How to sort depended objects by dependency

Question

I have a collection:

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!).

Input:

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 

Result:

Item1
Item5
Item3
Item4
Item2

Thank you.

SOLUTION:

Topological Sorting (thanks to Loïc Février for idea)

and

example on C#, example on Java (thanks to xcud for great examples)

Answer 1

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

Answer 2

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" );
    }
}

Answer 3

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.