# SMAWK Algorithm in Rust

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This crate contains an implementation of the [SMAWK algorithm][smawk] for
finding the smallest element per row in a totally monotone matrix.

The SMAWK algorithm allows you to lower the running time of some algorithms from
O(*n*²) to just O(_n_). In other words, you can turn a quadratic time complexity
(which is often too expensive) into linear time complexity.

Finding optimal line breaks in a paragraph of text is an example of an algorithm
which would normally take O(*n*²) time for _n_ words. With this crate, the
running time becomes linear. Please see the [textwrap crate][textwrap] for an
example of this.

## Usage

Add this to your `Cargo.toml`:

```toml
[dependencies]
smawk = "0.3"
```

You can now efficiently find row and column minima. Here is an example where we
find the column minima:

```rust
use smawk::Matrix;

let matrix = vec![
    vec![3, 2, 4, 5, 6],
    vec![2, 1, 3, 3, 4],
    vec![2, 1, 3, 3, 4],
    vec![3, 2, 4, 3, 4],
    vec![4, 3, 2, 1, 1],
];
let minima = vec![1, 1, 4, 4, 4];
assert_eq!(smawk::column_minima(&matrix), minima);
```

The `minima` vector gives the index of the minimum value per column, so
`minima[0] == 1` since the minimum value in the first column is 2 (row 1). Note
that the smallest row index is returned.

For dynamic programming problems where matrix elements depend on previously
computed values (online dynamic programming), you can use the online column
minima algorithm via `smawk::online_column_minima`.

### Cargo Features

This crate has an optional dependency on the
[`ndarray` crate](https://docs.rs/ndarray/), which provides an efficient matrix
implementation. Enable the `ndarray` Cargo feature to use it.

### `no_std` Support

SMAWK is a `no_std` crate by default. It requires the `alloc` crate for dynamic
memory allocation.

## Documentation

**[API documentation][api-docs]**

## Changelog

### Version 0.3.3 (2026-06-16)

This release contains optimizations that make our benchmarks about 28% faster by
eliminating heap allocations and vector bounds checks.

- [#89](https://github.com/mgeisler/smawk/pull/89): Add support for `no_std`.
- [#90](https://github.com/mgeisler/smawk/pull/90): Add GitHub Sponsors
  configuration.
- [#114](https://github.com/mgeisler/smawk/pull/114): Remove heap allocations by
  pre-allocating vectors up front. This improves benchmarks by 10%.
- [#115](https://github.com/mgeisler/smawk/pull/115): Eliminate bounds checks in
  `smawk_inner`. This improves benchmarks by another 20%.

### Version 0.3.2 (2023-09-17)

This release adds more documentation and renames the top-level SMAWK functions.
The old names have been kept for now to ensure backwards compatibility, but they
will be removed in a future release.

- [#65](https://github.com/mgeisler/smawk/pull/65): Forbid the use of unsafe
  code.
- [#69](https://github.com/mgeisler/smawk/pull/69): Migrate to the Rust 2021
  edition.
- [#73](https://github.com/mgeisler/smawk/pull/73): Add examples to all
  functions.
- [#74](https://github.com/mgeisler/smawk/pull/74): Add “mathematics” as a crate
  category.
- [#75](https://github.com/mgeisler/smawk/pull/75): Remove `smawk_` prefix from
  optimized functions.

### Version 0.3.1 (2021-01-30)

This release relaxes the bounds on the `smawk_row_minima`,
`smawk_column_minima`, and `online_column_minima` functions so that they work on
matrices containing floating point numbers.

- [#55](https://github.com/mgeisler/smawk/pull/55): Relax bounds to `PartialOrd`
  instead of `Ord`.
- [#56](https://github.com/mgeisler/smawk/pull/56): Update dependencies to their
  latest versions.
- [#59](https://github.com/mgeisler/smawk/pull/59): Give an example of what
  SMAWK does in the README.

### Version 0.3.0 (2020-09-02)

This release slims down the crate significantly by making `ndarray` an optional
dependency.

- [#45](https://github.com/mgeisler/smawk/pull/45): Move non-SMAWK code and unit
  tests out of lib and into separate modules.
- [#46](https://github.com/mgeisler/smawk/pull/46): Switch `smawk_row_minima`
  and `smawk_column_minima` functions to a new `Matrix` trait.
- [#47](https://github.com/mgeisler/smawk/pull/47): Make the dependency on the
  `ndarray` crate optional.
- [#48](https://github.com/mgeisler/smawk/pull/48): Let `is_monge` take a
  `Matrix` argument instead of `ndarray::Array2`.
- [#50](https://github.com/mgeisler/smawk/pull/50): Remove mandatory
  dependencies on `rand` and `num-traits` crates.

### Version 0.2.0 (2020-07-29)

This release updates the code to Rust 2018.

- [#18](https://github.com/mgeisler/smawk/pull/18): Make `online_column_minima`
  generic in matrix type.
- [#23](https://github.com/mgeisler/smawk/pull/23): Switch to the
  [Rust 2018][rust-2018] edition. We test against the latest stable and nightly
  version of Rust.
- [#29](https://github.com/mgeisler/smawk/pull/29): Drop strict Rust 2018
  compatibility by not testing with Rust 1.31.0.
- [#32](https://github.com/mgeisler/smawk/pull/32): Fix crash on overflow in
  `is_monge`.
- [#33](https://github.com/mgeisler/smawk/pull/33): Update `rand` dependency to
  latest version and get rid of `rand_derive`.
- [#34](https://github.com/mgeisler/smawk/pull/34): Bump `num-traits` and
  `version-sync` dependencies to latest versions.
- [#35](https://github.com/mgeisler/smawk/pull/35): Drop unnecessary Windows
  tests. The assumption is that the numeric computations we do are
  cross-platform.
- [#36](https://github.com/mgeisler/smawk/pull/36): Update `ndarray` dependency
  to the latest version.
- [#37](https://github.com/mgeisler/smawk/pull/37): Automate publishing new
  releases to crates.io.

### Version 0.1.0 — August 7th, 2018

First release with the classical offline SMAWK algorithm as well as a newer
online version where the matrix entries can depend on previously computed column
minima.

## License

SMAWK can be distributed according to the [MIT license][mit]. Contributions will
be accepted under the same license.

[build-status]: https://github.com/mgeisler/smawk/actions?query=branch%3Amaster+workflow%3Abuild
[crates-io]: https://crates.io/crates/smawk
[codecov]: https://codecov.io/gh/mgeisler/smawk
[textwrap]: https://crates.io/crates/textwrap
[smawk]: https://en.wikipedia.org/wiki/SMAWK_algorithm
[api-docs]: https://docs.rs/smawk/
[rust-2018]: https://doc.rust-lang.org/edition-guide/rust-2018/
[mit]: LICENSE
