我的任务是找出矩阵中一个点到另一个点的最短路径，且只能按照上下左右移动
0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 F 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 S 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0
S - 起点
F - 终点
0 - 可以穿过的点
1 - 不能穿过的点
很明显广度优先搜索是解决该问题的最佳方法，我知道Boost库支持该算法，但是我对Boost库不是特别熟悉。
我如何使用Boost库的广度优先搜索算法解决我的问题？据我了解，Boost库的广度优先搜索算法是专门为图而设计的，我感觉把m*n的矩阵转换成一个包含m*n个点和m*(n-1) + (m-1)*n条边的图不是一个好主意
我可以直接将Boost库的广度优先搜索算法应用于矩阵（不是转换成图）吗，或者是能使用我自己定义的函数就更好了？
注：以上是对提问者的翻译
以下是对回答者的翻译：
（首先很抱歉给的答案篇幅这么长。我使用Boost Graph Library已经有些日子了，写这些也可以很好的复习一下。全部代码在最底部）
Boost图形库（和通常的泛型编程）的好处就在于你不需要在既定的算法中使用特定的数据结构。你上述提到的遍历矩阵的规则已经和图差不多了,你需要做的就是将这些规则归纳成可以被BGL（Boost图形库）算法使用的traits class。
明确的说，就是我们要为你的graph定义一个特定的boost::graph_traits<T>结构。让我们假定你的矩阵是一个以行优先的int型的一维数组。但很不幸的是，只包含int[N]的graph_traits是不够的，因为它没有提供矩阵中维度的信息。所以我们按照以下形式定义你的graph：
namespace matrix
{
typedef int cell;
static const int FREE = 0;
static const int WALL = 1;
template< size_t ROWS, size_t COLS >
struct graph
{
cell cells[ROWS*COLS];
};
}
我这里使用了一个数组来表示单元格数据，如果在外面管理这些数据的话你可以使用指针更简单一些。现在我们已经有了一个可以用于graph_traits的表示矩阵的类型了，但是首先让我们定义一些我们需要的类型和函数：
顶点类型和辅助函数：
namespace matrix
{
typedef size_t vertex_descriptor;
template< size_t ROWS, size_t COLS >
size_t get_row(
vertex_descriptor vertex,
graph< ROWS, COLS > const & )
{
return vertex / COLS;
}
template< size_t ROWS, size_t COLS >
size_t get_col(
vertex_descriptor vertex,
graph< ROWS, COLS > const & )
{
return vertex % COLS;
}
template< size_t ROWS, size_t COLS >
vertex_descriptor make_vertex(
size_t row,
size_t col,
graph< ROWS, COLS > const & )
{
return row * COLS + col;
}
}
遍历顶点的类型和函数：
namespace matrix
{
typedef const cell * vertex_iterator;
template< size_t ROWS, size_t COLS >
std::pair< vertex_iterator, vertex_iterator >
vertices( graph< ROWS, COLS > const & g )
{
return std::make_pair( g.cells, g.cells + ROWS*COLS );
}
typedef size_t vertices_size_type;
template< size_t ROWS, size_t COLS >
vertices_size_type
num_vertices( graph< ROWS, COLS > const & g )
{
return ROWS*COLS;
}
}namespace matrix
{
typedef std::pair< vertex_descriptor, vertex_descriptor > edge_descriptor;
bool operator==(
edge_descriptor const & lhs,
edge_descriptor const & rhs )
{
return
lhs.first == rhs.first && lhs.second == rhs.second ||
lhs.first == rhs.second && lhs.second == rhs.first;
}
bool operator!=(
edge_descriptor const & lhs,
edge_descriptor const & rhs )
{
return !(lhs == rhs);
}
}namespace matrix
{
template< size_t ROWS, size_t COLS >
vertex_descriptor
source(
edge_descriptor const & edge,
graph< ROWS, COLS > const & )
{
return edge.first;
}
template< size_t ROWS, size_t COLS >
vertex_descriptor
target(
edge_descriptor const & edge,
graph< ROWS, COLS > const & )
{
return edge.second;
}
typedef boost::shared_container_iterator< std::vector< edge_descriptor > > out_edge_iterator;
template< size_t ROWS, size_t COLS >
std::pair< out_edge_iterator, out_edge_iterator >
out_edges(
vertex_descriptor vertex,
graph< ROWS, COLS > const & g )
{
boost::shared_ptr< std::vector< edge_descriptor > > edges( new std::vector< edge_descriptor >() );
if( g.cells[vertex] == FREE )
{
size_t
row = get_row( vertex, g ),
col = get_col( vertex, g );
if( row != 0 )
{
vertex_descriptor up = make_vertex( row - 1, col, g );
if( g.cells[up] == FREE )
edges->push_back( edge_descriptor( vertex, up ) );
}
if( row != ROWS-1 )
{
vertex_descriptor down = make_vertex( row + 1, col, g );
if( g.cells[down] == FREE )
edges->push_back( edge_descriptor( vertex, down ) );
}
if( col != 0 )
{
vertex_descriptor left = make_vertex( row, col - 1, g );
if( g.cells[left] == FREE )
edges->push_back( edge_descriptor( vertex, left ) );
}
if( col != COLS-1 )
{
vertex_descriptor right = make_vertex( row, col + 1, g );
if( g.cells[right] == FREE )
edges->push_back( edge_descriptor( vertex, right ) );
}
}
return boost::make_shared_container_range( edges );
}
typedef size_t degree_size_type;
template< size_t ROWS, size_t COLS >
degree_size_type
out_degree(
vertex_descriptor vertex,
graph< ROWS, COLS > const & g )
{
std::pair< out_edge_iterator, out_edge_iterator > edges = out_edges( vertex, g );
return std::distance( edges.first, edges.second );
}
}
到现在未知我们已经定义好了我们需要的boost::graph_traits结构
namespace boost
{
template< size_t ROWS, size_t COLS >
struct graph_traits< matrix::graph< ROWS, COLS > >
{
typedef matrix::vertex_descriptor vertex_descriptor;
typedef matrix::edge_descriptor edge_descriptor;
typedef matrix::out_edge_iterator out_edge_iterator;
typedef matrix::vertex_iterator vertex_iterator;
typedef boost::undirected_tag directed_category;
typedef boost::disallow_parallel_edge_tag edge_parallel_category;
struct traversal_category :
virtual boost::vertex_list_graph_tag,
virtual boost::incidence_graph_tag {};
typedef matrix::vertices_size_type vertices_size_type;
typedef matrix::degree_size_type degree_size_type;
static vertex_descriptor null_vertex() { return ROWS*COLS; }
};
}
接下来就是如何展示使用BFS算法查找最短路径：
int main()
{
const size_t rows = 8, cols = 8;
using namespace matrix;
typedef graph< rows, cols > my_graph;
my_graph g =
{
FREE, FREE, FREE, FREE, WALL, FREE, FREE, FREE,
WALL, FREE, FREE, FREE, FREE, FREE, FREE, FREE,
FREE, FREE, FREE, WALL, FREE, WALL, FREE, FREE,
FREE, WALL, FREE, WALL, FREE, FREE, FREE, FREE,
FREE, FREE, FREE, WALL, FREE, FREE, FREE, FREE,
FREE, FREE, FREE, WALL, FREE, FREE, WALL, FREE,
FREE, FREE, FREE, FREE, FREE, FREE, WALL, FREE,
FREE, FREE, FREE, FREE, FREE, FREE, WALL, FREE,
};
const vertex_descriptor
start_vertex = make_vertex( 5, 1, g ),
finish_vertex = make_vertex( 2, 6, g );
vertex_descriptor predecessors[rows*cols] = { 0 };
using namespace boost;
breadth_first_search(
g,
start_vertex,
visitor( make_bfs_visitor( record_predecessors( predecessors, on_tree_edge() ) ) ).
vertex_index_map( identity_property_map() ) );
typedef std::list< vertex_descriptor > path;
path p;
for( vertex_descriptor vertex = finish_vertex; vertex != start_vertex; vertex = predecessors[vertex] )
p.push_front( vertex );
p.push_front( start_vertex );
for( path::const_iterator cell = p.begin(); cell != p.end(); ++cell )
std::cout << "[" << get_row( *cell, g ) << ", " << get_col( *cell, g ) << "]\n" ;
return 0;
}
以下是输出的从起点到终点的最短路径：
[5, 1] [4, 1] [4, 2] [3, 2] [2, 2] [1, 2] [1, 3] [1, 4] [1, 5] [1, 6] [2, 6]
源码如下：
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/breadth_first_search.hpp>
#include <boost/graph/visitors.hpp>
#include <boost/shared_container_iterator.hpp>
#include <boost/shared_ptr.hpp>
#include <vector>
#include <boost/iterator/counting_iterator.hpp>
#include <list>
namespace matrix
{
typedef int cell;
static const int FREE = 0;
static const int WALL = 1;
template< size_t ROWS, size_t COLS >
struct graph
{
cell cells[ROWS*COLS];
};
typedef size_t vertex_descriptor;
template< size_t ROWS, size_t COLS >
size_t get_row(
vertex_descriptor vertex,
graph< ROWS, COLS > const & )
{
return vertex / COLS;
}
template< size_t ROWS, size_t COLS >
size_t get_col(
vertex_descriptor vertex,
graph< ROWS, COLS > const & )
{
return vertex % COLS;
}
template< size_t ROWS, size_t COLS >
vertex_descriptor make_vertex(
size_t row,
size_t col,
graph< ROWS, COLS > const & )
{
return row * COLS + col;
}
typedef const cell * vertex_iterator;
template< size_t ROWS, size_t COLS >
std::pair< vertex_iterator, vertex_iterator >
vertices( graph< ROWS, COLS > const & g )
{
return std::make_pair( g.cells, g.cells + ROWS*COLS );
}
typedef size_t vertices_size_type;
template< size_t ROWS, size_t COLS >
vertices_size_type
num_vertices( graph< ROWS, COLS > const & g )
{
return ROWS*COLS;
}
typedef std::pair< vertex_descriptor, vertex_descriptor > edge_descriptor;
bool operator==(
edge_descriptor const & lhs,
edge_descriptor const & rhs )
{
return
lhs.first == rhs.first && lhs.second == rhs.second ||
lhs.first == rhs.second && lhs.second == rhs.first;
}
bool operator!=(
edge_descriptor const & lhs,
edge_descriptor const & rhs )
{
return !(lhs == rhs);
}
template< size_t ROWS, size_t COLS >
vertex_descriptor
source(
edge_descriptor const & edge,
graph< ROWS, COLS > const & )
{
return edge.first;
}
template< size_t ROWS, size_t COLS >
vertex_descriptor
target(
edge_descriptor const & edge,
graph< ROWS, COLS > const & )
{
return edge.second;
}
typedef boost::shared_container_iterator< std::vector< edge_descriptor > > out_edge_iterator;
template< size_t ROWS, size_t COLS >
std::pair< out_edge_iterator, out_edge_iterator >
out_edges(
vertex_descriptor vertex,
graph< ROWS, COLS > const & g )
{
boost::shared_ptr< std::vector< edge_descriptor > > edges( new std::vector< edge_descriptor >() );
if( g.cells[vertex] == FREE )
{
size_t
row = get_row( vertex, g ),
col = get_col( vertex, g );
if( row != 0 )
{
vertex_descriptor up = make_vertex( row - 1, col, g );
if( g.cells[up] == FREE )
edges->push_back( edge_descriptor( vertex, up ) );
}
if( row != ROWS-1 )
{
vertex_descriptor down = make_vertex( row + 1, col, g );
if( g.cells[down] == FREE )
edges->push_back( edge_descriptor( vertex, down ) );
}
if( col != 0 )
{
vertex_descriptor left = make_vertex( row, col - 1, g );
if( g.cells[left] == FREE )
edges->push_back( edge_descriptor( vertex, left ) );
}
if( col != COLS-1 )
{
vertex_descriptor right = make_vertex( row, col + 1, g );
if( g.cells[right] == FREE )
edges->push_back( edge_descriptor( vertex, right ) );
}
}
return boost::make_shared_container_range( edges );
}
typedef size_t degree_size_type;
template< size_t ROWS, size_t COLS >
degree_size_type
out_degree(
vertex_descriptor vertex,
graph< ROWS, COLS > const & g )
{
std::pair< out_edge_iterator, out_edge_iterator > edges = out_edges( vertex, g );
return std::distance( edges.first, edges.second );
}
}
namespace boost
{
template< size_t ROWS, size_t COLS >
struct graph_traits< matrix::graph< ROWS, COLS > >
{
typedef matrix::vertex_descriptor vertex_descriptor;
typedef matrix::edge_descriptor edge_descriptor;
typedef matrix::out_edge_iterator out_edge_iterator;
typedef matrix::vertex_iterator vertex_iterator;
typedef boost::undirected_tag directed_category;
typedef boost::disallow_parallel_edge_tag edge_parallel_category;
struct traversal_category :
virtual boost::vertex_list_graph_tag,
virtual boost::incidence_graph_tag {};
typedef matrix::vertices_size_type vertices_size_type;
typedef matrix::degree_size_type degree_size_type;
static vertex_descriptor null_vertex() { return ROWS*COLS; }
};
}
int main()
{
const size_t rows = 8, cols = 8;
using namespace matrix;
typedef matrix::graph< rows, cols > my_graph;
my_graph g =
{
FREE, FREE, FREE, FREE, WALL, FREE, FREE, FREE,
WALL, FREE, FREE, FREE, FREE, FREE, FREE, FREE,
FREE, FREE, FREE, WALL, FREE, WALL, FREE, FREE,
FREE, WALL, FREE, WALL, FREE, FREE, FREE, FREE,
FREE, FREE, FREE, WALL, FREE, FREE, FREE, FREE,
FREE, FREE, FREE, WALL, FREE, FREE, WALL, FREE,
FREE, FREE, FREE, FREE, FREE, FREE, WALL, FREE,
FREE, FREE, FREE, FREE, FREE, FREE, WALL, FREE,
};
const vertex_descriptor
start_vertex = make_vertex( 5, 1, g ),
finish_vertex = make_vertex( 2, 6, g );
vertex_descriptor predecessors[rows*cols] = { 0 };
using namespace boost;
breadth_first_search(
g,
start_vertex,
visitor( make_bfs_visitor( record_predecessors( predecessors, on_tree_edge() ) ) ).
vertex_index_map( boost::identity_property_map() ) );
typedef std::list< vertex_descriptor > path;
path p;
for( vertex_descriptor vertex = finish_vertex; vertex != start_vertex; vertex = predecessors[vertex] )
p.push_front( vertex );
p.push_front( start_vertex );
for( path::const_iterator cell = p.begin(); cell != p.end(); ++cell )
std::cout << "[" << get_row( *cell, g ) << ", " << get_col( *cell, g ) << "]\n" ;
return 0;
}
输出：
[5, 1]
[4, 1]
[4, 2]
[3, 2]
[2, 2]
[1, 2]
[1, 3]
[1, 4]
[1, 5]
[1, 6]
[2, 6]怎样通过boost库的breadth_first_search算法查找点到点的最短路径,布布扣,bubuko.com
怎样通过boost库的breadth_first_search算法查找点到点的最短路径
原文地址：http://blog.csdn.net/yuanhubilie/article/details/35986783
