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803 lines
26 KiB
C++
803 lines
26 KiB
C++
#include <Interpreters/ComparisonGraph.h>
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#include <Parsers/IAST.h>
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#include <Parsers/ASTLiteral.h>
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#include <Parsers/ASTFunction.h>
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#include <Parsers/queryToString.h>
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#include <Common/FieldVisitorsAccurateComparison.h>
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#include <Analyzer/FunctionNode.h>
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#include <Analyzer/ConstantNode.h>
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#include <Functions/FunctionFactory.h>
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namespace DB
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{
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namespace ErrorCodes
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{
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extern const int VIOLATED_CONSTRAINT;
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}
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namespace
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{
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/// Make function a > b or a >= b
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ASTPtr normalizeAtom(const ASTPtr & atom, ContextPtr)
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{
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static const std::map<std::string, std::string> inverse_relations =
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{
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{"lessOrEquals", "greaterOrEquals"},
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{"less", "greater"},
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};
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ASTPtr res = atom->clone();
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if (const auto * func = res->as<ASTFunction>())
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{
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if (const auto it = inverse_relations.find(func->name); it != std::end(inverse_relations))
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res = makeASTFunction(it->second, func->arguments->children[1]->clone(), func->arguments->children[0]->clone());
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}
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return res;
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}
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QueryTreeNodePtr normalizeAtom(const QueryTreeNodePtr & atom, const ContextPtr & context)
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{
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static const std::map<std::string, std::string> inverse_relations =
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{
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{"lessOrEquals", "greaterOrEquals"},
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{"less", "greater"},
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};
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if (const auto * function_node = atom->as<FunctionNode>())
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{
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if (const auto it = inverse_relations.find(function_node->getFunctionName()); it != inverse_relations.end())
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{
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auto inverted_node = function_node->clone();
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auto * inverted_function_node = inverted_node->as<FunctionNode>();
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auto function_resolver = FunctionFactory::instance().get(it->second, context);
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auto & arguments = inverted_function_node->getArguments().getNodes();
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assert(arguments.size() == 2);
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std::swap(arguments[0], arguments[1]);
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inverted_function_node->resolveAsFunction(function_resolver);
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return inverted_node;
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}
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}
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return atom;
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}
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const FunctionNode * tryGetFunctionNode(const QueryTreeNodePtr & node)
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{
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return node->as<FunctionNode>();
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}
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const ASTFunction * tryGetFunctionNode(const ASTPtr & node)
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{
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return node->as<ASTFunction>();
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}
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std::string functionName(const QueryTreeNodePtr & node)
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{
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return node->as<FunctionNode &>().getFunctionName();
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}
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std::string functionName(const ASTPtr & node)
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{
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return node->as<ASTFunction &>().name;
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}
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const Field * tryGetConstantValue(const QueryTreeNodePtr & node)
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{
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if (const auto * constant = node->as<ConstantNode>())
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return &constant->getValue();
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return nullptr;
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}
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const Field * tryGetConstantValue(const ASTPtr & node)
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{
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if (const auto * constant = node->as<ASTLiteral>())
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return &constant->value;
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return nullptr;
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}
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template <typename Node>
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const Field & getConstantValue(const Node & node)
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{
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const auto * constant = tryGetConstantValue(node);
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assert(constant);
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return *constant;
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}
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const auto & getNode(const Analyzer::CNF::AtomicFormula & atom)
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{
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return atom.node_with_hash.node;
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}
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const auto & getNode(const CNFQuery::AtomicFormula & atom)
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{
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return atom.ast;
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}
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std::string nodeToString(const ASTPtr & ast)
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{
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return queryToString(ast);
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}
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std::string nodeToString(const QueryTreeNodePtr & node)
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{
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return queryToString(node->toAST());
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}
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const auto & getArguments(const ASTFunction * function)
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{
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return function->arguments->children;
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}
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const auto & getArguments(const FunctionNode * function)
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{
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return function->getArguments().getNodes();
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}
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bool less(const Field & lhs, const Field & rhs) { return applyVisitor(FieldVisitorAccurateLess{}, lhs, rhs); }
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bool greater(const Field & lhs, const Field & rhs) { return applyVisitor(FieldVisitorAccurateLess{}, rhs, lhs); }
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bool equals(const Field & lhs, const Field & rhs) { return applyVisitor(FieldVisitorAccurateEquals{}, lhs, rhs); }
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ComparisonGraphCompareResult functionNameToCompareResult(const std::string & name)
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{
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using enum ComparisonGraphCompareResult;
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static const std::unordered_map<std::string, ComparisonGraphCompareResult> relation_to_compare =
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{
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{"equals", EQUAL},
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{"notEquals", NOT_EQUAL},
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{"less", LESS},
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{"lessOrEquals", LESS_OR_EQUAL},
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{"greaterOrEquals", GREATER_OR_EQUAL},
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{"greater", GREATER},
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};
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const auto it = relation_to_compare.find(name);
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return it == std::end(relation_to_compare) ? UNKNOWN : it->second;
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}
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ComparisonGraphCompareResult inverseCompareResult(ComparisonGraphCompareResult result)
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{
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using enum ComparisonGraphCompareResult;
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static const std::unordered_map<ComparisonGraphCompareResult, ComparisonGraphCompareResult> inverse_relations =
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{
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{NOT_EQUAL, EQUAL},
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{EQUAL, NOT_EQUAL},
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{GREATER_OR_EQUAL, LESS},
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{GREATER, LESS_OR_EQUAL},
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{LESS, GREATER_OR_EQUAL},
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{LESS_OR_EQUAL, GREATER},
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{UNKNOWN, UNKNOWN},
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};
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return inverse_relations.at(result);
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}
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}
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template <ComparisonGraphNodeType Node>
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ComparisonGraph<Node>::ComparisonGraph(const NodeContainer & atomic_formulas, ContextPtr context)
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{
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if (atomic_formulas.empty())
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return;
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static const std::unordered_map<std::string, typename Edge::Type> relation_to_enum =
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{
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{"equals", Edge::EQUAL},
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{"greater", Edge::GREATER},
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{"greaterOrEquals", Edge::GREATER_OR_EQUAL},
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};
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/// Firstly build an intermediate graph,
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/// in which each vertex corresponds to one expression.
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/// That means that if we have edge (A, B) with type GREATER, then always A > B.
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/// If we have EQUAL relation, then we add both edges (A, B) and (B, A).
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Graph g;
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for (const auto & atom_raw : atomic_formulas)
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{
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const auto atom = normalizeAtom(atom_raw, context);
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auto get_index = [](const Node & node, Graph & nodes_graph) -> std::optional<size_t>
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{
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const auto it = nodes_graph.node_hash_to_component.find(Graph::getHash(node));
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if (it != std::end(nodes_graph.node_hash_to_component))
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{
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if (!std::any_of(
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std::cbegin(nodes_graph.vertices[it->second].nodes),
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std::cend(nodes_graph.vertices[it->second].nodes),
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[node](const Node & constraint_node)
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{
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if constexpr (with_ast)
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return constraint_node->getTreeHash(/*ignore_aliases=*/ true) == node->getTreeHash(/*ignore_aliases=*/ true)
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&& constraint_node->getColumnName() == node->getColumnName();
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else
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return constraint_node->isEqual(*node);
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}))
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{
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return {};
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}
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return it->second;
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}
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else
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{
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nodes_graph.node_hash_to_component[Graph::getHash(node)] = nodes_graph.vertices.size();
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nodes_graph.vertices.push_back(EqualComponent{{node}, std::nullopt});
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nodes_graph.edges.emplace_back();
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return nodes_graph.vertices.size() - 1;
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}
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};
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const auto * function_node = tryGetFunctionNode(atom);
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if (function_node)
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{
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const auto & arguments = getArguments(function_node);
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if (arguments.size() == 2)
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{
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auto index_left = get_index(arguments[0], g);
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auto index_right = get_index(arguments[1], g);
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if (index_left && index_right)
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{
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if (const auto it = relation_to_enum.find(functionName(atom)); it != std::end(relation_to_enum))
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{
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g.edges[*index_left].push_back(Edge{it->second, *index_right});
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if (it->second == Edge::EQUAL)
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g.edges[*index_right].push_back(Edge{it->second, *index_left});
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}
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}
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}
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}
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}
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/// Now expressions A and B are equal, if and only if
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/// we have both paths from A to B and from B to A in graph.
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/// That means that equivalence classes of expressions
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/// are the same as strongly connected components in graph.
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/// So, we find such components and build graph on them.
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/// All expressions from one equivalence class will be stored
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/// in the corresponding vertex of new graph.
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graph = buildGraphFromNodesGraph(g);
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dists = buildDistsFromGraph(graph);
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std::tie(node_const_lower_bound, node_const_upper_bound) = buildConstBounds();
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/// Find expressions that are known to be unequal.
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static const std::unordered_set<String> not_equals_functions = {"notEquals", "greater"};
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/// Explicitly save unequal components.
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/// TODO: Build a graph for unequal components.
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for (const auto & atom_raw : atomic_formulas)
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{
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const auto atom = normalizeAtom(atom_raw, context);
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const auto * function_node = tryGetFunctionNode(atom);
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if (function_node && not_equals_functions.contains(functionName(atom)))
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{
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const auto & arguments = getArguments(function_node);
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if (arguments.size() == 2)
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{
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auto index_left = graph.node_hash_to_component.at(Graph::getHash(arguments[0]));
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auto index_right = graph.node_hash_to_component.at(Graph::getHash(arguments[1]));
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if (index_left == index_right)
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{
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throw Exception(ErrorCodes::VIOLATED_CONSTRAINT,
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"Found expression '{}', but its arguments considered equal according to constraints",
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nodeToString(atom));
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}
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not_equal.emplace(index_left, index_right);
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not_equal.emplace(index_right, index_left);
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}
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}
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}
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}
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template <ComparisonGraphNodeType Node>
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ComparisonGraphCompareResult ComparisonGraph<Node>::pathToCompareResult(Path path, bool inverse)
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{
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switch (path)
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{
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case Path::GREATER: return inverse ? ComparisonGraphCompareResult::LESS : ComparisonGraphCompareResult::GREATER;
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case Path::GREATER_OR_EQUAL: return inverse ? ComparisonGraphCompareResult::LESS_OR_EQUAL : ComparisonGraphCompareResult::GREATER_OR_EQUAL;
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}
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UNREACHABLE();
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}
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template <ComparisonGraphNodeType Node>
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std::optional<typename ComparisonGraph<Node>::Path> ComparisonGraph<Node>::findPath(size_t start, size_t finish) const
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{
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const auto it = dists.find(std::make_pair(start, finish));
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if (it == std::end(dists))
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return {};
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/// Since path can be only GREATER or GREATER_OR_EQUALS,
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/// we can strengthen the condition.
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return not_equal.contains({start, finish}) ? Path::GREATER : it->second;
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}
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template <ComparisonGraphNodeType Node>
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ComparisonGraphCompareResult ComparisonGraph<Node>::compare(const Node & left, const Node & right) const
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{
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size_t start = 0;
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size_t finish = 0;
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/// TODO: check full ast
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const auto it_left = graph.node_hash_to_component.find(Graph::getHash(left));
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const auto it_right = graph.node_hash_to_component.find(Graph::getHash(right));
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if (it_left == std::end(graph.node_hash_to_component) || it_right == std::end(graph.node_hash_to_component))
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{
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auto result = ComparisonGraphCompareResult::UNKNOWN;
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{
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const auto left_bound = getConstLowerBound(left);
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const auto right_bound = getConstUpperBound(right);
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if (left_bound && right_bound)
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{
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if (greater(left_bound->first, right_bound->first))
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result = ComparisonGraphCompareResult::GREATER;
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else if (equals(left_bound->first, right_bound->first))
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result = left_bound->second || right_bound->second
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? ComparisonGraphCompareResult::GREATER : ComparisonGraphCompareResult::GREATER_OR_EQUAL;
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}
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}
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{
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const auto left_bound = getConstUpperBound(left);
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const auto right_bound = getConstLowerBound(right);
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if (left_bound && right_bound)
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{
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if (less(left_bound->first, right_bound->first))
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result = ComparisonGraphCompareResult::LESS;
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else if (equals(left_bound->first, right_bound->first))
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result = left_bound->second || right_bound->second
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? ComparisonGraphCompareResult::LESS : ComparisonGraphCompareResult::LESS_OR_EQUAL;
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}
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}
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return result;
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}
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else
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{
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start = it_left->second;
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finish = it_right->second;
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}
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if (start == finish)
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return ComparisonGraphCompareResult::EQUAL;
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if (auto path = findPath(start, finish))
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return pathToCompareResult(*path, /*inverse=*/ false);
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if (auto path = findPath(finish, start))
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return pathToCompareResult(*path, /*inverse=*/ true);
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if (not_equal.contains({start, finish}))
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return ComparisonGraphCompareResult::NOT_EQUAL;
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return ComparisonGraphCompareResult::UNKNOWN;
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}
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template <ComparisonGraphNodeType Node>
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bool ComparisonGraph<Node>::isPossibleCompare(ComparisonGraphCompareResult expected, const Node & left, const Node & right) const
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{
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const auto result = compare(left, right);
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using enum ComparisonGraphCompareResult;
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if (expected == UNKNOWN || result == UNKNOWN)
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return true;
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if (expected == result)
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return true;
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static const std::set<std::pair<ComparisonGraphCompareResult, ComparisonGraphCompareResult>> possible_pairs =
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{
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{EQUAL, LESS_OR_EQUAL},
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{EQUAL, GREATER_OR_EQUAL},
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{LESS_OR_EQUAL, LESS},
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{LESS_OR_EQUAL, EQUAL},
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{LESS_OR_EQUAL, NOT_EQUAL},
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{GREATER_OR_EQUAL, GREATER},
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{GREATER_OR_EQUAL, EQUAL},
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{GREATER_OR_EQUAL, NOT_EQUAL},
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{LESS, LESS},
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{LESS, LESS_OR_EQUAL},
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{LESS, NOT_EQUAL},
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{GREATER, GREATER},
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{GREATER, GREATER_OR_EQUAL},
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{GREATER, NOT_EQUAL},
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{NOT_EQUAL, LESS},
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{NOT_EQUAL, GREATER},
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{NOT_EQUAL, LESS_OR_EQUAL},
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{NOT_EQUAL, GREATER_OR_EQUAL},
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};
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return possible_pairs.contains({expected, result});
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}
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template <ComparisonGraphNodeType Node>
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bool ComparisonGraph<Node>::isAlwaysCompare(ComparisonGraphCompareResult expected, const Node & left, const Node & right) const
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{
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const auto result = compare(left, right);
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using enum ComparisonGraphCompareResult;
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if (expected == UNKNOWN || result == UNKNOWN)
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return false;
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if (expected == result)
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return true;
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static const std::set<std::pair<ComparisonGraphCompareResult, ComparisonGraphCompareResult>> possible_pairs =
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{
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{LESS_OR_EQUAL, LESS},
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{LESS_OR_EQUAL, EQUAL},
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{GREATER_OR_EQUAL, GREATER},
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{GREATER_OR_EQUAL, EQUAL},
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{NOT_EQUAL, GREATER},
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{NOT_EQUAL, LESS},
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};
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return possible_pairs.contains({expected, result});
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}
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template <ComparisonGraphNodeType Node>
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typename ComparisonGraph<Node>::NodeContainer ComparisonGraph<Node>::getEqual(const Node & node) const
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{
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const auto res = getComponentId(node);
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if (!res)
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return {};
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else
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return getComponent(res.value());
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}
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template <ComparisonGraphNodeType Node>
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std::optional<size_t> ComparisonGraph<Node>::getComponentId(const Node & node) const
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{
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const auto hash_it = graph.node_hash_to_component.find(Graph::getHash(node));
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if (hash_it == std::end(graph.node_hash_to_component))
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return {};
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const size_t index = hash_it->second;
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if (std::any_of(
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std::cbegin(graph.vertices[index].nodes),
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std::cend(graph.vertices[index].nodes),
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[node](const Node & constraint_node)
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{
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if constexpr (with_ast)
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return constraint_node->getTreeHash(/*ignore_aliases=*/ true) == node->getTreeHash(/*ignore_aliases=*/ true)
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&& constraint_node->getColumnName() == node->getColumnName();
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else
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return constraint_node->getTreeHash() == node->getTreeHash();
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}))
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{
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return index;
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}
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else
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{
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return {};
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}
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}
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template <ComparisonGraphNodeType Node>
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bool ComparisonGraph<Node>::hasPath(size_t left, size_t right) const
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{
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return findPath(left, right) || findPath(right, left);
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}
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template <ComparisonGraphNodeType Node>
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typename ComparisonGraph<Node>::NodeContainer ComparisonGraph<Node>::getComponent(size_t id) const
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{
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return graph.vertices[id].nodes;
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}
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template <ComparisonGraphNodeType Node>
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bool ComparisonGraph<Node>::EqualComponent::hasConstant() const
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{
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return constant_index.has_value();
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}
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template <ComparisonGraphNodeType Node>
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Node ComparisonGraph<Node>::EqualComponent::getConstant() const
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{
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assert(constant_index);
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return nodes[*constant_index];
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}
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template <ComparisonGraphNodeType Node>
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void ComparisonGraph<Node>::EqualComponent::buildConstants()
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{
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constant_index.reset();
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for (size_t i = 0; i < nodes.size(); ++i)
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{
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if (tryGetConstantValue(nodes[i]) != nullptr)
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{
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constant_index = i;
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return;
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}
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}
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}
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template <ComparisonGraphNodeType Node>
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ComparisonGraphCompareResult ComparisonGraph<Node>::atomToCompareResult(const typename CNF::AtomicFormula & atom)
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{
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const auto & node = getNode(atom);
|
||
if (tryGetFunctionNode(node) != nullptr)
|
||
{
|
||
auto expected = functionNameToCompareResult(functionName(node));
|
||
if (atom.negative)
|
||
expected = inverseCompareResult(expected);
|
||
return expected;
|
||
}
|
||
|
||
return ComparisonGraphCompareResult::UNKNOWN;
|
||
}
|
||
|
||
template <ComparisonGraphNodeType Node>
|
||
std::optional<Node> ComparisonGraph<Node>::getEqualConst(const Node & node) const
|
||
{
|
||
const auto hash_it = graph.node_hash_to_component.find(Graph::getHash(node));
|
||
if (hash_it == std::end(graph.node_hash_to_component))
|
||
return std::nullopt;
|
||
|
||
const size_t index = hash_it->second;
|
||
|
||
if (!graph.vertices[index].hasConstant())
|
||
return std::nullopt;
|
||
|
||
if constexpr (with_ast)
|
||
return graph.vertices[index].getConstant();
|
||
else
|
||
{
|
||
const auto & constant = getConstantValue(graph.vertices[index].getConstant());
|
||
auto constant_node = std::make_shared<ConstantNode>(constant, node->getResultType());
|
||
return constant_node;
|
||
}
|
||
}
|
||
|
||
template <ComparisonGraphNodeType Node>
|
||
std::optional<std::pair<Field, bool>> ComparisonGraph<Node>::getConstUpperBound(const Node & node) const
|
||
{
|
||
if (const auto * constant = tryGetConstantValue(node))
|
||
return std::make_pair(*constant, false);
|
||
|
||
const auto it = graph.node_hash_to_component.find(Graph::getHash(node));
|
||
if (it == std::end(graph.node_hash_to_component))
|
||
return std::nullopt;
|
||
|
||
const size_t to = it->second;
|
||
const ssize_t from = node_const_upper_bound[to];
|
||
if (from == -1)
|
||
return std::nullopt;
|
||
|
||
return std::make_pair(getConstantValue(graph.vertices[from].getConstant()), dists.at({from, to}) == Path::GREATER);
|
||
}
|
||
|
||
template <ComparisonGraphNodeType Node>
|
||
std::optional<std::pair<Field, bool>> ComparisonGraph<Node>::getConstLowerBound(const Node & node) const
|
||
{
|
||
if (const auto * constant = tryGetConstantValue(node))
|
||
return std::make_pair(*constant, false);
|
||
|
||
const auto it = graph.node_hash_to_component.find(Graph::getHash(node));
|
||
if (it == std::end(graph.node_hash_to_component))
|
||
return std::nullopt;
|
||
|
||
const size_t from = it->second;
|
||
const ssize_t to = node_const_lower_bound[from];
|
||
if (to == -1)
|
||
return std::nullopt;
|
||
|
||
return std::make_pair(getConstantValue(graph.vertices[to].getConstant()), dists.at({from, to}) == Path::GREATER);
|
||
}
|
||
|
||
template <ComparisonGraphNodeType Node>
|
||
void ComparisonGraph<Node>::dfsOrder(const Graph & nodes_graph, size_t v, std::vector<bool> & visited, std::vector<size_t> & order)
|
||
{
|
||
visited[v] = true;
|
||
for (const auto & edge : nodes_graph.edges[v])
|
||
if (!visited[edge.to])
|
||
dfsOrder(nodes_graph, edge.to, visited, order);
|
||
|
||
order.push_back(v);
|
||
}
|
||
|
||
template <ComparisonGraphNodeType Node>
|
||
typename ComparisonGraph<Node>::Graph ComparisonGraph<Node>::reverseGraph(const Graph & nodes_graph)
|
||
{
|
||
Graph g;
|
||
g.node_hash_to_component = nodes_graph.node_hash_to_component;
|
||
g.vertices = nodes_graph.vertices;
|
||
g.edges.resize(g.vertices.size());
|
||
|
||
for (size_t v = 0; v < nodes_graph.vertices.size(); ++v)
|
||
for (const auto & edge : nodes_graph.edges[v])
|
||
g.edges[edge.to].push_back(Edge{edge.type, v});
|
||
|
||
return g;
|
||
}
|
||
|
||
template <ComparisonGraphNodeType Node>
|
||
std::vector<typename ComparisonGraph<Node>::NodeContainer> ComparisonGraph<Node>::getVertices() const
|
||
{
|
||
std::vector<NodeContainer> result;
|
||
for (const auto & vertex : graph.vertices)
|
||
{
|
||
result.emplace_back();
|
||
for (const auto & node : vertex.nodes)
|
||
result.back().push_back(node);
|
||
}
|
||
return result;
|
||
}
|
||
|
||
template <ComparisonGraphNodeType Node>
|
||
void ComparisonGraph<Node>::dfsComponents(
|
||
const Graph & reversed_graph, size_t v,
|
||
OptionalIndices & components, size_t component)
|
||
{
|
||
components[v] = component;
|
||
for (const auto & edge : reversed_graph.edges[v])
|
||
if (!components[edge.to])
|
||
dfsComponents(reversed_graph, edge.to, components, component);
|
||
}
|
||
|
||
template <ComparisonGraphNodeType Node>
|
||
typename ComparisonGraph<Node>::Graph ComparisonGraph<Node>::buildGraphFromNodesGraph(const Graph & nodes_graph)
|
||
{
|
||
/// Find strongly connected component by using 2 dfs traversals.
|
||
/// https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm
|
||
const auto n = nodes_graph.vertices.size();
|
||
|
||
std::vector<size_t> order;
|
||
{
|
||
std::vector<bool> visited(n, false);
|
||
for (size_t v = 0; v < n; ++v)
|
||
{
|
||
if (!visited[v])
|
||
dfsOrder(nodes_graph, v, visited, order);
|
||
}
|
||
}
|
||
|
||
OptionalIndices components(n);
|
||
size_t component = 0;
|
||
{
|
||
const Graph reversed_graph = reverseGraph(nodes_graph);
|
||
for (auto it = order.rbegin(); it != order.rend(); ++it)
|
||
{
|
||
if (!components[*it])
|
||
{
|
||
dfsComponents(reversed_graph, *it, components, component);
|
||
++component;
|
||
}
|
||
}
|
||
}
|
||
|
||
Graph result;
|
||
result.vertices.resize(component);
|
||
result.edges.resize(component);
|
||
for (const auto & [hash, index] : nodes_graph.node_hash_to_component)
|
||
{
|
||
assert(components[index]);
|
||
result.node_hash_to_component[hash] = *components[index];
|
||
result.vertices[*components[index]].nodes.insert(
|
||
std::end(result.vertices[*components[index]].nodes),
|
||
std::begin(nodes_graph.vertices[index].nodes),
|
||
std::end(nodes_graph.vertices[index].nodes)); // asts_graph has only one ast per vertex
|
||
}
|
||
|
||
/// Calculate constants
|
||
for (auto & vertex : result.vertices)
|
||
vertex.buildConstants();
|
||
|
||
/// For each edge in initial graph, we add an edge between components in condensation graph.
|
||
for (size_t v = 0; v < n; ++v)
|
||
{
|
||
for (const auto & edge : nodes_graph.edges[v])
|
||
result.edges[*components[v]].push_back(Edge{edge.type, *components[edge.to]});
|
||
|
||
/// TODO: make edges unique (left most strict)
|
||
}
|
||
|
||
/// If we have constansts in two components, we can compare them and add and extra edge.
|
||
for (size_t v = 0; v < result.vertices.size(); ++v)
|
||
{
|
||
for (size_t u = 0; u < result.vertices.size(); ++u)
|
||
{
|
||
if (v != u && result.vertices[v].hasConstant() && result.vertices[u].hasConstant())
|
||
{
|
||
const auto & left = getConstantValue(result.vertices[v].getConstant());
|
||
const auto & right = getConstantValue(result.vertices[u].getConstant());
|
||
|
||
/// Only GREATER. Equal constant fields = equal literals so it was already considered above.
|
||
if (greater(left, right))
|
||
result.edges[v].push_back(Edge{Edge::GREATER, u});
|
||
}
|
||
}
|
||
}
|
||
|
||
return result;
|
||
}
|
||
|
||
template <ComparisonGraphNodeType Node>
|
||
std::map<std::pair<size_t, size_t>, typename ComparisonGraph<Node>::Path> ComparisonGraph<Node>::buildDistsFromGraph(const Graph & g)
|
||
{
|
||
/// Min path : -1 means GREATER, 0 means GREATER_OR_EQUALS.
|
||
/// We use Floyd–Warshall algorithm to find distances between all pairs of vertices.
|
||
/// https://en.wikipedia.org/wiki/Floyd–Warshall_algorithm
|
||
|
||
constexpr auto inf = std::numeric_limits<Int8>::max();
|
||
const size_t n = g.vertices.size();
|
||
std::vector<std::vector<Int8>> results(n, std::vector<Int8>(n, inf));
|
||
|
||
for (size_t v = 0; v < n; ++v)
|
||
{
|
||
results[v][v] = 0;
|
||
for (const auto & edge : g.edges[v])
|
||
results[v][edge.to] = std::min(results[v][edge.to], static_cast<Int8>(edge.type == Edge::GREATER ? -1 : 0));
|
||
}
|
||
|
||
for (size_t k = 0; k < n; ++k)
|
||
for (size_t v = 0; v < n; ++v)
|
||
for (size_t u = 0; u < n; ++u)
|
||
if (results[v][k] != inf && results[k][u] != inf)
|
||
results[v][u] = std::min(results[v][u], std::min(results[v][k], results[k][u]));
|
||
|
||
std::map<std::pair<size_t, size_t>, Path> path;
|
||
for (size_t v = 0; v < n; ++v)
|
||
for (size_t u = 0; u < n; ++u)
|
||
if (results[v][u] != inf)
|
||
path[std::make_pair(v, u)] = (results[v][u] == -1 ? Path::GREATER : Path::GREATER_OR_EQUAL);
|
||
|
||
return path;
|
||
}
|
||
|
||
template <ComparisonGraphNodeType Node>
|
||
std::pair<std::vector<ssize_t>, std::vector<ssize_t>> ComparisonGraph<Node>::buildConstBounds() const
|
||
{
|
||
const size_t n = graph.vertices.size();
|
||
std::vector<ssize_t> lower(n, -1);
|
||
std::vector<ssize_t> upper(n, -1);
|
||
|
||
auto get_value = [this](const size_t vertex) -> Field
|
||
{
|
||
return getConstantValue(graph.vertices[vertex].getConstant());
|
||
};
|
||
|
||
for (const auto & [edge, path] : dists)
|
||
{
|
||
const auto [from, to] = edge;
|
||
|
||
if (graph.vertices[to].hasConstant())
|
||
{
|
||
if (lower[from] == -1
|
||
|| greater(get_value(to), get_value(lower[from]))
|
||
|| (equals(get_value(to), get_value(lower[from])) && path == Path::GREATER))
|
||
lower[from] = to;
|
||
}
|
||
|
||
if (graph.vertices[from].hasConstant())
|
||
{
|
||
if (upper[to] == -1
|
||
|| less(get_value(from), get_value(upper[to]))
|
||
|| (equals(get_value(from), get_value(upper[to])) && path == Path::GREATER))
|
||
upper[to] = from;
|
||
}
|
||
}
|
||
|
||
return {std::move(lower), std::move(upper)};
|
||
}
|
||
|
||
template class ComparisonGraph<ASTPtr>;
|
||
template class ComparisonGraph<QueryTreeNodePtr>;
|
||
|
||
}
|