# Boost C++ Libraries

...one of the most highly regarded and expertly designed C++ library projects in the world.

# floyd_warshall_all_pairs_shortest_paths

// Named parameters version
template <class VertexListGraph, class DistanceMatrix,
class P, class T, class R>
bool floyd_warshall_initialized_all_pairs_shortest_paths(
const VertexListGraph& g, DistanceMatrix& d,
const bgl_named_params<P, T, R>& params)

template <class VertexAndEdgeListGraph, class DistanceMatrix,
class P, class T, class R>
bool floyd_warshall_all_pairs_shortest_paths(
const VertexAndEdgeListGraph& g, DistanceMatrix& d,
const bgl_named_params<P, T, R>& params)

// Positional parameter versions
\begin{verbatim}
template <typename VertexListGraph, typename DistanceMatrix,
typename BinaryPredicate, typename BinaryFunction,
typename Infinity, typename Zero>
bool floyd_warshall_initialized_all_pairs_shortest_paths(
const VertexListGraph& g, DistanceMatrix& d,
const BinaryPredicate& compare, const BinaryFunction& combine,
const Infinity& inf, const Zero& zero)

template <typename VertexAndEdgeListGraph, typename DistanceMatrix,
typename WeightMap, typename BinaryPredicate,
typename BinaryFunction, typename Infinity, typename Zero>
bool floyd_warshall_all_pairs_shortest_paths(
const VertexAndEdgeListGraph& g, DistanceMatrix& d,
const WeightMap& w, const BinaryPredicate& compare,
const BinaryFunction& combine,
const Infinity& inf, const Zero& zero)

These algorithms find the shortest distance between every pair of vertices in the graph. The algorithms return false if there is a negative weight cycle in the graph, true otherwise. The shortest distance between each pair of vertices is stored in the distance matrix d. The difference between the two algorithms is in whether the distance matrix is assumed to be initialized or not, as discussed below under the OUT parameter description.

### Parameters

IN: Graph& g
A directed or undirected graph. The graph must be a model of Vertex List Graph for calls to floyd_warshall_initialized_all_pairs_shortest_paths, and Vertex And Edge List Graph for calls to floyd_warshall_all_pairs_shortest_paths.
OUT: DistanceMatrix& d
The length of the shortest path between each pair of vertices u,v are stored in the matrix at location D[u][v]. The DistanceMatrix must be of type {M, I, V} where I is of type vertex_descriptor and V is the type of the weight_map. The set of types must be a model of BasicMatrix, with the exceptions that it isn't required to run in constant time, and it must be mutable. The matrix must be properly initialized when it is passed to the function floyd_warshall_initialized_all_pairs_shortest_paths. If the function floyd_warshall_all_pairs_shortest_paths is used then the matrix will be initialized for the user.

### Named Parameters

IN: weight_map(WeightMap w)
The weight of length of each edge in the graph. The WeightMap must be a model of Readable Property Map. The edge descriptor type of the graph needs to be usable as the key type for the weight map. The value_type of the weight map must be the type of the DistanceMatrix, and must always either be part of the graph passed to the function, or passed in as a parameter.
Default: get(edge_weight, g)
IN: distance_compare(CompareFunction cmp)
The function used to compare distances to determine which target vertex is closer to the source vertex. The CompareFunction must be a model of BinaryPredicate. The argument types must match the value type of the WeightMap.
Default: std::less<WM>with WM = typename property_traits<WeightMap>::value_type
IN: distance_combine(CombineFunction cmb)
The function used to combine distance to compute the distance of a path. The CombineFunction must be a model of BinaryFunction. The argument types must match the value type of the WeightMap. The result type must be the same as the distance value type.
Default: boost::closed_plus<WM> with WM = typename property_traits<WeightMap>::value_type
IN: distance_inf(WM inf)
The value used to initialize the distance for each vertex before starting the algorithm, and to represent the distance between vertices for which there is not path. Should be larger than any possible valid path length. The argument type must match the value type of the  WeightMap.
Default: std::numeric_limits<WM>::max() with WM = typename property_traits<WeightMap>::value_type
IN: distance_zero(WM zero)
The value used to represent the distance from a vertex to itself, and to determine if a value is negative. The argument type must match the value type of the WeightMap.
Default: 0

### Complexity

The time complexity is O(V3).

 Copyright © 2002-2004 Lauren Foutz, Rensselaer Polytechnic Institute Scott Hill, Rensselaer Polytechnic Institute