absl/synchronization/internal/graphcycles_test.cc - third_party/github/abseil/abseil-cpp - Git at Google

 // Copyright 2017 The Abseil Authors.
 //
 // Licensed under the Apache License, Version 2.0 (the "License");
 // you may not use this file except in compliance with the License.
 // You may obtain a copy of the License at
 //
 //      https://www.apache.org/licenses/LICENSE-2.0
 //
 // Unless required by applicable law or agreed to in writing, software
 // distributed under the License is distributed on an "AS IS" BASIS,
 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 // See the License for the specific language governing permissions and
 // limitations under the License.

 #include "absl/synchronization/internal/graphcycles.h"

 #include <map>
 #include <random>
 #include <unordered_set>
 #include <utility>
 #include <vector>

 #include "gtest/gtest.h"
 #include "absl/base/macros.h"
 #include "absl/log/check.h"
 #include "absl/log/log.h"

 namespace absl {
 ABSL_NAMESPACE_BEGIN
 namespace synchronization_internal {

 // We emulate a GraphCycles object with a node vector and an edge vector.
 // We then compare the two implementations.

 using Nodes = std::vector<int>;
 struct Edge {
   int from;
   int to;
 };
 using Edges = std::vector<Edge>;
 using RandomEngine = std::mt19937_64;

 // Mapping from integer index to GraphId.
 typedef std::map<int, GraphId> IdMap;
 static GraphId Get(const IdMap& id, int num) {
   auto iter = id.find(num);
   return (iter == id.end()) ? InvalidGraphId() : iter->second;
 }

 // Return whether "to" is reachable from "from".
 static bool IsReachable(Edges *edges, int from, int to,
                         std::unordered_set<int> *seen) {
   seen->insert(from);     // we are investigating "from"; don't do it again
   if (from == to) return true;
   for (const auto &edge : *edges) {
     if (edge.from == from) {
       if (edge.to == to) {  // success via edge directly
         return true;
       } else if (seen->find(edge.to) == seen->end() &&  // success via edge
                  IsReachable(edges, edge.to, to, seen)) {
         return true;
       }
     }
   }
   return false;
 }

 static void PrintEdges(Edges *edges) {
   LOG(INFO) << "EDGES (" << edges->size() << ")";
   for (const auto &edge : *edges) {
     int a = edge.from;
     int b = edge.to;
     LOG(INFO) << a << " " << b;
   }
   LOG(INFO) << "---";
 }

 static void PrintGCEdges(Nodes *nodes, const IdMap &id, GraphCycles *gc) {
   LOG(INFO) << "GC EDGES";
   for (int a : *nodes) {
     for (int b : *nodes) {
       if (gc->HasEdge(Get(id, a), Get(id, b))) {
         LOG(INFO) << a << " " << b;
       }
     }
   }
   LOG(INFO) << "---";
 }

 static void PrintTransitiveClosure(Nodes *nodes, Edges *edges) {
   LOG(INFO) << "Transitive closure";
   for (int a : *nodes) {
     for (int b : *nodes) {
       std::unordered_set<int> seen;
       if (IsReachable(edges, a, b, &seen)) {
         LOG(INFO) << a << " " << b;
       }
     }
   }
   LOG(INFO) << "---";
 }

 static void PrintGCTransitiveClosure(Nodes *nodes, const IdMap &id,
                                      GraphCycles *gc) {
   LOG(INFO) << "GC Transitive closure";
   for (int a : *nodes) {
     for (int b : *nodes) {
       if (gc->IsReachable(Get(id, a), Get(id, b))) {
         LOG(INFO) << a << " " << b;
       }
     }
   }
   LOG(INFO) << "---";
 }

 static void CheckTransitiveClosure(Nodes *nodes, Edges *edges, const IdMap &id,
                                    GraphCycles *gc) {
   std::unordered_set<int> seen;
   for (const auto &a : *nodes) {
     for (const auto &b : *nodes) {
       seen.clear();
       bool gc_reachable = gc->IsReachable(Get(id, a), Get(id, b));
       bool reachable = IsReachable(edges, a, b, &seen);
       if (gc_reachable != reachable) {
         PrintEdges(edges);
         PrintGCEdges(nodes, id, gc);
         PrintTransitiveClosure(nodes, edges);
         PrintGCTransitiveClosure(nodes, id, gc);
         LOG(FATAL) << "gc_reachable " << gc_reachable << " reachable "
                    << reachable << " a " << a << " b " << b;
       }
     }
   }
 }

 static void CheckEdges(Nodes *nodes, Edges *edges, const IdMap &id,
                        GraphCycles *gc) {
   int count = 0;
   for (const auto &edge : *edges) {
     int a = edge.from;
     int b = edge.to;
     if (!gc->HasEdge(Get(id, a), Get(id, b))) {
       PrintEdges(edges);
       PrintGCEdges(nodes, id, gc);
       LOG(FATAL) << "!gc->HasEdge(" << a << ", " << b << ")";
     }
   }
   for (const auto &a : *nodes) {
     for (const auto &b : *nodes) {
       if (gc->HasEdge(Get(id, a), Get(id, b))) {
         count++;
       }
     }
   }
   if (count != edges->size()) {
     PrintEdges(edges);
     PrintGCEdges(nodes, id, gc);
     LOG(FATAL) << "edges->size() " << edges->size() << "  count " << count;
   }
 }

 static void CheckInvariants(const GraphCycles &gc) {
   CHECK(gc.CheckInvariants()) << "CheckInvariants";
 }

 // Returns the index of a randomly chosen node in *nodes.
 // Requires *nodes be non-empty.
 static int RandomNode(RandomEngine* rng, Nodes *nodes) {
   std::uniform_int_distribution<int> uniform(0, nodes->size()-1);
   return uniform(*rng);
 }

 // Returns the index of a randomly chosen edge in *edges.
 // Requires *edges be non-empty.
 static int RandomEdge(RandomEngine* rng, Edges *edges) {
   std::uniform_int_distribution<int> uniform(0, edges->size()-1);
   return uniform(*rng);
 }

 // Returns the index of edge (from, to) in *edges or -1 if it is not in *edges.
 static int EdgeIndex(Edges *edges, int from, int to) {
   int i = 0;
   while (i != edges->size() &&
          ((*edges)[i].from != from || (*edges)[i].to != to)) {
     i++;
   }
   return i == edges->size()? -1 : i;
 }

 TEST(GraphCycles, RandomizedTest) {
   int next_node = 0;
   Nodes nodes;
   Edges edges;   // from, to
   IdMap id;
   GraphCycles graph_cycles;
   static const int kMaxNodes = 7;  // use <= 7 nodes to keep test short
   static const int kDataOffset = 17;  // an offset to the node-specific data
   int n = 100000;
   int op = 0;
   RandomEngine rng(testing::UnitTest::GetInstance()->random_seed());
   std::uniform_int_distribution<int> uniform(0, 5);

   auto ptr = [](intptr_t i) {
     return reinterpret_cast<void*>(i + kDataOffset);
   };

   for (int iter = 0; iter != n; iter++) {
     for (const auto &node : nodes) {
       ASSERT_EQ(graph_cycles.Ptr(Get(id, node)), ptr(node)) << " node " << node;
     }
     CheckEdges(&nodes, &edges, id, &graph_cycles);
     CheckTransitiveClosure(&nodes, &edges, id, &graph_cycles);
     op = uniform(rng);
     switch (op) {
     case 0:     // Add a node
       if (nodes.size() < kMaxNodes) {
         int new_node = next_node++;
         GraphId new_gnode = graph_cycles.GetId(ptr(new_node));
         ASSERT_NE(new_gnode, InvalidGraphId());
         id[new_node] = new_gnode;
         ASSERT_EQ(ptr(new_node), graph_cycles.Ptr(new_gnode));
         nodes.push_back(new_node);
       }
       break;

     case 1:    // Remove a node
       if (nodes.size() > 0) {
         int node_index = RandomNode(&rng, &nodes);
         int node = nodes[node_index];
         nodes[node_index] = nodes.back();
         nodes.pop_back();
         graph_cycles.RemoveNode(ptr(node));
         ASSERT_EQ(graph_cycles.Ptr(Get(id, node)), nullptr);
         id.erase(node);
         int i = 0;
         while (i != edges.size()) {
           if (edges[i].from == node || edges[i].to == node) {
             edges[i] = edges.back();
             edges.pop_back();
           } else {
             i++;
           }
         }
       }
       break;

     case 2:   // Add an edge
       if (nodes.size() > 0) {
         int from = RandomNode(&rng, &nodes);
         int to = RandomNode(&rng, &nodes);
         if (EdgeIndex(&edges, nodes[from], nodes[to]) == -1) {
           if (graph_cycles.InsertEdge(id[nodes[from]], id[nodes[to]])) {
             Edge new_edge;
             new_edge.from = nodes[from];
             new_edge.to = nodes[to];
             edges.push_back(new_edge);
           } else {
             std::unordered_set<int> seen;
             ASSERT_TRUE(IsReachable(&edges, nodes[to], nodes[from], &seen))
                 << "Edge " << nodes[to] << "->" << nodes[from];
           }
         }
       }
       break;

     case 3:    // Remove an edge
       if (edges.size() > 0) {
         int i = RandomEdge(&rng, &edges);
         int from = edges[i].from;
         int to = edges[i].to;
         ASSERT_EQ(i, EdgeIndex(&edges, from, to));
         edges[i] = edges.back();
         edges.pop_back();
         ASSERT_EQ(-1, EdgeIndex(&edges, from, to));
         graph_cycles.RemoveEdge(id[from], id[to]);
       }
       break;

     case 4:   // Check a path
       if (nodes.size() > 0) {
         int from = RandomNode(&rng, &nodes);
         int to = RandomNode(&rng, &nodes);
         GraphId path[2*kMaxNodes];
         int path_len = graph_cycles.FindPath(id[nodes[from]], id[nodes[to]],
                                              ABSL_ARRAYSIZE(path), path);
         std::unordered_set<int> seen;
         bool reachable = IsReachable(&edges, nodes[from], nodes[to], &seen);
         bool gc_reachable =
             graph_cycles.IsReachable(Get(id, nodes[from]), Get(id, nodes[to]));
         ASSERT_EQ(path_len != 0, reachable);
         ASSERT_EQ(path_len != 0, gc_reachable);
         // In the following line, we add one because a node can appear
         // twice, if the path is from that node to itself, perhaps via
         // every other node.
         ASSERT_LE(path_len, kMaxNodes + 1);
         if (path_len != 0) {
           ASSERT_EQ(id[nodes[from]], path[0]);
           ASSERT_EQ(id[nodes[to]], path[path_len-1]);
           for (int i = 1; i < path_len; i++) {
             ASSERT_TRUE(graph_cycles.HasEdge(path[i-1], path[i]));
           }
         }
       }
       break;

     case 5:  // Check invariants
       CheckInvariants(graph_cycles);
       break;

     default:
       LOG(FATAL) << "op " << op;
     }

     // Very rarely, test graph expansion by adding then removing many nodes.
     std::bernoulli_distribution one_in_1024(1.0 / 1024);
     if (one_in_1024(rng)) {
       CheckEdges(&nodes, &edges, id, &graph_cycles);
       CheckTransitiveClosure(&nodes, &edges, id, &graph_cycles);
       for (int i = 0; i != 256; i++) {
         int new_node = next_node++;
         GraphId new_gnode = graph_cycles.GetId(ptr(new_node));
         ASSERT_NE(InvalidGraphId(), new_gnode);
         id[new_node] = new_gnode;
         ASSERT_EQ(ptr(new_node), graph_cycles.Ptr(new_gnode));
         for (const auto &node : nodes) {
           ASSERT_NE(node, new_node);
         }
         nodes.push_back(new_node);
       }
       for (int i = 0; i != 256; i++) {
         ASSERT_GT(nodes.size(), 0);
         int node_index = RandomNode(&rng, &nodes);
         int node = nodes[node_index];
         nodes[node_index] = nodes.back();
         nodes.pop_back();
         graph_cycles.RemoveNode(ptr(node));
         id.erase(node);
         int j = 0;
         while (j != edges.size()) {
           if (edges[j].from == node || edges[j].to == node) {
             edges[j] = edges.back();
             edges.pop_back();
           } else {
             j++;
           }
         }
       }
       CheckInvariants(graph_cycles);
     }
   }
 }

 class GraphCyclesTest : public ::testing::Test {
  public:
   IdMap id_;
   GraphCycles g_;

   static void* Ptr(int i) {
     return reinterpret_cast<void*>(static_cast<uintptr_t>(i));
   }

   static int Num(void* ptr) {
     return static_cast<int>(reinterpret_cast<uintptr_t>(ptr));
   }

   // Test relies on ith NewNode() call returning Node numbered i
   GraphCyclesTest() {
     for (int i = 0; i < 100; i++) {
       id_[i] = g_.GetId(Ptr(i));
     }
     CheckInvariants(g_);
   }

   bool AddEdge(int x, int y) {
     return g_.InsertEdge(Get(id_, x), Get(id_, y));
   }

   void AddMultiples() {
     // For every node x > 0: add edge to 2*x, 3*x
     for (int x = 1; x < 25; x++) {
       EXPECT_TRUE(AddEdge(x, 2*x)) << x;
       EXPECT_TRUE(AddEdge(x, 3*x)) << x;
     }
     CheckInvariants(g_);
   }

   std::string Path(int x, int y) {
     GraphId path[5];
     int np = g_.FindPath(Get(id_, x), Get(id_, y), ABSL_ARRAYSIZE(path), path);
     std::string result;
     for (int i = 0; i < np; i++) {
       if (i >= ABSL_ARRAYSIZE(path)) {
         result += " ...";
         break;
       }
       if (!result.empty()) result.push_back(' ');
       char buf[20];
       snprintf(buf, sizeof(buf), "%d", Num(g_.Ptr(path[i])));
       result += buf;
     }
     return result;
   }
 };

 TEST_F(GraphCyclesTest, NoCycle) {
   AddMultiples();
   CheckInvariants(g_);
 }

 TEST_F(GraphCyclesTest, SimpleCycle) {
   AddMultiples();
   EXPECT_FALSE(AddEdge(8, 4));
   EXPECT_EQ("4 8", Path(4, 8));
   CheckInvariants(g_);
 }

 TEST_F(GraphCyclesTest, IndirectCycle) {
   AddMultiples();
   EXPECT_TRUE(AddEdge(16, 9));
   CheckInvariants(g_);
   EXPECT_FALSE(AddEdge(9, 2));
   EXPECT_EQ("2 4 8 16 9", Path(2, 9));
   CheckInvariants(g_);
 }

 TEST_F(GraphCyclesTest, LongPath) {
   ASSERT_TRUE(AddEdge(2, 4));
   ASSERT_TRUE(AddEdge(4, 6));
   ASSERT_TRUE(AddEdge(6, 8));
   ASSERT_TRUE(AddEdge(8, 10));
   ASSERT_TRUE(AddEdge(10, 12));
   ASSERT_FALSE(AddEdge(12, 2));
   EXPECT_EQ("2 4 6 8 10 ...", Path(2, 12));
   CheckInvariants(g_);
 }

 TEST_F(GraphCyclesTest, RemoveNode) {
   ASSERT_TRUE(AddEdge(1, 2));
   ASSERT_TRUE(AddEdge(2, 3));
   ASSERT_TRUE(AddEdge(3, 4));
   ASSERT_TRUE(AddEdge(4, 5));
   g_.RemoveNode(g_.Ptr(id_[3]));
   id_.erase(3);
   ASSERT_TRUE(AddEdge(5, 1));
 }

 TEST_F(GraphCyclesTest, ManyEdges) {
   const int N = 50;
   for (int i = 0; i < N; i++) {
     for (int j = 1; j < N; j++) {
       ASSERT_TRUE(AddEdge(i, i+j));
     }
   }
   CheckInvariants(g_);
   ASSERT_TRUE(AddEdge(2*N-1, 0));
   CheckInvariants(g_);
   ASSERT_FALSE(AddEdge(10, 9));
   CheckInvariants(g_);
 }

 }  // namespace synchronization_internal
 ABSL_NAMESPACE_END
 }  // namespace absl
	// Copyright 2017 The Abseil Authors.
	//
	// Licensed under the Apache License, Version 2.0 (the "License");
	// you may not use this file except in compliance with the License.
	// You may obtain a copy of the License at
	//
	// https://www.apache.org/licenses/LICENSE-2.0
	//
	// Unless required by applicable law or agreed to in writing, software
	// distributed under the License is distributed on an "AS IS" BASIS,
	// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	// See the License for the specific language governing permissions and
	// limitations under the License.

	#include "absl/synchronization/internal/graphcycles.h"

	#include <map>
	#include <random>
	#include <unordered_set>
	#include <utility>
	#include <vector>

	#include "gtest/gtest.h"
	#include "absl/base/macros.h"
	#include "absl/log/check.h"
	#include "absl/log/log.h"

	namespace absl {
	ABSL_NAMESPACE_BEGIN
	namespace synchronization_internal {

	// We emulate a GraphCycles object with a node vector and an edge vector.
	// We then compare the two implementations.

	using Nodes = std::vector<int>;
	struct Edge {
	int from;
	int to;
	};
	using Edges = std::vector<Edge>;
	using RandomEngine = std::mt19937_64;

	// Mapping from integer index to GraphId.
	typedef std::map<int, GraphId> IdMap;
	static GraphId Get(const IdMap& id, int num) {
	auto iter = id.find(num);
	return (iter == id.end()) ? InvalidGraphId() : iter->second;
	}

	// Return whether "to" is reachable from "from".
	static bool IsReachable(Edges *edges, int from, int to,
	std::unordered_set<int> *seen) {
	seen->insert(from); // we are investigating "from"; don't do it again
	if (from == to) return true;
	for (const auto &edge : *edges) {
	if (edge.from == from) {
	if (edge.to == to) { // success via edge directly
	return true;
	} else if (seen->find(edge.to) == seen->end() && // success via edge
	IsReachable(edges, edge.to, to, seen)) {
	return true;
	}
	}
	}
	return false;
	}

	static void PrintEdges(Edges *edges) {
	LOG(INFO) << "EDGES (" << edges->size() << ")";
	for (const auto &edge : *edges) {
	int a = edge.from;
	int b = edge.to;
	LOG(INFO) << a << " " << b;
	}
	LOG(INFO) << "---";
	}

	static void PrintGCEdges(Nodes nodes, const IdMap &id, GraphCycles gc) {
	LOG(INFO) << "GC EDGES";
	for (int a : *nodes) {
	for (int b : *nodes) {
	if (gc->HasEdge(Get(id, a), Get(id, b))) {
	LOG(INFO) << a << " " << b;
	}
	}
	}
	LOG(INFO) << "---";
	}

	static void PrintTransitiveClosure(Nodes nodes, Edges edges) {
	LOG(INFO) << "Transitive closure";
	for (int a : *nodes) {
	for (int b : *nodes) {
	std::unordered_set<int> seen;
	if (IsReachable(edges, a, b, &seen)) {
	LOG(INFO) << a << " " << b;
	}
	}
	}
	LOG(INFO) << "---";
	}

	static void PrintGCTransitiveClosure(Nodes *nodes, const IdMap &id,
	GraphCycles *gc) {
	LOG(INFO) << "GC Transitive closure";
	for (int a : *nodes) {
	for (int b : *nodes) {
	if (gc->IsReachable(Get(id, a), Get(id, b))) {
	LOG(INFO) << a << " " << b;
	}
	}
	}
	LOG(INFO) << "---";
	}

	static void CheckTransitiveClosure(Nodes nodes, Edges edges, const IdMap &id,
	GraphCycles *gc) {
	std::unordered_set<int> seen;
	for (const auto &a : *nodes) {
	for (const auto &b : *nodes) {
	seen.clear();
	bool gc_reachable = gc->IsReachable(Get(id, a), Get(id, b));
	bool reachable = IsReachable(edges, a, b, &seen);
	if (gc_reachable != reachable) {
	PrintEdges(edges);
	PrintGCEdges(nodes, id, gc);
	PrintTransitiveClosure(nodes, edges);
	PrintGCTransitiveClosure(nodes, id, gc);
	LOG(FATAL) << "gc_reachable " << gc_reachable << " reachable "
	<< reachable << " a " << a << " b " << b;
	}
	}
	}
	}

	static void CheckEdges(Nodes nodes, Edges edges, const IdMap &id,
	GraphCycles *gc) {
	int count = 0;
	for (const auto &edge : *edges) {
	int a = edge.from;
	int b = edge.to;
	if (!gc->HasEdge(Get(id, a), Get(id, b))) {
	PrintEdges(edges);
	PrintGCEdges(nodes, id, gc);
	LOG(FATAL) << "!gc->HasEdge(" << a << ", " << b << ")";
	}
	}
	for (const auto &a : *nodes) {
	for (const auto &b : *nodes) {
	if (gc->HasEdge(Get(id, a), Get(id, b))) {
	count++;
	}
	}
	}
	if (count != edges->size()) {
	PrintEdges(edges);
	PrintGCEdges(nodes, id, gc);
	LOG(FATAL) << "edges->size() " << edges->size() << " count " << count;
	}
	}

	static void CheckInvariants(const GraphCycles &gc) {
	CHECK(gc.CheckInvariants()) << "CheckInvariants";
	}

	// Returns the index of a randomly chosen node in *nodes.
	// Requires *nodes be non-empty.
	static int RandomNode(RandomEngine* rng, Nodes *nodes) {
	std::uniform_int_distribution<int> uniform(0, nodes->size()-1);
	return uniform(*rng);
	}

	// Returns the index of a randomly chosen edge in *edges.
	// Requires *edges be non-empty.
	static int RandomEdge(RandomEngine* rng, Edges *edges) {
	std::uniform_int_distribution<int> uniform(0, edges->size()-1);
	return uniform(*rng);
	}

	// Returns the index of edge (from, to) in edges or -1 if it is not in edges.
	static int EdgeIndex(Edges *edges, int from, int to) {
	int i = 0;
	while (i != edges->size() &&
	((edges)[i].from != from \|\| (edges)[i].to != to)) {
	i++;
	}
	return i == edges->size()? -1 : i;
	}

	TEST(GraphCycles, RandomizedTest) {
	int next_node = 0;
	Nodes nodes;
	Edges edges; // from, to
	IdMap id;
	GraphCycles graph_cycles;
	static const int kMaxNodes = 7; // use <= 7 nodes to keep test short
	static const int kDataOffset = 17; // an offset to the node-specific data
	int n = 100000;
	int op = 0;
	RandomEngine rng(testing::UnitTest::GetInstance()->random_seed());
	std::uniform_int_distribution<int> uniform(0, 5);

	auto ptr = [](intptr_t i) {
	return reinterpret_cast<void*>(i + kDataOffset);
	};

	for (int iter = 0; iter != n; iter++) {
	for (const auto &node : nodes) {
	ASSERT_EQ(graph_cycles.Ptr(Get(id, node)), ptr(node)) << " node " << node;
	}
	CheckEdges(&nodes, &edges, id, &graph_cycles);
	CheckTransitiveClosure(&nodes, &edges, id, &graph_cycles);
	op = uniform(rng);
	switch (op) {
	case 0: // Add a node
	if (nodes.size() < kMaxNodes) {
	int new_node = next_node++;
	GraphId new_gnode = graph_cycles.GetId(ptr(new_node));
	ASSERT_NE(new_gnode, InvalidGraphId());
	id[new_node] = new_gnode;
	ASSERT_EQ(ptr(new_node), graph_cycles.Ptr(new_gnode));
	nodes.push_back(new_node);
	}
	break;

	case 1: // Remove a node
	if (nodes.size() > 0) {
	int node_index = RandomNode(&rng, &nodes);
	int node = nodes[node_index];
	nodes[node_index] = nodes.back();
	nodes.pop_back();
	graph_cycles.RemoveNode(ptr(node));
	ASSERT_EQ(graph_cycles.Ptr(Get(id, node)), nullptr);
	id.erase(node);
	int i = 0;
	while (i != edges.size()) {
	if (edges[i].from == node \|\| edges[i].to == node) {
	edges[i] = edges.back();
	edges.pop_back();
	} else {
	i++;
	}
	}
	}
	break;

	case 2: // Add an edge
	if (nodes.size() > 0) {
	int from = RandomNode(&rng, &nodes);
	int to = RandomNode(&rng, &nodes);
	if (EdgeIndex(&edges, nodes[from], nodes[to]) == -1) {
	if (graph_cycles.InsertEdge(id[nodes[from]], id[nodes[to]])) {
	Edge new_edge;
	new_edge.from = nodes[from];
	new_edge.to = nodes[to];
	edges.push_back(new_edge);
	} else {
	std::unordered_set<int> seen;
	ASSERT_TRUE(IsReachable(&edges, nodes[to], nodes[from], &seen))
	<< "Edge " << nodes[to] << "->" << nodes[from];
	}
	}
	}
	break;

	case 3: // Remove an edge
	if (edges.size() > 0) {
	int i = RandomEdge(&rng, &edges);
	int from = edges[i].from;
	int to = edges[i].to;
	ASSERT_EQ(i, EdgeIndex(&edges, from, to));
	edges[i] = edges.back();
	edges.pop_back();
	ASSERT_EQ(-1, EdgeIndex(&edges, from, to));
	graph_cycles.RemoveEdge(id[from], id[to]);
	}
	break;

	case 4: // Check a path
	if (nodes.size() > 0) {
	int from = RandomNode(&rng, &nodes);
	int to = RandomNode(&rng, &nodes);
	GraphId path[2*kMaxNodes];
	int path_len = graph_cycles.FindPath(id[nodes[from]], id[nodes[to]],
	ABSL_ARRAYSIZE(path), path);
	std::unordered_set<int> seen;
	bool reachable = IsReachable(&edges, nodes[from], nodes[to], &seen);
	bool gc_reachable =
	graph_cycles.IsReachable(Get(id, nodes[from]), Get(id, nodes[to]));
	ASSERT_EQ(path_len != 0, reachable);
	ASSERT_EQ(path_len != 0, gc_reachable);
	// In the following line, we add one because a node can appear
	// twice, if the path is from that node to itself, perhaps via
	// every other node.
	ASSERT_LE(path_len, kMaxNodes + 1);
	if (path_len != 0) {
	ASSERT_EQ(id[nodes[from]], path[0]);
	ASSERT_EQ(id[nodes[to]], path[path_len-1]);
	for (int i = 1; i < path_len; i++) {
	ASSERT_TRUE(graph_cycles.HasEdge(path[i-1], path[i]));
	}
	}
	}
	break;

	case 5: // Check invariants
	CheckInvariants(graph_cycles);
	break;

	default:
	LOG(FATAL) << "op " << op;
	}

	// Very rarely, test graph expansion by adding then removing many nodes.
	std::bernoulli_distribution one_in_1024(1.0 / 1024);
	if (one_in_1024(rng)) {
	CheckEdges(&nodes, &edges, id, &graph_cycles);
	CheckTransitiveClosure(&nodes, &edges, id, &graph_cycles);
	for (int i = 0; i != 256; i++) {
	int new_node = next_node++;
	GraphId new_gnode = graph_cycles.GetId(ptr(new_node));
	ASSERT_NE(InvalidGraphId(), new_gnode);
	id[new_node] = new_gnode;
	ASSERT_EQ(ptr(new_node), graph_cycles.Ptr(new_gnode));
	for (const auto &node : nodes) {
	ASSERT_NE(node, new_node);
	}
	nodes.push_back(new_node);
	}
	for (int i = 0; i != 256; i++) {
	ASSERT_GT(nodes.size(), 0);
	int node_index = RandomNode(&rng, &nodes);
	int node = nodes[node_index];
	nodes[node_index] = nodes.back();
	nodes.pop_back();
	graph_cycles.RemoveNode(ptr(node));
	id.erase(node);
	int j = 0;
	while (j != edges.size()) {
	if (edges[j].from == node \|\| edges[j].to == node) {
	edges[j] = edges.back();
	edges.pop_back();
	} else {
	j++;
	}
	}
	}
	CheckInvariants(graph_cycles);
	}
	}
	}

	class GraphCyclesTest : public ::testing::Test {
	public:
	IdMap id_;
	GraphCycles g_;

	static void* Ptr(int i) {
	return reinterpret_cast<void*>(static_cast<uintptr_t>(i));
	}

	static int Num(void* ptr) {
	return static_cast<int>(reinterpret_cast<uintptr_t>(ptr));
	}

	// Test relies on ith NewNode() call returning Node numbered i
	GraphCyclesTest() {
	for (int i = 0; i < 100; i++) {
	id_[i] = g_.GetId(Ptr(i));
	}
	CheckInvariants(g_);
	}

	bool AddEdge(int x, int y) {
	return g_.InsertEdge(Get(id_, x), Get(id_, y));
	}

	void AddMultiples() {
	// For every node x > 0: add edge to 2x, 3x
	for (int x = 1; x < 25; x++) {
	EXPECT_TRUE(AddEdge(x, 2*x)) << x;
	EXPECT_TRUE(AddEdge(x, 3*x)) << x;
	}
	CheckInvariants(g_);
	}

	std::string Path(int x, int y) {
	GraphId path[5];
	int np = g_.FindPath(Get(id_, x), Get(id_, y), ABSL_ARRAYSIZE(path), path);
	std::string result;
	for (int i = 0; i < np; i++) {
	if (i >= ABSL_ARRAYSIZE(path)) {
	result += " ...";
	break;
	}
	if (!result.empty()) result.push_back(' ');
	char buf[20];
	snprintf(buf, sizeof(buf), "%d", Num(g_.Ptr(path[i])));
	result += buf;
	}
	return result;
	}
	};

	TEST_F(GraphCyclesTest, NoCycle) {
	AddMultiples();
	CheckInvariants(g_);
	}

	TEST_F(GraphCyclesTest, SimpleCycle) {
	AddMultiples();
	EXPECT_FALSE(AddEdge(8, 4));
	EXPECT_EQ("4 8", Path(4, 8));
	CheckInvariants(g_);
	}

	TEST_F(GraphCyclesTest, IndirectCycle) {
	AddMultiples();
	EXPECT_TRUE(AddEdge(16, 9));
	CheckInvariants(g_);
	EXPECT_FALSE(AddEdge(9, 2));
	EXPECT_EQ("2 4 8 16 9", Path(2, 9));
	CheckInvariants(g_);
	}

	TEST_F(GraphCyclesTest, LongPath) {
	ASSERT_TRUE(AddEdge(2, 4));
	ASSERT_TRUE(AddEdge(4, 6));
	ASSERT_TRUE(AddEdge(6, 8));
	ASSERT_TRUE(AddEdge(8, 10));
	ASSERT_TRUE(AddEdge(10, 12));
	ASSERT_FALSE(AddEdge(12, 2));
	EXPECT_EQ("2 4 6 8 10 ...", Path(2, 12));
	CheckInvariants(g_);
	}

	TEST_F(GraphCyclesTest, RemoveNode) {
	ASSERT_TRUE(AddEdge(1, 2));
	ASSERT_TRUE(AddEdge(2, 3));
	ASSERT_TRUE(AddEdge(3, 4));
	ASSERT_TRUE(AddEdge(4, 5));
	g_.RemoveNode(g_.Ptr(id_[3]));
	id_.erase(3);
	ASSERT_TRUE(AddEdge(5, 1));
	}

	TEST_F(GraphCyclesTest, ManyEdges) {
	const int N = 50;
	for (int i = 0; i < N; i++) {
	for (int j = 1; j < N; j++) {
	ASSERT_TRUE(AddEdge(i, i+j));
	}
	}
	CheckInvariants(g_);
	ASSERT_TRUE(AddEdge(2*N-1, 0));
	CheckInvariants(g_);
	ASSERT_FALSE(AddEdge(10, 9));
	CheckInvariants(g_);
	}

	} // namespace synchronization_internal
	ABSL_NAMESPACE_END
	} // namespace absl