Directed.Sparse

java.lang.Object
- la.la.Value
- - graph.Graph
  - - graph.Directed
    - - graph.Directed.Sparse

All Implemented Interfaces:

Graph.Sparse, java.lang.Comparable<Value>

Direct Known Subclasses:

Directed.C, Directed.Sparse.Induced, Directed.Sparse.Renumbered

Enclosing class:

Directed
```
public static class Directed.Sparse
extends Directed
implements Graph.Sparse
```
The class of Sparse Directed Graphs. Also see Directed.Dense and Undirected.Sparse.

Nested Class Summary

Nested Classes
Modifier and Type	Class and Description
`class`	`Directed.Sparse.Induced` An induced subgraph of a Sparse Directed Graph is Sparse and Directed.
`class`	`Directed.Sparse.Renumbered` A Sparse Directed Graph renumbered accpording to `vs` is Sparse and Directed.

Nested classes/interfaces inherited from class graph.Directed
Directed.AsUndirected, Directed.C, Directed.Dense, Directed.Edge, Directed.Sparse, Directed.Vertex

Nested classes/interfaces inherited from class graph.Graph
Graph.Canonical, Graph.Contraction, Graph.Derived, Graph.SubGraph, Graph.SubGraphs, Graph.ToDirected, Graph.ToUndirected

Nested classes/interfaces inherited from class la.la.Value
Value.Atomic, Value.Bool, Value.Char, Value.Chars, Value.Cts, Value.Defer, Value.Discrete, Value.Enum, Value.Inc_Or, Value.Int, Value.Lambda, Value.List, Value.Maybe, Value.Option, Value.Real, Value.Scannable, Value.Structured, Value.Triv, Value.Tuple

Field Summary

Fields
Modifier and Type	Field and Description
`int[][]`	`es` The Edges of 'this' Sparse, as an int[E][2] array.
`int[][]`	`pred` Given an Edge ⟨v0, v1⟩, v1 is in (ascending) succ[v0], and v0 is in (ascending) pred[v1].
`int[][]`	`succ` Given an Edge ⟨v0, v1⟩, v1 is in (ascending) succ[v0], and v0 is in (ascending) pred[v1].

Fields inherited from class graph.Directed
unlabelled, unlabelled_O

Fields inherited from class la.la.Value
C, comparator, CR, eight, ffalse, five, fiveR, four, fourR, half, negCR, negOne, negOneR, negTenR, nilVal, nine, None, one, oneR, PI, PIby2, point01, point1, point5, point9, quarter, seven, six, ten, tenR, three, threeR, triv, ttrue, two, twoR, zero, zeroR

Constructor Summary

Constructors
Constructor and Description
`Sparse(int[][] es)` Assume that the max Vertex mentioned in es is the last Vertex.
`Sparse(Type t, int V, int[][] es)` Directed Edges es = {{v00, v01}, {v10, v11}, ...}.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Series.Int`	`directPredecessors(int v)` Only applicable to `Directed` Graphs.
`Series.Int`	`directSuccessors(int v)` Only applicable to `Directed` Graphs.
`int`	`eSize()` The number of Edges in 'this' Graph, \|E\|≥0.
`int`	`inDegree(int v)` O(1)-time.
`Directed.Sparse.Induced`	`induced(int[] vs)` An induced subgraph of a Sparse Directed Graph is Sparse and Directed.
`boolean`	`isEdge(int v0, int v1)` Is ⟨v0, v1⟩ an Edge in 'this' Graph? Also see `adjacent(v0,v1)`.
`Series.Int`	`joinedTo(int v)` An increasing Series of those Vertices 'w' `adjacent` to v, that is (v,w) is an Edge or (w,v) is (includes v, once, if there is a loop (v,v)).
`static int`	`maxV(int[][] es)` Return the largest Vertex number mentioned in `es`, which may or may not be the largest one in the Graph.
`int`	`outDegree(int v)` O(1)-time.
`Directed.Sparse.Renumbered`	`renumbered(int[] vs)` A renumbered Sparse Directed Graph is Sparse and Directed.
`java.lang.String`	`toString()` Used, for example, in `printing` of `constants`, and in calls to `Value.error(java.lang.String)`.
`Type`	`type()` Note, type(), `Graph.adjacent(int, int)`, `Graph.vLabelled()`, `Graph.vLabel(int)`, `Graph.eLabelled()`, and `Graph.eLabel(int, int)` must be consistent.
`int`	`vSize()` The number of Vertices, \|V\|≥1, V = {v₀, ..., v_(vSize()-1)}, of 'this' Graph.

Methods inherited from class graph.Directed
asUndirected, degree, dense, dense, dense, dense, dense, dense, main, sparse, toDirected

Methods inherited from class graph.Graph
A, adjacent, arrayA, byDegree, byDegree, canonical, canonical1, canonical1R, canonical2, canonical2R, checkProperties, contraction, edges, edgesCorrespond, eLabel, eLabelled, eLabels, eStats, flatten, hashCode, isDirected, isomorphic, isUndirected, localHash, maxEdges, nAutomorphisms, randomised, selfLoops, structurallyIdentical, subGraphs, subGraphs, toUndirected, vLabel, vLabelled, vLabels, vPair2n

Methods inherited from class la.la.Value
AoM, apply, bOp, compareTo, cons, cts, elt, errMsg, error, force, isTuple, just, n, nElts, nlAoM, pair, print, quad, real, RTE, triple, tuple, UOE, uOp, x

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - succ
```
public final int[][] succ
```
    Given an Edge ⟨v0, v1⟩, v1 is in (ascending) succ[v0], and v0 is in (ascending) pred[v1].
  - pred
```
public final int[][] pred
```
    Given an Edge ⟨v0, v1⟩, v1 is in (ascending) succ[v0], and v0 is in (ascending) pred[v1].
  - es
```
public final int[][] es
```
    The Edges of 'this' Sparse, as an int[E][2] array.
- Constructor Detail
  - Sparse
```
public Sparse(int[][] es)
```
    Assume that the max Vertex mentioned in es is the last Vertex.
  - Sparse
```
public Sparse(Type t,
              int V,
              int[][] es)
```
    Directed Edges es = {{v00, v01}, {v10, v11}, ...}.
- Method Detail
  - type
```
public Type type()
```
    Description copied from class: Graph
    
    Note, type(), Graph.adjacent(int, int), Graph.vLabelled(), Graph.vLabel(int), Graph.eLabelled(), and Graph.eLabel(int, int) must be consistent.
    
    Specified by:
    
    type in class Graph
  - vSize
```
public int vSize()
```
    Description copied from class: Graph
    
    The number of Vertices, |V|≥1, V = {v₀, ..., v_(vSize()-1)}, of 'this' Graph. The "null Graph" (|V|=0) is usually considered not to be a Graph. Also see eSize().
    
    Specified by:
    
    vSize in class Graph
  - eSize
```
public int eSize()
```
    Description copied from class: Graph
    
    The number of Edges in 'this' Graph, |E|≥0. By the way, the "empty Graph" (|E|=0), for a given |V|≥1, is a perfectly good Graph. Also see vSize().
    
    Overrides:
    
    eSize in class Graph
  - inDegree
```
public int inDegree(int v)
```
    O(1)-time.
    
    Overrides:
    
    inDegree in class Graph
  - outDegree
```
public int outDegree(int v)
```
    O(1)-time.
    
    Overrides:
    
    outDegree in class Graph
  - isEdge
```
public boolean isEdge(int v0,
                      int v1)
```
    Description copied from class: Graph
    
    Is ⟨v0, v1⟩ an Edge in 'this' Graph? Also see adjacent(v0,v1).
    
    Specified by:
    
    isEdge in class Graph
  - joinedTo
```
public Series.Int joinedTo(int v)
```
    Description copied from class: Graph
    
    An increasing Series of those Vertices 'w' adjacent to v, that is (v,w) is an Edge or (w,v) is (includes v, once, if there is a loop (v,v)). Note, this default is inefficient for sparse Graphs but also see joinedTo(int) and Undirected.Sparse.joinedTo(int).
    
    Overrides:
    
    joinedTo in class Graph
  - directPredecessors
```
public Series.Int directPredecessors(int v)
```
    Description copied from class: Graph
    
    Only applicable to Directed Graphs. An increasing Series of those Vertices 'p' such that ⟨p,v⟩ is an Edge (includes v if there is a loop ⟨v,v⟩). Note, this default is inefficient for sparse Graphs but see directPredecessors(int)
    
    Overrides:
    
    directPredecessors in class Graph
  - directSuccessors
```
public Series.Int directSuccessors(int v)
```
    Description copied from class: Graph
    
    Only applicable to Directed Graphs. An increasing Series of those Vertices 's' such that ⟨v,s⟩ is an Edge (includes v if there is a loop ⟨v,v⟩). Note, this default is inefficient for sparse Graphs but see directSuccessors(int).
    
    Overrides:
    
    directSuccessors in class Graph
  - maxV
```
public static int maxV(int[][] es)
```
    Return the largest Vertex number mentioned in es, which may or may not be the largest one in the Graph. Look at Sparse's constructors.
  - toString
```
public java.lang.String toString()
```
    Description copied from class: Value
    
    Used, for example, in printing of constants, and in calls to Value.error(java.lang.String). The result does not necessarily fully specify a large, or infinite(!), Value. (This default returns the Class Name of 'this'.) Also see print(ps).
    
    Overrides:
    
    toString in class Value
  - renumbered
```
public Directed.Sparse.Renumbered renumbered(int[] vs)
```
    A renumbered Sparse Directed Graph is Sparse and Directed.
    
    Overrides:
    
    renumbered in class Graph
  - induced
```
public Directed.Sparse.Induced induced(int[] vs)
```
    An induced subgraph of a Sparse Directed Graph is Sparse and Directed.
    
    Overrides:
    
    induced in class Graph

Class Directed.Sparse

Nested Class Summary

Nested classes/interfaces inherited from class graph.Directed

Nested classes/interfaces inherited from class graph.Graph

Nested classes/interfaces inherited from class la.la.Value

Field Summary

Fields inherited from class graph.Directed

Fields inherited from class la.la.Value

Constructor Summary

Method Summary

Methods inherited from class graph.Directed

Methods inherited from class graph.Graph

Methods inherited from class la.la.Value

Methods inherited from class java.lang.Object

Field Detail

succ

pred

es

Constructor Detail

Sparse

Sparse

Method Detail

type

vSize

eSize

inDegree

outDegree

isEdge

joinedTo

directPredecessors

directSuccessors

maxV

toString

renumbered

induced