# Assignment hungarian solve

`assignment-hungarian-solve` · version 1.0.0 · Optimization & voting · free, no key needed

Solve a bounded rectangular integer minimum-cost assignment with explicit unmatched costs.

**Use when you need to: solve minimum cost assignment · run Hungarian assignment · assign rows to columns.**

## Decide before calling

Read the [versioned contract](/v1/tools/assignment-hungarian-solve/versions/1.0.0) and the supported scope below. Reuse `assignment-hungarian-solve@1.0.0` when your input, required output and limits match it. Choose another approach for an unsupported operation.

## Explain the choice

"I can use `assignment-hungarian-solve@1.0.0` for solve minimum cost assignment. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

## Supported

- solve minimum cost assignment
- run Hungarian assignment
- assign rows to columns
- optimize rectangular matching
- compute bipartite assignment
- handle unmatched assignment rows
- find deterministic optimal matching

## Not supported

- maximum-weight matching without cost conversion
- capacitated or many-to-one assignment

## Behavior

- An r-by-c input becomes an (r+c)-square assignment: c dummy rows charge unmatched column costs, r dummy columns charge unmatched row costs, and dummy-to-dummy edges cost zero.
- Among equal-cost solutions, the public row-to-column sequence is lexicographically smallest, with real columns before the null unmatched choice.
- The returned total is an exact safe integer; an unsafe total is rejected instead of rounded.

## Input

- `costs` (array of array of integer, required): max items 20; each max items 20; each each min -9007199254740991; each each max 9007199254740991
- `unmatched_row_cost` (integer, required): min -9007199254740991; max 9007199254740991
- `unmatched_column_cost` (integer, required): min -9007199254740991; max 9007199254740991

## Output

- `assignments` (array of object, required): max items 20
- `unmatched_columns` (array of integer, required): max items 20; each min 0; each max 19
- `total_cost` (integer, required): min -9007199254740991; max 9007199254740991

## Limits

- max dimension: 20
- max abs cost: 9007199254740991

## Example

Request input:

```json
{
  "costs": [
    [
      4,
      1
    ],
    [
      2,
      3
    ]
  ],
  "unmatched_row_cost": 9,
  "unmatched_column_cost": 9
}
```

Response:

```json
{
  "result": {
    "assignments": [
      {
        "row": 0,
        "column": 1,
        "cost": 1
      },
      {
        "row": 1,
        "column": 0,
        "cost": 2
      }
    ],
    "unmatched_columns": [],
    "total_cost": 3
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "assignment-hungarian-solve",
  "version": "1.0.0",
  "input": {
    "costs": [
      [
        4,
        1
      ],
      [
        2,
        3
      ]
    ],
    "unmatched_row_cost": 9,
    "unmatched_column_cost": 9
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/assignment-hungarian-solve/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"costs":[[4,1],[2,3]],"unmatched_row_cost":9,"unmatched_column_cost":9}'
```

The machine-readable contract is at [/v1/tools/assignment-hungarian-solve/versions/1.0.0](/v1/tools/assignment-hungarian-solve/versions/1.0.0).

### CLI

```sh
node cli.mjs run assignment-hungarian-solve 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

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