ss-15916040
  • https://www.slideshare.net/bonprosoft/the-wavelet-matrix

• The original inventor's pdf:

  • http://www.dcc.uchile.cl/~gnavarro/ps/spire12.4.pdf