introduce topological sort for graph (#247)

* implement topological sort based on dfs * add benchmark for topological sort * add basic test for topological sort Co-authored-by: suncanghuai <[email protected]>
ZigRazor · Nov 3, 2022 · be05a46 · be05a46
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diff --git a/benchmark/TopologicalSort_BM.cpp b/benchmark/TopologicalSort_BM.cpp
@@ -0,0 +1,33 @@
+#include <benchmark/benchmark.h>
+#include "CXXGraph.hpp"
+#include "Utilities.hpp"
+
+
+static void TopologicalSort_X(benchmark::State &state)
+{
+    CXXGRAPH::Graph<int> g;
+    auto range_start = edges.begin();
+    auto range_end = edges.find(state.range(0));
+    std::unordered_map<unsigned long, CXXGRAPH::Edge<int> *> edgesX;
+    edgesX.insert(range_start, range_end);
+    for (auto e : edgesX)
+    {
+        g.addEdge(&(*e.second));
+    }
+    for (auto _ : state)
+    {
+        const auto &result = g.topologicalSort();
+    }
+}
+BENCHMARK(TopologicalSort_X)->RangeMultiplier(16)->Range((unsigned long)1, (unsigned long)1 << 16);
+
+static void TopologicalSort_FromReadedCitHep(benchmark::State &state)
+{
+    auto edgeSet = cit_graph_ptr->getEdgeSet();
+    for (auto _ : state)
+    {
+        const auto &result = cit_graph_ptr->topologicalSort();
+    }
+}
+
+BENCHMARK(TopologicalSort_FromReadedCitHep);
diff --git a/include/Graph/Graph.hpp b/include/Graph/Graph.hpp
@@ -350,6 +350,14 @@ namespace CXXGRAPH
 		 */
 		virtual bool isStronglyConnectedGraph() const;
 
+        /**
+		 * @brief This function sort nodes in topological order.
+		 * 	Applicable for Directed Acyclic Graph
+		 *
+		 * @return a vector containing nodes in topological order
+		 */
+		virtual TopoSortResult<T> topologicalSort() const;
+
 		/**
 		* \brief
 		* This function performs performs the kosaraju algorthm on the graph to find the strongly connected components.
@@ -1971,6 +1979,64 @@ namespace CXXGRAPH
 		}
 	}
 
+    template <typename T>
+	TopoSortResult<T> Graph<T>::topologicalSort() const
+    {
+        TopoSortResult<T> result;
+        result.success = false;
+
+        if (!isDirectedGraph())
+		{
+            result.errorMessage = ERR_UNDIR_GRAPH;
+			return result;
+		}
+        else if (isCyclicDirectedGraphBFS())
+        {
+            result.errorMessage = ERR_CYCLIC_GRAPH;
+            return result;
+        }
+        else 
+        {
+            const auto &adjMatrix = getAdjMatrix();
+            const auto &nodeSet = getNodeSet();
+            std::unordered_map<const Node<T> *, bool> visited;
+
+            std::function<void(const Node<T> *)> postorder_helper = [&postorder_helper, &adjMatrix, &visited, &result] (const Node<T> *curNode)
+            {
+                visited[curNode] = true;
+
+                if (adjMatrix.find(curNode) != adjMatrix.end())
+                {
+                    for (const auto &edge : adjMatrix.at(curNode))
+                    {
+                        const auto &nextNode = edge.first;
+                        if (false == visited[nextNode]) 
+                        {
+                            postorder_helper(nextNode);
+                        }
+                    }
+                }
+
+                result.nodesInTopoOrder.push_back(*curNode);
+            }; 
+
+            int numNodes = adjMatrix.size();
+            result.nodesInTopoOrder.reserve(numNodes);
+
+            for (const auto &node : nodeSet)
+            {
+                if (false == visited[node])
+                {
+                    postorder_helper(node);
+                }
+            }
+
+            result.success = true;
+            std::reverse(result.nodesInTopoOrder.begin(), result.nodesInTopoOrder.end());
+            return result;
+        }
+    }
+
 	template <typename T>
 	std::vector<std::vector<Node<T>>> Graph<T>::kosaraju() const
 	{

diff --git a/include/Utility/ConstString.hpp b/include/Utility/ConstString.hpp
@@ -27,6 +27,8 @@ namespace CXXGRAPH
     //STRING ERROR CONST EXPRESSION
 	constexpr char ERR_NO_DIR_OR_UNDIR_EDGE[] = "Edge are neither Directed neither Undirected";
 	constexpr char ERR_DIR_GRAPH[] = "Graph is directed";
+    constexpr char ERR_UNDIR_GRAPH[] = "Graph is undirected";
+    constexpr char ERR_CYCLIC_GRAPH[] = "Graph is cyclic";
 	constexpr char ERR_NO_WEIGHTED_EDGE[] = "Edge are not Weighted";
 	constexpr char ERR_NEGATIVE_WEIGHTED_EDGE[] = "Edge negative Weighted";
 	constexpr char ERR_TARGET_NODE_NOT_REACHABLE[] = "Target Node not Reachable";

diff --git a/include/Utility/Typedef.hpp b/include/Utility/Typedef.hpp
@@ -134,6 +134,25 @@ namespace CXXGRAPH
 	};
 	typedef DialResult_struct DialResult;
 
+    /// Struct that contains the information about TopologicalSort's Algorithm results
+    template <typename T>
+	struct TopoSortResult_struct
+	{
+		bool success = false;								// TRUE if the function does not return error, FALSE otherwise
+		std::string errorMessage = "";					    //message of error
+		std::vector<Node<T>> nodesInTopoOrder = {};         //result a vector that contains the nodes in topological order (valid only if success is TRUE)
+
+        /*
+        TopoSortResult & operator=(TopoSortResult_struct && res) 
+            : success(res.success),
+              errorMessage(move(res.errorMessage))
+              nodesInTopoOrder(move(res.nodesInTopoOrder))
+        {}
+        */
+    };
+    template <typename T>
+    using TopoSortResult = TopoSortResult_struct<T>;
+
 	/// Struct that contains the information about the partitioning statistics
 
 

diff --git a/test/TopologicalSortTest.cpp b/test/TopologicalSortTest.cpp
@@ -0,0 +1,105 @@
+#include "gtest/gtest.h"
+#include "CXXGraph.hpp"
+#include "Utility/Typedef.hpp"
+#include "Utility/ConstString.hpp"
+
+// topological sort test in a cyclic graph
+TEST(TopologicalSortTest, test_1)
+{
+    CXXGRAPH::Node<int> node1("1", 1);
+    CXXGRAPH::Node<int> node2("2", 2);
+    CXXGRAPH::Node<int> node3("3", 3);
+    std::pair<const CXXGRAPH::Node<int> *, const CXXGRAPH::Node<int> *> pairNode(&node1, &node2);
+    CXXGRAPH::DirectedWeightedEdge<int> edge1(1, pairNode, 1);
+    CXXGRAPH::DirectedWeightedEdge<int> edge2(2, node2, node3, 2);
+    CXXGRAPH::DirectedWeightedEdge<int> edge3(3, node3, node1, 3);
+    CXXGRAPH::T_EdgeSet<int> edgeSet;
+    edgeSet.insert(&edge1);
+    edgeSet.insert(&edge2);
+    edgeSet.insert(&edge3);
+    CXXGRAPH::Graph<int> graph(edgeSet);
+
+    CXXGRAPH::TopoSortResult<int> && res = graph.topologicalSort();
+    ASSERT_EQ(res.success, false);
+    ASSERT_EQ(res.errorMessage, CXXGRAPH::ERR_CYCLIC_GRAPH);
+}
+
+// topogical sort test in a undirected graph
+TEST(TopologicalSortTest, test_2)
+{
+    CXXGRAPH::Node<int> node1("1", 1);
+    CXXGRAPH::Node<int> node2("2", 2);
+    CXXGRAPH::Node<int> node3("3", 3);
+    CXXGRAPH::Node<int> node4("4", 4);
+    CXXGRAPH::Node<int> node5("5", 5);
+    std::pair<const CXXGRAPH::Node<int> *, const CXXGRAPH::Node<int> *> pairNode(&node1, &node2);
+    CXXGRAPH::UndirectedWeightedEdge<int> edge1(1, pairNode, 1);
+    CXXGRAPH::UndirectedWeightedEdge<int> edge2(2, node2, node3, 1);
+    CXXGRAPH::UndirectedWeightedEdge<int> edge3(3, node3, node4, 1);
+    CXXGRAPH::UndirectedWeightedEdge<int> edge4(3, node3, node5, 1);
+    CXXGRAPH::T_EdgeSet<int> edgeSet;
+    edgeSet.insert(&edge1);
+    edgeSet.insert(&edge2);
+    edgeSet.insert(&edge3);
+    edgeSet.insert(&edge4);
+    CXXGRAPH::Graph<int> graph(edgeSet);
+
+    CXXGRAPH::TopoSortResult<int> && res = graph.topologicalSort();
+    ASSERT_EQ(res.success, false);
+    ASSERT_EQ(res.errorMessage, CXXGRAPH::ERR_UNDIR_GRAPH);
+}
+
+// topogical sort test in a tiny graph
+TEST(TopologicalSortTest, test_3)
+{
+    CXXGRAPH::Node<int> node1("1", 1);
+    CXXGRAPH::Node<int> node2("2", 2);
+    CXXGRAPH::Node<int> node3("3", 3);
+    CXXGRAPH::Node<int> node4("4", 4);
+    CXXGRAPH::Node<int> node5("5", 5);
+    CXXGRAPH::Node<int> node6("6", 6);
+    CXXGRAPH::Node<int> node7("7", 7);
+    CXXGRAPH::Node<int> node8("8", 8);
+    std::pair<const CXXGRAPH::Node<int> *, const CXXGRAPH::Node<int> *> pairNode(&node1, &node2);
+    CXXGRAPH::DirectedWeightedEdge<int> edge1(1, pairNode, 1);
+    CXXGRAPH::DirectedWeightedEdge<int> edge2(2, node2, node3, 1);
+    CXXGRAPH::DirectedWeightedEdge<int> edge3(3, node2, node6, 6);
+    CXXGRAPH::DirectedWeightedEdge<int> edge4(3, node3, node4, 6);
+    CXXGRAPH::DirectedWeightedEdge<int> edge5(3, node3, node5, 6);
+    CXXGRAPH::DirectedWeightedEdge<int> edge6(3, node6, node7, 6);
+    CXXGRAPH::DirectedWeightedEdge<int> edge7(3, node8, node6, 6);
+    CXXGRAPH::DirectedWeightedEdge<int> edge8(3, node8, node7, 6);
+    CXXGRAPH::T_EdgeSet<int> edgeSet;
+    edgeSet.insert(&edge1);
+    edgeSet.insert(&edge2);
+    edgeSet.insert(&edge3);
+    edgeSet.insert(&edge4);
+    edgeSet.insert(&edge5);
+    edgeSet.insert(&edge6);
+    edgeSet.insert(&edge7);
+    edgeSet.insert(&edge8);
+    CXXGRAPH::Graph<int> graph(edgeSet);
+
+    CXXGRAPH::TopoSortResult<int> && res = graph.topologicalSort();
+    ASSERT_EQ(res.success, true);
+    ASSERT_TRUE(res.errorMessage.empty());
+    ASSERT_EQ(res.nodesInTopoOrder.size(), 8);
+
+    // check topological order of nodes  
+    std::unordered_map<unsigned long, int> nodeToOrder;
+    for (int i = 0; i < res.nodesInTopoOrder.size(); ++i)
+    {
+        nodeToOrder[res.nodesInTopoOrder[i].getId()] = i;
+    }
+
+    for (const auto & edge : edgeSet) 
+    {
+        auto node_id1 = edge->getNodePair().first->getId();     
+        auto node_id2 = edge->getNodePair().second->getId();
+
+        ASSERT_TRUE(nodeToOrder.count(node_id1) && nodeToOrder.count(node_id2));
+        ASSERT_LT(nodeToOrder[node_id1], nodeToOrder[node_id2]);
+    }
+}
+
+// more test cases to be needed