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Rewrite in Scala 3: fix optimality bugs, add tests, CLI, modern tooling
The 2016 implementation had the same epsilon-scaling termination bug as the C++ sibling (final phase ran too coarse, so tie-heavy instances came back suboptimal — its own harness printed 'Percentage correct') and its fixed 0.3 starting epsilon meant no assignment was ever produced for n <= 2. Old source preserved in legacy/. Now Scala 3.3 with no runtime deps beyond scala-parallel-collections: Auction.solve (min/max, exact optimality, deterministic parallel bidding mode), the same .apf problem format and CLI as AuctionAlgorithmCPP (cross-checked: identical output on shared instances), 18 munit tests with brute-force verification, scalafmt + fatal warnings, justfile, CI. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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‎.gitattributes‎

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* text=auto eol=lf

‎.github/workflows/ci.yml‎

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name: CI
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on:
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push:
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branches: [master, main]
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pull_request:
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jobs:
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test:
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runs-on: ubuntu-latest
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steps:
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- uses: actions/checkout@v4
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- name: Set up JDK
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uses: actions/setup-java@v4
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with:
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distribution: temurin
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java-version: 17
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cache: sbt
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- name: Install sbt
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uses: sbt/setup-sbt@v1
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- name: Check formatting
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run: sbt -batch scalafmtCheckAll scalafmtSbtCheck
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- name: Run tests
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run: sbt -batch test

‎.gitignore‎

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#### joe made this: http://goel.io/joe
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#####=== Scala ===#####
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*.class
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*.log
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# sbt specific
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.cache
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.history
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.lib/
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dist/*
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target/
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lib_managed/
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src_managed/
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project/boot/
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project/plugins/project/
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# Scala-IDE specific
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.scala_dependencies
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.worksheet
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#####=== JetBrains ===#####
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# Covers JetBrains IDEs: IntelliJ, RubyMine, PhpStorm, AppCode, PyCharm, CLion, Android Studio
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*.iml
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## Directory-based project format:
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project/target/
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project/project/
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.bsp/
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.metals/
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.bloop/
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.idea/
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# if you remove the above rule, at least ignore the following:
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# User-specific stuff:
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# .idea/workspace.xml
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# .idea/tasks.xml
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# .idea/dictionaries
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# Sensitive or high-churn files:
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# .idea/dataSources.ids
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# .idea/dataSources.xml
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# .idea/sqlDataSources.xml
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# .idea/dynamic.xml
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# .idea/uiDesigner.xml
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# Gradle:
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# .idea/gradle.xml
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# .idea/libraries
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# Mongo Explorer plugin:
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# .idea/mongoSettings.xml
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## File-based project format:
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*.ipr
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*.iws
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## Plugin-specific files:
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# IntelliJ
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/out/
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# mpeltonen/sbt-idea plugin
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.idea_modules/
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# JIRA plugin
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atlassian-ide-plugin.xml
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# Crashlytics plugin (for Android Studio and IntelliJ)
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com_crashlytics_export_strings.xml
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crashlytics.properties
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crashlytics-build.properties
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*.class

‎.scalafmt.conf‎

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version = 3.8.3
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runner.dialect = scala3
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maxColumn = 100
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align.preset = some
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rewrite.scala3.convertToNewSyntax = true
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rewrite.scala3.removeOptionalBraces = yes

‎README.md‎

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# Auction Algorithm Scala
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This is a repo contains a `Scala` implementation of [Bertsekas's Auction Algorithm](http://dspace.mit.edu/bitstream/handle/1721.1/3233/P-2064-24690022.pdf?sequence=1). The algorithm solves the problem of optimally assigning M objects to N people given the preferences specified in a given cost matrix.
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A Scala 3 implementation of [Bertsekas' auction algorithm](http://dspace.mit.edu/bitstream/handle/1721.1/3233/P-2064-24690022.pdf?sequence=1) for the n-by-n assignment problem: optimally assigning n objects to n people given a cost matrix. Sibling of [AuctionAlgorithmCPP](https://github.com/EvanOman/AuctionAlgorithmCPP) — same algorithm, same problem-file format, interchangeable CLIs.
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After a bit of optimization, this implementation can solve a size 500 assignment problem in ~.125 seconds. I have also implemented a parallel version, which seems to outperform the sequential version once the problem size is over 5000. This implementation is still being optimized.
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[![CI](https://github.com/EvanOman/AuctionAlgorithmScala/actions/workflows/ci.yml/badge.svg)](https://github.com/EvanOman/AuctionAlgorithmScala/actions/workflows/ci.yml)
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Originally written in 2016 (Scala 2.11 + Breeze); rewritten in 2026. The old implementation had the same epsilon-scaling termination bug as the original C++ version (the final scaling phase ran too coarse, so tie-heavy instances came back suboptimal — its own test harness literally printed "Percentage correct"), and its fixed starting epsilon of 0.3 meant it produced **no assignment at all** for n ≤ 2. Full bug taxonomy in the [C++ repo's docs/BUGS.md](https://github.com/EvanOman/AuctionAlgorithmCPP/blob/master/docs/BUGS.md); the old source is preserved at `legacy/`.
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## What's here
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- **`Auction.solve(costs, n, options)`** — the solver. Row-major `IndexedSeq[Long]` costs, `Minimize` (default) or `Maximize`, exact optimality for integer costs (the final scaling phase runs with n·ε < 1). An optional **parallel bidding mode** (`Options(parallel = true)`) computes each round's bids concurrently with deterministic results — the feature that distinguished the 2016 version, kept and made correct.
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- **`Problem`** — parser/formatter for the text problem format shared with the C++ repo.
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- **CLI** — `solve` / `generate` subcommands mirroring the C++ `auction` binary.
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- **Tests** — munit suite: brute-force cross-checks over hundreds of random instances, Machol–Wien closed-form cases, the tie-heavy regression instance, n ≤ 2 regressions, parallel-equals-sequential.
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## Usage
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Requires JDK 11+ and [sbt](https://www.scala-sbt.org/) ([just](https://github.com/casey/just) optional but recommended).
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```bash
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just test # run the test suite
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just solve problem.apf # solve a problem file
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just generate 10 --seed 42 # emit a random 10x10 instance
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```
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Problem file format (`#` comments and blank lines ignored; `objective` defaults to `min`):
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```
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objective min
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n 3
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4 1 3
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2 0 5
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3 2 2
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```
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Output:
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```
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objective: min
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n: 3
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total_cost: 5
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phases: 3
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rounds: 7
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assignment:
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0 -> 1
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1 -> 0
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2 -> 2
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```
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Add `--json` for machine-readable output, `--parallel` for parallel bidding.
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As a library:
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```scala
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import com.evan.auctionalgorithm.*
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val costs = Vector[Long](4, 1, 3, 2, 0, 5, 3, 2, 2)
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val result = Auction.solve(costs, 3) // minimize by default
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// result.assignment == Vector(1, 0, 2), result.totalCost == 5
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```
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## Development
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`just fc` before committing (format + tests). CI runs `scalafmtCheckAll` and the test suite on every push. Compiler warnings are fatal (`-Werror`).

‎build.sbt‎

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name := "AuctionAlgorithmScala"
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name := "auction-algorithm"
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organization := "com.evan"
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version := "1.0.0"
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scalaVersion := "2.11.7"
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scalaVersion := "3.3.4"
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libraryDependencies += "org.scalanlp" % "breeze_2.11" % "0.12"
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scalacOptions ++= Seq(
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"-deprecation",
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"-feature",
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"-unchecked",
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"-Wunused:all",
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"-Werror"
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)
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connectInput in run := true
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libraryDependencies ++= Seq(
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"org.scala-lang.modules" %% "scala-parallel-collections" % "1.0.4",
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"org.scalameta" %% "munit" % "1.0.2" % Test
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)
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Compile / run / connectInput := true
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Compile / mainClass := Some("com.evan.auctionalgorithm.Main")

‎justfile‎

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set shell := ["bash", "-cu"]
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# List available recipes.
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default:
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@just --list
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# Compile the project.
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build:
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sbt -batch compile
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# Run the test suite.
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test:
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sbt -batch test
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# Format all Scala sources and build files in place.
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fmt:
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sbt -batch scalafmtAll scalafmtSbt
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# Check formatting without modifying files.
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format-check:
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sbt -batch scalafmtCheckAll scalafmtSbtCheck
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# Lint is the format check plus fatal compiler warnings (enabled in build.sbt).
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lint: format-check build
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# Format, then run the full test suite. Run before committing.
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fc: fmt test
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# Run everything CI runs.
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ci: format-check test
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# Solve a problem file: just solve path/to/problem.apf [--json] [--parallel]
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solve *ARGS:
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sbt -batch --error "run solve {{ ARGS }}"
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# Generate a random problem: just generate N [--lo A --hi B --seed S --objective min|max]
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generate *ARGS:
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sbt -batch --error "run generate {{ ARGS }}"
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# Remove build artifacts.
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clean:
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sbt -batch clean

src/main/scala-2.11/com/evan/auctionalgorithm/AssignmentProblem.scala renamed to legacy/AssignmentProblem.scala

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src/main/scala-2.11/com/evan/auctionalgorithm/Test.scala renamed to legacy/Test.scala

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‎project/build.properties‎

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sbt.version=1.10.7

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