如何根据依赖关系对依赖对象进行排序

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List<VPair<Item, List<Item>> dependencyHierarchy;

The first item in pair is some object (item) and the second one is a collection of the same type objects that the first one depends on. I want to get a List<Item> in order of dependency, so there are not items that depend on the first element and so on (no cycled dependency!).

输入:

Item4 depends on Item3 and Item5
Item3 depends on Item1
Item1 does not depend on any one
Item2 depends on Item4
Item5 does not depend on any one

结果:

Item1
Item5
Item3
Item4
Item2

谢谢你。

解决方案:

拓扑排序 (感谢 Loic Février的创意)

还有

C # ，例子上的示例(感谢 我不知道提供了很好的示例)

30826 次浏览
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最佳答案

Perfect example to use a topological sort:

http://en.wikipedia.org/wiki/Topological_sorting

It will give you exactly what you need.

You can either use Kahn's algorithm:

L ← Empty list that will contain the sorted elements
S ← Set of all nodes with no incoming edge


while S is not empty do
remove a node n from S
add n to L
for each node m with an edge e from n to m do
remove edge e from the graph
if m has no other incoming edges then
insert m into S


if graph has edges then
return error   (graph has at least one cycle)
else
return L   (a topologically sorted order)

...or you can use Depth-first search:

L ← Empty list that will contain the sorted nodes
while exists nodes without a permanent mark do
select an unmarked node n
visit(n)


function visit(node n)
if n has a permanent mark then
return
if n has a temporary mark then
stop   (not a DAG)


mark n with a temporary mark


for each node m with an edge from n to m do
visit(m)


remove temporary mark from n
mark n with a permanent mark
add n to head of L
小开

I would make this easier on myself by storing the dependencies of an Item within the Item itself:

public class Item
{
private List<Item> m_Dependencies = new List<Item>();


protected AddDependency(Item _item) { m_Dependencies.Add(_item); }


public Item()
{
}; // eo ctor


public List<Item> Dependencies {get{return(m_Dependencies);};}
} // eo class Item

Then, given this you can implement a custom Sort delegate for List that sorts based on whether the given Item is contained within the other's list of dependencies:

int CompareItem(Item _1, Item _2)
{
if(_2.Dependencies.Contains(_1))
return(-1);
else if(_1.Dependencies.Contains(_2))
return(1);
else
return(0);
}
小开

This is my own re-implementation of Topological sorting, the idea is based on http://tawani.blogspot.com/2009/02/topological-sorting-and-cyclic.html (The ported Java source code consumes too much memory, checking 50k objects costs 50k*50k*4 = 10GB which is unacceptable. In addition, it still has Java coding convention some places)

using System.Collections.Generic;
using System.Diagnostics;


namespace Modules
{
/// <summary>
/// Provides fast-algorithm and low-memory usage to sort objects based on their dependencies.
/// </summary>
/// <remarks>
/// Definition: http://en.wikipedia.org/wiki/Topological_sorting
/// Source code credited to: http://tawani.blogspot.com/2009/02/topological-sorting-and-cyclic.html
/// Original Java source code: http://www.java2s.com/Code/Java/Collections-Data-Structure/Topologicalsorting.htm
/// </remarks>
/// <author>ThangTran</author>
/// <history>
/// 2012.03.21 - ThangTran: rewritten based on <see cref="TopologicalSorter"/>.
/// </history>
public class DependencySorter<T>
{
//**************************************************
//
// Private members
//
//**************************************************


#region Private members


/// <summary>
/// Gets the dependency matrix used by this instance.
/// </summary>
private readonly Dictionary<T, Dictionary<T, object>> _matrix = new Dictionary<T, Dictionary<T, object>>();


#endregion




//**************************************************
//
// Public methods
//
//**************************************************


#region Public methods


/// <summary>
/// Adds a list of objects that will be sorted.
/// </summary>
public void AddObjects(params T[] objects)
{
// --- Begin parameters checking code -----------------------------
Debug.Assert(objects != null);
Debug.Assert(objects.Length > 0);
// --- End parameters checking code -------------------------------


// add to matrix
foreach (T obj in objects)
{
// add to dictionary
_matrix.Add(obj, new Dictionary<T, object>());
}
}


/// <summary>
/// Sets dependencies of given object.
/// This means <paramref name="obj"/> depends on these <paramref name="dependsOnObjects"/> to run.
/// Please make sure objects given in the <paramref name="obj"/> and <paramref name="dependsOnObjects"/> are added first.
/// </summary>
public void SetDependencies(T obj, params T[] dependsOnObjects)
{
// --- Begin parameters checking code -----------------------------
Debug.Assert(dependsOnObjects != null);
// --- End parameters checking code -------------------------------


// set dependencies
Dictionary<T, object> dependencies = _matrix[obj];
dependencies.Clear();


// for each depended objects, add to dependencies
foreach (T dependsOnObject in dependsOnObjects)
{
dependencies.Add(dependsOnObject, null);
}
}


/// <summary>
/// Sorts objects based on this dependencies.
/// Note: because of the nature of algorithm and memory usage efficiency, this method can be used only one time.
/// </summary>
public T[] Sort()
{
// prepare result
List<T> result = new List<T>(_matrix.Count);


// while there are still object to get
while (_matrix.Count > 0)
{
// get an independent object
T independentObject;
if (!this.GetIndependentObject(out independentObject))
{
// circular dependency found
throw new CircularReferenceException();
}


// add to result
result.Add(independentObject);


// delete processed object
this.DeleteObject(independentObject);
}


// return result
return result.ToArray();
}


#endregion




//**************************************************
//
// Private methods
//
//**************************************************


#region Private methods


/// <summary>
/// Returns independent object or returns NULL if no independent object is found.
/// </summary>
private bool GetIndependentObject(out T result)
{
// for each object
foreach (KeyValuePair<T, Dictionary<T, object>> pair in _matrix)
{
// if the object contains any dependency
if (pair.Value.Count > 0)
{
// has dependency, skip it
continue;
}


// found
result = pair.Key;
return true;
}


// not found
result = default(T);
return false;
}


/// <summary>
/// Deletes given object from the matrix.
/// </summary>
private void DeleteObject(T obj)
{
// delete object from matrix
_matrix.Remove(obj);


// for each object, remove the dependency reference
foreach (KeyValuePair<T, Dictionary<T, object>> pair in _matrix)
{
// if current object depends on deleting object
pair.Value.Remove(obj);
}
}




#endregion
}


/// <summary>
/// Represents a circular reference exception when sorting dependency objects.
/// </summary>
public class CircularReferenceException : Exception
{
/// <summary>
/// Initializes a new instance of the <see cref="CircularReferenceException"/> class.
/// </summary>
public CircularReferenceException()
: base("Circular reference found.")
{
}
}
}
小开

Having struggled with this for a while, here's my attempt at a Linq style TSort extension method:

public static IEnumerable<T> TSort<T>( this IEnumerable<T> source, Func<T, IEnumerable<T>> dependencies, bool throwOnCycle = false )
{
var sorted = new List<T>();
var visited = new HashSet<T>();


foreach( var item in source )
Visit( item, visited, sorted, dependencies, throwOnCycle );


return sorted;
}


private static void Visit<T>( T item, HashSet<T> visited, List<T> sorted, Func<T, IEnumerable<T>> dependencies, bool throwOnCycle )
{
if( !visited.Contains( item ) )
{
visited.Add( item );


foreach( var dep in dependencies( item ) )
Visit( dep, visited, sorted, dependencies, throwOnCycle );


sorted.Add( item );
}
else
{
if( throwOnCycle && !sorted.Contains( item ) )
throw new Exception( "Cyclic dependency found" );
}
}
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A different idea, for cases with only one "parent" depending:

Instead of deps, you'd store the parents.
So you can tell very easily whether an issue is a dependency of some other.
And then use Comparable<T>, which would claim the dependencies "lesser" and the dependency "greater".
And then simply call Collections.sort( List<T>, ParentComparator<T>);

For multi-parent scenario, a tree search would be needed which would result in slow execution. But that could be solved by a cache in a form of A* sort matrix.

小开

I merged DMM's idea with the depth-first-search algorithm on Wikipedia. It works perfect for what I needed.

public static class TopologicalSorter
{
public static List<string> LastCyclicOrder = new List<string>(); //used to see what caused the cycle


sealed class ItemTag
{
public enum SortTag
{
NotMarked,
TempMarked,
Marked
}


public string Item { get; set; }
public SortTag Tag { get; set; }


public ItemTag(string item)
{
Item = item;
Tag = SortTag.NotMarked;
}
}


public static IEnumerable<string> TSort(this IEnumerable<string> source, Func<string, IEnumerable<string>> dependencies)
{
TopologicalSorter.LastCyclicOrder.Clear();


List<ItemTag> allNodes = new List<ItemTag>();
HashSet<string> sorted = new HashSet<string>(StringComparer.OrdinalIgnoreCase);


foreach (string item in source)
{
if (!allNodes.Where(n => string.Equals(n.Item, item, StringComparison.OrdinalIgnoreCase)).Any())
{
allNodes.Add(new ItemTag(item)); //don't insert duplicates
}
foreach (string dep in dependencies(item))
{
if (allNodes.Where(n => string.Equals(n.Item, dep, StringComparison.OrdinalIgnoreCase)).Any()) continue; //don't insert duplicates
allNodes.Add(new ItemTag(dep));
}
}


foreach (ItemTag tag in allNodes)
{
Visit(tag, allNodes, dependencies, sorted);
}


return sorted;
}


static void Visit(ItemTag tag, List<ItemTag> allNodes, Func<string, IEnumerable<string>> dependencies, HashSet<string> sorted)
{
if (tag.Tag == ItemTag.SortTag.TempMarked)
{
throw new GraphIsCyclicException();
}
else if (tag.Tag == ItemTag.SortTag.NotMarked)
{
tag.Tag = ItemTag.SortTag.TempMarked;
LastCyclicOrder.Add(tag.Item);


foreach (ItemTag dep in dependencies(tag.Item).Select(s => allNodes.Where(t => string.Equals(s, t.Item, StringComparison.OrdinalIgnoreCase)).First())) //get item tag which falls with used string
Visit(dep, allNodes, dependencies, sorted);


LastCyclicOrder.Remove(tag.Item);
tag.Tag = ItemTag.SortTag.Marked;
sorted.Add(tag.Item);
}
}
}
小开

There's a nuget for that.

For those of us who prefer not to re-invent the wheel: use nuget to install the QuickGraph .NET library, which includes multiple graph algorithms including topological sort.

To use it, you need to create an instance of AdjacencyGraph<,> such as AdjacencyGraph<String, SEdge<String>>. Then, if you include the appropriate extensions:

using QuickGraph.Algorithms;

You can call:

var sorted = myGraph.TopologicalSort();

To get a list of sorted nodes.

小开

I liked DMM's answer, but it assumes that the input nodes are leaves (which may or may not be what is expected).

I am posting an alternate solution using LINQ that does not make this assumption. In addition, this solution uses yield return to be able to quickly return the leaves (using e.g. TakeWhile).

public static IEnumerable<T> TopologicalSort<T>(this IEnumerable<T> nodes,
Func<T, IEnumerable<T>> connected)
{
var elems = nodes.ToDictionary(node => node,
node => new HashSet<T>(connected(node)));
while (elems.Count > 0)
{
var elem = elems.FirstOrDefault(x => x.Value.Count == 0);
if (elem.Key == null)
{
throw new ArgumentException("Cyclic connections are not allowed");
}
elems.Remove(elem.Key);
foreach (var selem in elems)
{
selem.Value.Remove(elem.Key);
}
yield return elem.Key;
}
}
小开

This is refactored code from post https://stackoverflow.com/a/9991916/4805491.

// Version 1
public static class TopologicalSorter<T> where T : class {


public struct Item {
public readonly T Object;
public readonly T Dependency;
public Item(T @object, T dependency) {
Object = @object;
Dependency = dependency;
}
}




public static T[] Sort(T[] objects, Func<T, T, bool> isDependency) {
return Sort( objects.ToList(), isDependency ).ToArray();
}


public static T[] Sort(T[] objects, Item[] dependencies) {
return Sort( objects.ToList(), dependencies.ToList() ).ToArray();
}




private static List<T> Sort(List<T> objects, Func<T, T, bool> isDependency) {
return Sort( objects, GetDependencies( objects, isDependency ) );
}


private static List<T> Sort(List<T> objects, List<Item> dependencies) {
var result = new List<T>( objects.Count );


while (objects.Any()) {
var obj = GetIndependentObject( objects, dependencies );
RemoveObject( obj, objects, dependencies );
result.Add( obj );
}


return result;
}


private static List<Item> GetDependencies(List<T> objects, Func<T, T, bool> isDependency) {
var dependencies = new List<Item>();


for (var i = 0; i < objects.Count; i++) {
var obj1 = objects[i];
for (var j = i + 1; j < objects.Count; j++) {
var obj2 = objects[j];
if (isDependency( obj1, obj2 )) dependencies.Add( new Item( obj1, obj2 ) ); // obj2 is dependency of obj1
if (isDependency( obj2, obj1 )) dependencies.Add( new Item( obj2, obj1 ) ); // obj1 is dependency of obj2
}
}


return dependencies;
}




private static T GetIndependentObject(List<T> objects, List<Item> dependencies) {
foreach (var item in objects) {
if (!GetDependencies( item, dependencies ).Any()) return item;
}
throw new Exception( "Circular reference found" );
}


private static IEnumerable<Item> GetDependencies(T obj, List<Item> dependencies) {
return dependencies.Where( i => i.Object == obj );
}


private static void RemoveObject(T obj, List<T> objects, List<Item> dependencies) {
objects.Remove( obj );
dependencies.RemoveAll( i => i.Object == obj || i.Dependency == obj );
}


}




// Version 2
public class TopologicalSorter {


public static T[] Sort<T>(T[] source, Func<T, T, bool> isDependency) {
var list = new LinkedList<T>( source );
var result = new List<T>();


while (list.Any()) {
var obj = GetIndependentObject( list, isDependency );
list.Remove( obj );
result.Add( obj );
}


return result.ToArray();
}


private static T GetIndependentObject<T>(IEnumerable<T> list, Func<T, T, bool> isDependency) {
return list.First( i => !GetDependencies( i, list, isDependency ).Any() );
}


private static IEnumerable<T> GetDependencies<T>(T obj, IEnumerable<T> list, Func<T, T, bool> isDependency) {
return list.Where( i => isDependency( obj, i ) ); // i is dependency of obj
}


}
小开

I don't like recursive methods so DMM is out. Krumelur looks good but seems to use a lot of memory? Made an alternative stack based method that seems to work. Uses same DFS logic as DMM 's and I used this solutions as comparison when testing.

    public static IEnumerable<T> TopogicalSequenceDFS<T>(this IEnumerable<T> source, Func<T, IEnumerable<T>> deps)
{
HashSet<T> yielded = new HashSet<T>();
HashSet<T> visited = new HashSet<T>();
Stack<Tuple<T, IEnumerator<T>>> stack = new Stack<Tuple<T, IEnumerator<T>>>();


foreach (T t in source)
{
stack.Clear();
if (visited.Add(t))
stack.Push(new Tuple<T, IEnumerator<T>>(t, deps(t).GetEnumerator()));


while (stack.Count > 0)
{
var p = stack.Peek();
bool depPushed = false;
while (p.Item2.MoveNext())
{
var curr = p.Item2.Current;
if (visited.Add(curr))
{
stack.Push(new Tuple<T, IEnumerator<T>>(curr, deps(curr).GetEnumerator()));
depPushed = true;
break;
}
else if (!yielded.Contains(curr))
throw new Exception("cycle");
}


if (!depPushed)
{
p = stack.Pop();
if (!yielded.Add(p.Item1))
throw new Exception("bug");
yield return p.Item1;
}
}
}
}

Here is also a simpler stack based BFS variant. It will produce different result than the above, but still valid. I'm not sure if there is any advantage to using the DFS variant above, but it was fun creating it.

    public static IEnumerable<T> TopologicalSequenceBFS<T>(this IEnumerable<T> source, Func<T, IEnumerable<T>> dependencies)
{
var yielded = new HashSet<T>();
var visited = new HashSet<T>();
var stack = new Stack<Tuple<T, bool>>(source.Select(s => new Tuple<T, bool>(s, false))); // bool signals Add to sorted


while (stack.Count > 0)
{
var item = stack.Pop();
if (!item.Item2)
{
if (visited.Add(item.Item1))
{
stack.Push(new Tuple<T, bool>(item.Item1, true)); // To be added after processing the dependencies
foreach (var dep in dependencies(item.Item1))
stack.Push(new Tuple<T, bool>(dep, false));
}
else if (!yielded.Contains(item.Item1))
throw new Exception("cyclic");
}
else
{
if (!yielded.Add(item.Item1))
throw new Exception("bug");
yield return item.Item1;
}
}
}

For .NET 4.7+ I suggest replacing Tuple with ValueTuple for lower memory use. In older .NET versions Tuple can be replaced with KeyValuePair.


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