定义偏序关系的接口：
interface IPartialComparer<T> {
int? Compare(T x, T y);
}
Compare应该返回-1if x < y、0if x = y、1ify < x和nullifx且y不可比较。
我们的目标是以尊重枚举的部分顺序返回元素的顺序。也就是说，我们e_1, e_2, e_3, ..., e_n以偏序寻找元素的序列，使得 ifi <= j和e_i与e_jthen可比e_i <= e_j。我将使用深度优先搜索来做到这一点。
使用深度优先搜索实现拓扑排序的类：
class TopologicalSorter {
class DepthFirstSearch<TElement, TKey> {
readonly IEnumerable<TElement> _elements;
readonly Func<TElement, TKey> _selector;
readonly IPartialComparer<TKey> _comparer;
HashSet<TElement> _visited;
Dictionary<TElement, TKey> _keys;
List<TElement> _sorted;
public DepthFirstSearch(
IEnumerable<TElement> elements,
Func<TElement, TKey> selector,
IPartialComparer<TKey> comparer
) {
_elements = elements;
_selector = selector;
_comparer = comparer;
var referenceComparer = new ReferenceEqualityComparer<TElement>();
_visited = new HashSet<TElement>(referenceComparer);
_keys = elements.ToDictionary(
e => e,
e => _selector(e),
referenceComparer
);
_sorted = new List<TElement>();
}
public IEnumerable<TElement> VisitAll() {
foreach (var element in _elements) {
Visit(element);
}
return _sorted;
}
void Visit(TElement element) {
if (!_visited.Contains(element)) {
_visited.Add(element);
var predecessors = _elements.Where(
e => _comparer.Compare(_keys[e], _keys[element]) < 0
);
foreach (var e in predecessors) {
Visit(e);
}
_sorted.Add(element);
}
}
}
public IEnumerable<TElement> ToplogicalSort<TElement, TKey>(
IEnumerable<TElement> elements,
Func<TElement, TKey> selector, IPartialComparer<TKey> comparer
) {
var search = new DepthFirstSearch<TElement, TKey>(
elements,
selector,
comparer
);
return search.VisitAll();
}
}
在进行深度优先搜索时将节点标记为已访问所需的辅助类：
class ReferenceEqualityComparer<T> : IEqualityComparer<T> {
public bool Equals(T x, T y) {
return Object.ReferenceEquals(x, y);
}
public int GetHashCode(T obj) {
return obj.GetHashCode();
}
}
我没有声称这是算法的最佳实现，但我相信它是正确的实现。此外，我没有IOrderedEnumerable按照您的要求返回，但是一旦我们到了这一点，这很容易做到。
如果我们已经将所有前辈添加到排序中，则该算法通过对元素进行深度优先搜索来工作，将元素添加e到线性排序（在算法中表示为） 。因此，对于每个元素，如果我们还没有访问过它，请访问它的前辈，然后添加。因此，这是算法的核心：_sortedeee
public void Visit(TElement element) {
// if we haven't already visited the element
if (!_visited.Contains(element)) {
// mark it as visited
_visited.Add(element);
var predecessors = _elements.Where(
e => _comparer.Compare(_keys[e], _keys[element]) < 0
);
// visit its predecessors
foreach (var e in predecessors) {
Visit(e);
}
// add it to the ordering
// at this point we are certain that
// its predecessors are already in the ordering
_sorted.Add(element);
}
}
例如，考虑{1, 2, 3}在X < YifX是 的子集的子集上定义的偏序Y。我按如下方式实现：
public class SetComparer : IPartialComparer<HashSet<int>> {
public int? Compare(HashSet<int> x, HashSet<int> y) {
bool xSubsety = x.All(i => y.Contains(i));
bool ySubsetx = y.All(i => x.Contains(i));
if (xSubsety) {
if (ySubsetx) {
return 0;
}
return -1;
}
if (ySubsetx) {
return 1;
}
return null;
}
}
然后sets定义为子集列表{1, 2, 3}
List<HashSet<int>> sets = new List<HashSet<int>>() {
new HashSet<int>(new List<int>() {}),
new HashSet<int>(new List<int>() { 1, 2, 3 }),
new HashSet<int>(new List<int>() { 2 }),
new HashSet<int>(new List<int>() { 2, 3}),
new HashSet<int>(new List<int>() { 3 }),
new HashSet<int>(new List<int>() { 1, 3 }),
new HashSet<int>(new List<int>() { 1, 2 }),
new HashSet<int>(new List<int>() { 1 })
};
TopologicalSorter s = new TopologicalSorter();
var sorted = s.ToplogicalSort(sets, set => set, new SetComparer());
这导致排序：
{}, {2}, {3}, {2, 3}, {1}, {1, 3}, {1, 2}, {1, 2, 3}
尊重偏序。
那很有趣。谢谢。