61 lines
2.5 KiB
C++
61 lines
2.5 KiB
C++
// Copyright 2010-2025 Google LLC
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#ifndef ORTOOLS_GRAPH_DAG_CONNECTIVITY_H_
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#define ORTOOLS_GRAPH_DAG_CONNECTIVITY_H_
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#include <cstdint>
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#include <utility>
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#include <vector>
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#include "absl/types/span.h"
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#include "ortools/util/bitset.h"
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namespace operations_research {
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// Given a directed graph, as defined by the arc list "arcs", computes either:
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// 1. If the graph is acyclic, the matrix of values x, where x[i][j] indicates
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// that there is a directed path from i to j.
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// 2. If the graph is cyclic, "error_cycle_out" is set to contain the cycle,
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// and the return value is empty.
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//
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// The algorithm runs in O(num_nodes^2 + num_nodes*num_arcs).
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//
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// Inputs:
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// arcs: each a in "arcs" is a directed edge from a.first to a.second. Must
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// have a.first, a.second >= 0. The graph is assumed to have nodes
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// {0,1,...,max_{a in arcs} max(a.first, a.second)}, or have no nodes
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// if arcs is the empty list.
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// error_was_cyclic: output arg, is set to true if a cycle is detected.
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// error_cycle_out: output arg, if a cycle is detected, error_cycle_out is
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// set to contain the nodes of the cycle in order.
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//
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// Note: useful for computing the transitive closure of a binary relation, e.g.
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// given the relation i < j for i,j in S that is transitive and some known
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// values i < j, create a node for each i in S and an arc for each known
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// relationship. Then any relationship implied by transitivity is given by
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// the resulting matrix produced, or if the relation fails transitivity, a cycle
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// proving this is produced.
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std::vector<Bitset64<int64_t>> ComputeDagConnectivity(
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absl::Span<const std::pair<int, int>> arcs, bool* error_was_cyclic,
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std::vector<int>* error_cycle_out);
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// Like above, but will CHECK fail if the digraph with arc list "arcs"
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// contains a cycle.
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std::vector<Bitset64<int64_t>> ComputeDagConnectivityOrDie(
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absl::Span<const std::pair<int, int>> arcs);
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} // namespace operations_research
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#endif // ORTOOLS_GRAPH_DAG_CONNECTIVITY_H_
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