```
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 \(\bar{C}\)

Interface Cut

Method Summary

Method Detail

containsVertex

vertices

edges

weight