// Copyright 2010-2021 Google LLC
// 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
//
//     http://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.

// Protobuf representing a flow problem on a graph. It supports several problem
// types. Depending on the type, the message is interpreted differently as
// explained under each type description below.
//
// LINEAR_SUM_ASSIGNMENT: the algorithm computes the minimum-cost perfect
// matching if there is one.
//  - Arcs are assumed to be from a left node to a right node. In particular
//    the id space of the left and right nodes can be the same. That is an arc
//    from the left node 0 to the right node 0 will be coded as (0, 0).
//  - If a perfect matching does not exist, the problem is not feasible.
//  - Capacity and supply values are ignored.
//
// MAX_FLOW: The algorithm computes the maximum flow under the arc capacity
// constraints.
//  - Only one source (with supply > 0) and one sink (with supply < 0), the
//    supply values are not important. Only the signs are.
//  - The costs are ignored.
//
// MIN_COST_FLOW: the algorithm computes the flow of minimum cost. If a feasible
// flow does not exist (in particular if the sum of supplies is not 0), the
// problem is not feasible.

syntax = "proto2";

package operations_research;

option java_package = "com.google.ortools.graph";
option java_multiple_files = true;
option csharp_namespace = "Google.OrTools.Graph";

message FlowArcProto {
  // A directed arc goes from a tail node to a head node.
  // Node ids must be non-negative (>= 0).
  optional int64 tail = 1;
  optional int64 head = 2;

  // Capacity of the arc. Must be non-negative (>= 0). If the capacity is zero,
  // it is equivalent to not including the arc in the FlowModelProto.
  optional int64 capacity = 3 [default = 1];

  // Cost of this arc per unit of flow.
  // Note that it can take any positive, negative or null value.
  optional int64 unit_cost = 4 [default = 0];
}

message FlowNodeProto {
  // The ids must be non-negative (>= 0). They should be dense for good
  // performance. Note that it is not mandatory to include nodes with no supply
  // in a FlowModelProto.
  optional int64 id = 1;

  // The supply can be positive or negative in which case it means demand.
  // The sum of the supplies over all nodes must always be 0.
  optional int64 supply = 2 [default = 0];
}

// Holds a flow problem, see NodeProto and ArcProto for more details.
message FlowModelProto {
  repeated FlowNodeProto nodes = 1;
  repeated FlowArcProto arcs = 2;

  // The type of problem to solve.
  enum ProblemType {
    LINEAR_SUM_ASSIGNMENT = 0;
    MAX_FLOW = 1;
    MIN_COST_FLOW = 2;
  }
  optional ProblemType problem_type = 3;
}