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# Introduction

The Munkres module provides an implementation of the Munkres algorithm (also called the Hungarian algorithm or the Kuhn-Munkres algorithm), useful for solving the Assignment Problem.

For complete usage documentation, see: http://software.clapper.org/munkres/

var DISALLOWED

## Functions

def make_cost_matrix(

profit_matrix, inversion_function=None)

Create a cost matrix from a profit matrix by calling `inversion_function()` to invert each value. The inversion function must take one numeric argument (of any type) and return another numeric argument which is presumed to be the cost inverse of the original profit value. If the inversion function is not provided, a given cell's inverted value is calculated as `max(matrix) - value`.

This is a static method. Call it like this:

```from munkres import Munkres
cost_matrix = Munkres.make_cost_matrix(matrix, inversion_func)
```

For example:

```from munkres import Munkres
cost_matrix = Munkres.make_cost_matrix(matrix, lambda x : sys.maxsize - x)
```

Parameters

• `profit_matrix` (list of lists of numbers): The matrix to convert from profit to cost values.
• `inversion_function` (`function`): The function to use to invert each entry in the profit matrix.

Returns

A new matrix representing the inversion of `profix_matrix`.

## Classes

class Munkres

Calculate the Munkres solution to the classical assignment problem. See the module documentation for usage.

### Static methods

def __init__(

self)

Create a new instance

def compute(

self, cost_matrix)

Compute the indexes for the lowest-cost pairings between rows and columns in the database. Returns a list of `(row, column)` tuples that can be used to traverse the matrix.

WARNING: This code handles square and rectangular matrices. It does not handle irregular matrices.

Parameters

• `cost_matrix` (list of lists of numbers): The cost matrix. If this cost matrix is not square, it will be padded with zeros, via a call to `pad_matrix()`. (This method does not modify the caller's matrix. It operates on a copy of the matrix.)

Returns

A list of `(row, column)` tuples that describe the lowest cost path through the matrix

Pad a possibly non-square matrix to make it square.

Parameters

• `matrix` (list of lists of numbers): matrix to pad
• `pad_value` (`int`): value to use to pad the matrix

Returns

var C

var Z0_c

var Z0_r

var col_covered

var marked

var n

var path

var row_covered