152 lines
5.6 KiB
Markdown
152 lines
5.6 KiB
Markdown
# SMAWK Algorithm in Rust
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[][build-status]
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[][codecov]
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[][crates-io]
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[][api-docs]
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This crate contains an implementation of the [SMAWK algorithm][smawk] for
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finding the smallest element per row in a totally monotone matrix.
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The SMAWK algorithm allows you to lower the running time of some algorithms from
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O(_n_²) to just O(_n_). In other words, you can turn a quadratic time complexity
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(which is often too expensive) into linear time complexity.
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Finding optimal line breaks in a paragraph of text is an example of an algorithm
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which would normally take O(_n_²) time for _n_ words. With this crate, the
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running time becomes linear. Please see the [textwrap crate][textwrap] for an
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example of this.
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## Usage
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Add this to your `Cargo.toml`:
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```toml
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[dependencies]
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smawk = "0.3"
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```
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You can now efficiently find row and column minima. Here is an example where we
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find the column minima:
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```rust
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use smawk::Matrix;
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let matrix = vec![
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vec![3, 2, 4, 5, 6],
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vec![2, 1, 3, 3, 4],
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vec![2, 1, 3, 3, 4],
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vec![3, 2, 4, 3, 4],
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vec![4, 3, 2, 1, 1],
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];
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let minima = vec![1, 1, 4, 4, 4];
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assert_eq!(smawk::column_minima(&matrix), minima);
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```
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The `minima` vector gives the index of the minimum value per column, so
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`minima[0] == 1` since the minimum value in the first column is 2 (row 1). Note
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that the smallest row index is returned.
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### Cargo Features
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This crate has an optional dependency on the
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[`ndarray` crate](https://docs.rs/ndarray/), which provides an efficient matrix
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implementation. Enable the `ndarray` Cargo feature to use it.
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## Documentation
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**[API documentation][api-docs]**
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## Changelog
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### Version 0.3.2 (2023-09-17)
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This release adds more documentation and renames the top-level SMAWK functions.
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The old names have been kept for now to ensure backwards compatibility, but they
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will be removed in a future release.
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- [#65](https://github.com/mgeisler/smawk/pull/65): Forbid the use of unsafe
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code.
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- [#69](https://github.com/mgeisler/smawk/pull/69): Migrate to the Rust 2021
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edition.
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- [#73](https://github.com/mgeisler/smawk/pull/73): Add examples to all
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functions.
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- [#74](https://github.com/mgeisler/smawk/pull/74): Add “mathematics” as a crate
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category.
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- [#75](https://github.com/mgeisler/smawk/pull/75): Remove `smawk_` prefix from
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optimized functions.
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### Version 0.3.1 (2021-01-30)
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This release relaxes the bounds on the `smawk_row_minima`,
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`smawk_column_minima`, and `online_column_minima` functions so that they work on
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matrices containing floating point numbers.
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- [#55](https://github.com/mgeisler/smawk/pull/55): Relax bounds to `PartialOrd`
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instead of `Ord`.
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- [#56](https://github.com/mgeisler/smawk/pull/56): Update dependencies to their
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latest versions.
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- [#59](https://github.com/mgeisler/smawk/pull/59): Give an example of what
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SMAWK does in the README.
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### Version 0.3.0 (2020-09-02)
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This release slims down the crate significantly by making `ndarray` an optional
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dependency.
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- [#45](https://github.com/mgeisler/smawk/pull/45): Move non-SMAWK code and unit
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tests out of lib and into separate modules.
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- [#46](https://github.com/mgeisler/smawk/pull/46): Switch `smawk_row_minima`
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and `smawk_column_minima` functions to a new `Matrix` trait.
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- [#47](https://github.com/mgeisler/smawk/pull/47): Make the dependency on the
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`ndarray` crate optional.
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- [#48](https://github.com/mgeisler/smawk/pull/48): Let `is_monge` take a
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`Matrix` argument instead of `ndarray::Array2`.
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- [#50](https://github.com/mgeisler/smawk/pull/50): Remove mandatory
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dependencies on `rand` and `num-traits` crates.
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### Version 0.2.0 (2020-07-29)
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This release updates the code to Rust 2018.
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- [#18](https://github.com/mgeisler/smawk/pull/18): Make `online_column_minima`
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generic in matrix type.
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- [#23](https://github.com/mgeisler/smawk/pull/23): Switch to the
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[Rust 2018][rust-2018] edition. We test against the latest stable and nightly
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version of Rust.
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- [#29](https://github.com/mgeisler/smawk/pull/29): Drop strict Rust 2018
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compatibility by not testing with Rust 1.31.0.
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- [#32](https://github.com/mgeisler/smawk/pull/32): Fix crash on overflow in
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`is_monge`.
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- [#33](https://github.com/mgeisler/smawk/pull/33): Update `rand` dependency to
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latest version and get rid of `rand_derive`.
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- [#34](https://github.com/mgeisler/smawk/pull/34): Bump `num-traits` and
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`version-sync` dependencies to latest versions.
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- [#35](https://github.com/mgeisler/smawk/pull/35): Drop unnecessary Windows
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tests. The assumption is that the numeric computations we do are
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cross-platform.
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- [#36](https://github.com/mgeisler/smawk/pull/36): Update `ndarray` dependency
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to the latest version.
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- [#37](https://github.com/mgeisler/smawk/pull/37): Automate publishing new
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releases to crates.io.
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### Version 0.1.0 — August 7th, 2018
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First release with the classical offline SMAWK algorithm as well as a newer
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online version where the matrix entries can depend on previously computed column
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minima.
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## License
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SMAWK can be distributed according to the [MIT license][mit]. Contributions will
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be accepted under the same license.
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[build-status]: https://github.com/mgeisler/smawk/actions?query=branch%3Amaster+workflow%3Abuild
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[crates-io]: https://crates.io/crates/smawk
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[codecov]: https://codecov.io/gh/mgeisler/smawk
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[textwrap]: https://crates.io/crates/textwrap
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[smawk]: https://en.wikipedia.org/wiki/SMAWK_algorithm
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[api-docs]: https://docs.rs/smawk/
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[rust-2018]: https://doc.rust-lang.org/edition-guide/rust-2018/
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[mit]: LICENSE
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