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// Copyright (c) .NET Foundation. All rights reserved.
// Licensed under the Apache License, Version 2.0. See License.txt in the project root for license information.
using System;
using System.Collections.Generic;
using System.Linq;
using JetBrains.Annotations;
using Microsoft.EntityFrameworkCore.Diagnostics;
namespace Microsoft.EntityFrameworkCore.Utilities
{
internal class Multigraph<TVertex, TEdge> : Graph<TVertex>
{
private readonly HashSet<TVertex> _vertices = new HashSet<TVertex>();
private readonly Dictionary<TVertex, Dictionary<TVertex, List<TEdge>>> _successorMap =
new Dictionary<TVertex, Dictionary<TVertex, List<TEdge>>>();
private readonly Dictionary<TVertex, HashSet<TVertex>> _predecessorMap =
new Dictionary<TVertex, HashSet<TVertex>>();
public IEnumerable<TEdge> Edges
=> _successorMap.Values.SelectMany(s => s.Values).SelectMany(e => e).Distinct();
public IEnumerable<TEdge> GetEdges([NotNull] TVertex from, [NotNull] TVertex to)
{
if (_successorMap.TryGetValue(from, out var successorSet))
{
if (successorSet.TryGetValue(to, out var edgeList))
{
return edgeList;
}
}
return Enumerable.Empty<TEdge>();
}
public void AddVertex([NotNull] TVertex vertex)
=> _vertices.Add(vertex);
public void AddVertices([NotNull] IEnumerable<TVertex> vertices)
=> _vertices.UnionWith(vertices);
public void AddEdge([NotNull] TVertex from, [NotNull] TVertex to, [CanBeNull] TEdge edge)
{
#if DEBUG
if (!_vertices.Contains(from))
{
throw new InvalidOperationException(CoreStrings.GraphDoesNotContainVertex(from));
}
if (!_vertices.Contains(to))
{
throw new InvalidOperationException(CoreStrings.GraphDoesNotContainVertex(to));
}
#endif
if (!_successorMap.TryGetValue(from, out var successorEdges))
{
successorEdges = new Dictionary<TVertex, List<TEdge>>();
_successorMap.Add(from, successorEdges);
}
if (!successorEdges.TryGetValue(to, out var edgeList))
{
edgeList = new List<TEdge>();
successorEdges.Add(to, edgeList);
}
edgeList.Add(edge);
if (!_predecessorMap.TryGetValue(to, out var predecessors))
{
predecessors = new HashSet<TVertex>();
_predecessorMap.Add(to, predecessors);
}
predecessors.Add(from);
}
public void AddEdges([NotNull] TVertex from, [NotNull] TVertex to, [NotNull] IEnumerable<TEdge> edges)
{
#if DEBUG
if (!_vertices.Contains(from))
{
throw new InvalidOperationException(CoreStrings.GraphDoesNotContainVertex(from));
}
if (!_vertices.Contains(to))
{
throw new InvalidOperationException(CoreStrings.GraphDoesNotContainVertex(to));
}
#endif
if (!_successorMap.TryGetValue(from, out var successorEdges))
{
successorEdges = new Dictionary<TVertex, List<TEdge>>();
_successorMap.Add(from, successorEdges);
}
if (!successorEdges.TryGetValue(to, out var edgeList))
{
edgeList = new List<TEdge>();
successorEdges.Add(to, edgeList);
}
edgeList.AddRange(edges);
if (!_predecessorMap.TryGetValue(to, out var predecessors))
{
predecessors = new HashSet<TVertex>();
_predecessorMap.Add(to, predecessors);
}
predecessors.Add(from);
}
public override void Clear()
{
_vertices.Clear();
_successorMap.Clear();
_predecessorMap.Clear();
}
public IReadOnlyList<TVertex> TopologicalSort()
=> TopologicalSort(null, null);
public IReadOnlyList<TVertex> TopologicalSort(
[CanBeNull] Func<TVertex, TVertex, IEnumerable<TEdge>, bool> tryBreakEdge)
=> TopologicalSort(tryBreakEdge, null);
public IReadOnlyList<TVertex> TopologicalSort(
[CanBeNull] Func<IEnumerable<Tuple<TVertex, TVertex, IEnumerable<TEdge>>>, string> formatCycle)
=> TopologicalSort(null, formatCycle);
public IReadOnlyList<TVertex> TopologicalSort(
[CanBeNull] Func<TVertex, TVertex, IEnumerable<TEdge>, bool> tryBreakEdge,
[CanBeNull] Func<IReadOnlyList<Tuple<TVertex, TVertex, IEnumerable<TEdge>>>, string> formatCycle,
Func<string, string> formatException = null)
{
var sortedQueue = new List<TVertex>();
var predecessorCounts = new Dictionary<TVertex, int>();
foreach (var vertex in _vertices)
{
foreach (var outgoingNeighbor in GetOutgoingNeighbors(vertex))
{
if (predecessorCounts.ContainsKey(outgoingNeighbor))
{
predecessorCounts[outgoingNeighbor]++;
}
else
{
predecessorCounts[outgoingNeighbor] = 1;
}
}
}
foreach (var vertex in _vertices)
{
if (!predecessorCounts.ContainsKey(vertex))
{
sortedQueue.Add(vertex);
}
}
var index = 0;
while (sortedQueue.Count < _vertices.Count)
{
while (index < sortedQueue.Count)
{
var currentRoot = sortedQueue[index];
foreach (var successor in GetOutgoingNeighbors(currentRoot).Where(neighbor => predecessorCounts.ContainsKey(neighbor)))
{
// Decrement counts for edges from sorted vertices and append any vertices that no longer have predecessors
predecessorCounts[successor]--;
if (predecessorCounts[successor] == 0)
{
sortedQueue.Add(successor);
predecessorCounts.Remove(successor);
}
}
index++;
}
// Cycle breaking
if (sortedQueue.Count < _vertices.Count)
{
var broken = false;
var candidateVertices = predecessorCounts.Keys.ToList();
var candidateIndex = 0;
// Iterate over the unsorted vertices
while ((candidateIndex < candidateVertices.Count)
&& !broken
&& tryBreakEdge != null)
{
var candidateVertex = candidateVertices[candidateIndex];
// Find vertices in the unsorted portion of the graph that have edges to the candidate
var incomingNeighbors = GetIncomingNeighbors(candidateVertex)
.Where(neighbor => predecessorCounts.ContainsKey(neighbor)).ToList();
foreach (var incomingNeighbor in incomingNeighbors)
{
// Check to see if the edge can be broken
if (tryBreakEdge(incomingNeighbor, candidateVertex, _successorMap[incomingNeighbor][candidateVertex]))
{
predecessorCounts[candidateVertex]--;
if (predecessorCounts[candidateVertex] == 0)
{
sortedQueue.Add(candidateVertex);
predecessorCounts.Remove(candidateVertex);
broken = true;
break;
}
}
}
candidateIndex++;
}
if (!broken)
{
// Failed to break the cycle
var currentCycleVertex = _vertices.First(v => predecessorCounts.ContainsKey(v));
var cycle = new List<TVertex> { currentCycleVertex };
var finished = false;
while (!finished)
{
// Find a cycle
foreach (var predecessor in GetIncomingNeighbors(currentCycleVertex)
.Where(neighbor => predecessorCounts.ContainsKey(neighbor)))
{
if (predecessorCounts[predecessor] != 0)
{
predecessorCounts[currentCycleVertex] = -1;
currentCycleVertex = predecessor;
cycle.Add(currentCycleVertex);
finished = predecessorCounts[predecessor] == -1;
break;
}
}
}
cycle.Reverse();
ThrowCycle(cycle, formatCycle, formatException);
}
}
}
return sortedQueue;
}
private void ThrowCycle(
List<TVertex> cycle,
Func<IReadOnlyList<Tuple<TVertex, TVertex, IEnumerable<TEdge>>>, string> formatCycle,
Func<string, string> formatException = null)
{
string cycleString;
if (formatCycle == null)
{
cycleString = cycle.Select(ToString).Join(" ->" + Environment.NewLine);
}
else
{
var currentCycleVertex = cycle.First();
var cycleData = new List<Tuple<TVertex, TVertex, IEnumerable<TEdge>>>();
foreach (var vertex in cycle.Skip(1))
{
cycleData.Add(Tuple.Create(currentCycleVertex, vertex, GetEdges(currentCycleVertex, vertex)));
currentCycleVertex = vertex;
}
cycleString = formatCycle(cycleData);
}
var message = formatException == null ? CoreStrings.CircularDependency(cycleString) : formatException(cycleString);
throw new InvalidOperationException(message);
}
protected virtual string ToString(TVertex vertex)
=> vertex.ToString();
public IReadOnlyList<List<TVertex>> BatchingTopologicalSort()
=> BatchingTopologicalSort(null);
public IReadOnlyList<List<TVertex>> BatchingTopologicalSort(
[CanBeNull] Func<IReadOnlyList<Tuple<TVertex, TVertex, IEnumerable<TEdge>>>, string> formatCycle)
{
var currentRootsQueue = new List<TVertex>();
var predecessorCounts = new Dictionary<TVertex, int>();
foreach (var vertex in _vertices)
{
foreach (var outgoingNeighbor in GetOutgoingNeighbors(vertex))
{
if (predecessorCounts.ContainsKey(outgoingNeighbor))
{
predecessorCounts[outgoingNeighbor]++;
}
else
{
predecessorCounts[outgoingNeighbor] = 1;
}
}
}
foreach (var vertex in _vertices)
{
if (!predecessorCounts.ContainsKey(vertex))
{
currentRootsQueue.Add(vertex);
}
}
var result = new List<List<TVertex>>();
var nextRootsQueue = new List<TVertex>();
var currentRootIndex = 0;
while (currentRootIndex < currentRootsQueue.Count)
{
var currentRoot = currentRootsQueue[currentRootIndex];
currentRootIndex++;
// Remove edges from current root and add any exposed vertices to the next batch
foreach (var successor in GetOutgoingNeighbors(currentRoot))
{
predecessorCounts[successor]--;
if (predecessorCounts[successor] == 0)
{
nextRootsQueue.Add(successor);
}
}
// Roll lists over for next batch
if (currentRootIndex == currentRootsQueue.Count)
{
result.Add(currentRootsQueue);
currentRootsQueue = nextRootsQueue;
currentRootIndex = 0;
if (currentRootsQueue.Count != 0)
{
nextRootsQueue = new List<TVertex>();
}
}
}
if (result.Sum(b => b.Count) != _vertices.Count)
{
var currentCycleVertex = _vertices.First(
v => predecessorCounts.TryGetValue(v, out var predecessorNumber) ? predecessorNumber != 0 : false);
var cyclicWalk = new List<TVertex> { currentCycleVertex };
var finished = false;
while (!finished)
{
foreach (var predecessor in GetIncomingNeighbors(currentCycleVertex))
{
if (!predecessorCounts.TryGetValue(predecessor, out var predecessorCount))
{
continue;
}
if (predecessorCount != 0)
{
predecessorCounts[currentCycleVertex] = -1;
currentCycleVertex = predecessor;
cyclicWalk.Add(currentCycleVertex);
finished = predecessorCounts[predecessor] == -1;
break;
}
}
}
cyclicWalk.Reverse();
var cycle = new List<TVertex>();
var startingVertex = cyclicWalk.First();
cycle.Add(startingVertex);
foreach (var vertex in cyclicWalk.Skip(1))
{
if (!vertex.Equals(startingVertex))
{
cycle.Add(vertex);
}
else
{
break;
}
}
cycle.Add(startingVertex);
ThrowCycle(cycle, formatCycle);
}
return result;
}
public override IEnumerable<TVertex> Vertices
=> _vertices;
public override IEnumerable<TVertex> GetOutgoingNeighbors(TVertex from)
=> _successorMap.TryGetValue(from, out var successorSet)
? successorSet.Keys
: Enumerable.Empty<TVertex>();
public override IEnumerable<TVertex> GetIncomingNeighbors(TVertex to)
=> _predecessorMap.TryGetValue(to, out var predecessors)
? predecessors
: Enumerable.Empty<TVertex>();
}
}