Cut (JGAlgo - Parent 0.2.0 API)

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```
public interface Cut
```
A cut that partition the vertices of a graph into two sets.
Given a graph $G=(V,E)$ , a cut is a partition of $V$ into two sets $C, \bar{C} = V \setminus C$ . Given a weight function, the weight of a cut $(C,\bar{C})$ is the weight sum of all edges $(u,v)$ such that $u$ is in $C$ and $v$ is in $\bar{C}$ . When we say 'the cut' we often mean the first set $C$ .

Author:

Barak Ugav

See Also:

MinimumCutST

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method	Description
`boolean`	`containsVertex(int vertex)`	Check whether a vertex is in the cut.
`IntCollection`	`edges()`	Get the collection of all the edges that cross the cut.
`IntCollection`	`vertices()`	Get the collection of all the vertices in the cut.
`double`	`weight(WeightFunction w)`	Get the weight of the cut with respect to the given weight function.

- Method Detail
  - containsVertex
```
boolean containsVertex(int vertex)
```
    Check whether a vertex is in the cut.
    When we say 'the cut' we mean the first set $C$ out of the cut partition into two sets $C, \bar{C} = V \setminus C$ .
    
    Parameters:
    
    vertex - a vertex identifier
    
    Returns:
    
    true if vertex is in the first set of the partition, $C$
  - vertices
```
IntCollection vertices()
```
    Get the collection of all the vertices in the cut.
    When we say 'the cut' we mean the first set $C$ out of the cut partition into two sets $C, \bar{C} = V \setminus C$ .
    
    Returns:
    
    a collection of all the vertices of the first set of the partition, $C$
  - edges
```
IntCollection edges()
```
    Get the collection of all the edges that cross the cut.
    Given a cut $C, \bar{C} = V \setminus C$ , the edges that cross the cut are edges $(u,v)$ such that $u$ is in $C$ and $v$ is in $\bar{C}$ .
    
    Returns:
    
    a collection of all the edges that cross the cut partition
  - weight
```
double weight(WeightFunction w)
```
    Get the weight of the cut with respect to the given weight function.
    Given a weight function, the weight of a cut $(C,\bar{C})$ is the weight sum of all edges $(u,v)$ such that $u$ is in $C$ and $v$ is in $\bar{C}$ .
    
    Parameters:
    
    w - an edge weight function
    
    Returns:
    
    the sum of edge weights $(u,v)$ such that $u$ is in $C$ and $v$ is in $\bar{C}$