pgr_withPoints -拟议

pgr_withPoints - 返回图中带有附加临时顶点的最短路径。

Warning

下一版本的拟议功能。

  • 它们并未正式出现在当前版本中。

  • 它们可能会正式成为下一个版本的一部分:

    • 这些函数使用 ANY-INTEGER 和 ANY-NUMERICAL

    • 名字可能不会改变。(但仍然有可能改变)

    • 签名可能不会改变。(但仍然有可能改变)

    • 功能可能不会改变。(但仍然有可能改变)

    • pgTap 测试已经完成。 但可能需要更多。

    • 文档可能需要完善。

_images/boost-inside.jpeg

Boost 图内部

可用性

  • 版本3.2.0

    • 新的 拟议 函数:

      • pgr_withPoints(组合)

  • 版本 2.2.0

    • 拟议 函数

描述

Modify the graph to include points defined by points_sql. Using Dijkstra algorithm, find the shortest path

主要特点是:

  • 仅在具有正成本的边进行处理。

  • 图的顶点是:

    • 当它属于edges_sql时为

    • 当它属于 points_sql时为

  • 当存在路径时返回值。

    • 当起始顶点和结束顶点相同时,就没有路径。 - 非包含值 (v, v) 的 agg_cost 为 0

    • 当起始顶点和结束顶点不同并且没有路径时: - 不包含的值 (u, v) 的 agg_cost 为 ∞

  • 出于优化目的,start_vid 或 end_vid 中的任何重复值都将被忽略。

  • 返回值按以下顺序排列: - start_vid 升序 - end_vid 升序

  • 运行时间: \(O(|start\_vids|\times(V \log V + E))\)

签名

总结

pgr_withPoints(Edges SQL, Points SQL, start vid, end vid, [options])
pgr_withPoints(Edges SQL, Points SQL, start vid, end vids, [options])
pgr_withPoints(Edges SQL, Points SQL, start vids, end vid, [options])
pgr_withPoints(Edges SQL, Points SQL, start vids, end vids, [options])
pgr_withPoints(Edges SQL, Points SQL, Combinations SQL, [options])
options: [directed, driving_side, details])
返回 (seq, path_seq, [start_pid], [end_pid], node, edge, cost, agg_cost) 的集合
OR EMTPY SET

一对一

pgr_withPoints(Edges SQL, Points SQL, start vid, end vid, [options])
options: [directed, driving_side, details])
返回 (seq, path_seq, node, edge, cost, agg_cost) 的集合
OR EMTPY SET
示例:

从点 \(1\) 到顶点 \(10\) 的细节

SELECT * FROM pgr_withPoints(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  -1, 10,
  details => true);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |   -1 |    1 |  0.6 |        0
   2 |        2 |    6 |    4 |  0.7 |      0.6
   3 |        3 |   -6 |    4 |  0.3 |      1.3
   4 |        4 |    7 |    8 |    1 |      1.6
   5 |        5 |   11 |    9 |    1 |      2.6
   6 |        6 |   16 |   16 |    1 |      3.6
   7 |        7 |   15 |    3 |    1 |      4.6
   8 |        8 |   10 |   -1 |    0 |      5.6
(8 rows)

一对多

pgr_withPoints(Edges SQL, Points SQL, start vid, end vids, [options])
options: [directed, driving_side, details])
返回 (seq, path_seq, end_pid, node, edge, cost, agg_cost) 的集合
OR EMTPY SET
示例:

无向图上的点 \(1\) 到点 \(3\) 和顶点 \(7\)

SELECT * FROM pgr_withPoints(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  -1, ARRAY[-3, 7],
  directed => false);
 seq | path_seq | end_pid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |      -3 |   -1 |    1 |  0.6 |        0
   2 |        2 |      -3 |    6 |    4 |    1 |      0.6
   3 |        3 |      -3 |    7 |   10 |    1 |      1.6
   4 |        4 |      -3 |    8 |   12 |  0.6 |      2.6
   5 |        5 |      -3 |   -3 |   -1 |    0 |      3.2
   6 |        1 |       7 |   -1 |    1 |  0.6 |        0
   7 |        2 |       7 |    6 |    4 |    1 |      0.6
   8 |        3 |       7 |    7 |   -1 |    0 |      1.6
(8 rows)

多对一

pgr_withPoints(Edges SQL, Points SQL, start vids, end vid, [options])
options: [directed, driving_side, details])
返回 (seq, path_seq, start_pid, node, edge, cost, agg_cost) 的集合
OR EMTPY SET
示例:

从点 \(1\) 和顶点 \(6\) 到点 \(3\)

SELECT * FROM pgr_withPoints(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 6], -3);
 seq | path_seq | start_pid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |        -1 |   -1 |    1 |  0.6 |        0
   2 |        2 |        -1 |    6 |    4 |    1 |      0.6
   3 |        3 |        -1 |    7 |   10 |    1 |      1.6
   4 |        4 |        -1 |    8 |   12 |  0.6 |      2.6
   5 |        5 |        -1 |   -3 |   -1 |    0 |      3.2
   6 |        1 |         6 |    6 |    4 |    1 |        0
   7 |        2 |         6 |    7 |   10 |    1 |        1
   8 |        3 |         6 |    8 |   12 |  0.6 |        2
   9 |        4 |         6 |   -3 |   -1 |    0 |      2.6
(9 rows)

多对多

pgr_withPoints(Edges SQL, Points SQL, start vids, end vids, [options])
options: [directed, driving_side, details])
返回 (seq, path_seq, start_pid, end_pid, node, edge, cost, agg_cost) 的集合
OR EMTPY SET
示例:

从点 \(1\) 和顶点 \(6\) 到点 \(3\) 和顶点 \(1\)

SELECT * FROM pgr_withPoints(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[-1, 6], ARRAY[-3, 1]);
 seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        -1 |      -3 |   -1 |    1 |  0.6 |        0
   2 |        2 |        -1 |      -3 |    6 |    4 |    1 |      0.6
   3 |        3 |        -1 |      -3 |    7 |   10 |    1 |      1.6
   4 |        4 |        -1 |      -3 |    8 |   12 |  0.6 |      2.6
   5 |        5 |        -1 |      -3 |   -3 |   -1 |    0 |      3.2
   6 |        1 |        -1 |       1 |   -1 |    1 |  0.6 |        0
   7 |        2 |        -1 |       1 |    6 |    4 |    1 |      0.6
   8 |        3 |        -1 |       1 |    7 |    7 |    1 |      1.6
   9 |        4 |        -1 |       1 |    3 |    6 |    1 |      2.6
  10 |        5 |        -1 |       1 |    1 |   -1 |    0 |      3.6
  11 |        1 |         6 |      -3 |    6 |    4 |    1 |        0
  12 |        2 |         6 |      -3 |    7 |   10 |    1 |        1
  13 |        3 |         6 |      -3 |    8 |   12 |  0.6 |        2
  14 |        4 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
  15 |        1 |         6 |       1 |    6 |    4 |    1 |        0
  16 |        2 |         6 |       1 |    7 |    7 |    1 |        1
  17 |        3 |         6 |       1 |    3 |    6 |    1 |        2
  18 |        4 |         6 |       1 |    1 |   -1 |    0 |        3
(18 rows)

组合

pgr_withPoints(Edges SQL, Points SQL, Combinations SQL, [options])
options: [directed, driving_side, details])
返回 (seq, path_seq, start_pid, end_pid, node, edge, cost, agg_cost) 的集合
OR EMTPY SET
示例:

两种组合

从点 \(1\) 到顶点 \(10\),以及从顶点 \(6\) 到点 \(3\)右侧 行驶。

SELECT * FROM pgr_withPoints(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  'SELECT * FROM (VALUES (-1, 10), (6, -3)) AS combinations(source, target)',
  driving_side => 'r', details => true);
 seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        -1 |      10 |   -1 |    1 |  0.4 |        0
   2 |        2 |        -1 |      10 |    5 |    1 |    1 |      0.4
   3 |        3 |        -1 |      10 |    6 |    4 |  0.7 |      1.4
   4 |        4 |        -1 |      10 |   -6 |    4 |  0.3 |      2.1
   5 |        5 |        -1 |      10 |    7 |    8 |    1 |      2.4
   6 |        6 |        -1 |      10 |   11 |    9 |    1 |      3.4
   7 |        7 |        -1 |      10 |   16 |   16 |    1 |      4.4
   8 |        8 |        -1 |      10 |   15 |    3 |    1 |      5.4
   9 |        9 |        -1 |      10 |   10 |   -1 |    0 |      6.4
  10 |        1 |         6 |      -3 |    6 |    4 |  0.7 |        0
  11 |        2 |         6 |      -3 |   -6 |    4 |  0.3 |      0.7
  12 |        3 |         6 |      -3 |    7 |   10 |    1 |        1
  13 |        4 |         6 |      -3 |    8 |   12 |  0.6 |        2
  14 |        5 |         6 |      -3 |   -3 |   -1 |    0 |      2.6
(14 rows)

参数

类型

描述

Edges SQL

TEXT

Edges SQL 如下所述

Points SQL

TEXT

Points SQL 如下所述

Combinations SQL

TEXT

Combinations SQL 如下所述

start vid

BIGINT

路径起始顶点的标识符。 负值用于点的标识符。

start vids

ARRAY[BIGINT]

起始顶点的标识符数组。 负值用于点的标识符。

end vid

BIGINT

路径结束顶点的标识符。 负值用于点的标识符。

end vids

ARRAY[BIGINT]

结束顶点的标识符数组。 负值用于点的标识符。

可选参数

类型

默认

描述

directed

BOOLEAN

true

  • true 时,该图被视为有 有向

  • 如果为 false ,则该图被视为 无向

带点可选参数

参数

类型

默认

描述

driving_side

CHAR

b

[r, l, b] 中的值指示驱动侧是否为:

  • r 代表右驾驶侧。

  • l 代表左驾驶侧。

  • b 对于两者。

details

BOOLEAN

false

  • 如果为 true ,结果将包括路径中的点。

  • 如果为 false ,结果将不包括路径中的点。

内部查询

Edges SQL

类型

默认

描述

id

ANY-INTEGER

边的标识符。

source

ANY-INTEGER

边的第一个端点顶点的标识符。

target

ANY-INTEGER

边的第二个端点顶点的标识符。

cost

ANY-NUMERICAL

边(source, target)的权重

reverse_cost

ANY-NUMERICAL

-1

边(target, source)的权重

  • 当为负时:边( target, source )不存在,因此它不是图的一部分。

其中:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Points SQL

参数

类型

默认

描述

pid

ANY-INTEGER

value

点的标识符。

  • 使用正值,因为内部将转换为负值

  • 如果列存在,则它不能为 NULL。

  • 如果列不存在,将自动给出连续的负

edge_id

ANY-INTEGER

距离该点“最近”的边的标识符。

fraction

ANY-NUMERICAL

<0,1> 中的值指示距边缘第一个端点的相对位置。

side

CHAR

b

[b, r, l, NULL] 中的值指示该点是否为:

  • r 在右边,

  • l 在左边,

  • b, NULL 在两边

其中:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

分量 SQL

参数

类型

描述

source

ANY-INTEGER

出发顶点的标识符。

target

ANY-INTEGER

到达顶点的标识符。

其中:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

结果列

返回 (seq, path_seq [, start_pid] [, end_pid], node, edge, cost, agg_cost) 的集合

类型

描述

seq

INTEGER

1 开始的顺序值。

path_seq

INTEGER

路径中的相对位置。

  • 1 对于路径的第一行。

start_pid

BIGINT

路径起始顶点/点的标识符。

  • 当正数时是起始顶点的标识符。

  • 当负数时是起点的标识符。

  • 多对一多对多 的返回值

end_pid

BIGINT

路径结束顶点/点的标识符。

  • 当正数时是结束顶点的标识符。

  • 当负数时是终点的标识符。

  • 返回 一对多多对多

node

BIGINT

start_pidend_pid 路径中节点的标识符。

  • 当正数时是顶点的标识符。

  • 当负数时是a点的标识符。

edge

BIGINT

用于从路径序列中的 node 到下一个节点的边的标识符。

  • -1 表示路径的最后一行。

cost

FLOAT

从使用 edgenode 遍历到路径序列中的下一个节点的成本。

  • 0 表示路径的第一行。

agg_cost

FLOAT

start_vidnode 的总成本。

  • 0 表示路径的第一行。

其他示例

Points SQL 中使用 pgr_findCloseEdges

找到从顶点 \(1\) 到点 (2.9, 1.8) 图上两个最近位置的路线。

SELECT * FROM pgr_withPoints(
  $e$ SELECT * FROM edges $e$,
  $p$ SELECT edge_id, round(fraction::numeric, 2) AS fraction, side
      FROM pgr_findCloseEdges(
        $$SELECT id, geom FROM edges$$,
        (SELECT ST_POINT(2.9, 1.8)),
        0.5, cap => 2)
  $p$,
  1, ARRAY[-1, -2]);
 seq | path_seq | end_pid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |      -2 |    1 |    6 |    1 |        0
   2 |        2 |      -2 |    3 |    7 |    1 |        1
   3 |        3 |      -2 |    7 |    8 |  0.9 |        2
   4 |        4 |      -2 |   -2 |   -1 |    0 |      2.9
   5 |        1 |      -1 |    1 |    6 |    1 |        0
   6 |        2 |      -1 |    3 |    7 |    1 |        1
   7 |        3 |      -1 |    7 |    8 |    1 |        2
   8 |        4 |      -1 |   11 |    9 |    1 |        3
   9 |        5 |      -1 |   16 |   16 |    1 |        4
  10 |        6 |      -1 |   15 |    3 |    1 |        5
  11 |        7 |      -1 |   10 |    5 |  0.8 |        6
  12 |        8 |      -1 |   -1 |   -1 |    0 |      6.8
(12 rows)

  • \(-1`对应于距离点`(2.9, 1.8)\) 最近的边。

  • \(-2`对应于点`(2.9, 1.8)\) 的下一个闭合边。

用法变化

所有示例都是关于从点 \(1\) 和顶点 \(5\) 到点 \(\{2, 3, 6\}\) 和顶点 \(\{10, 11\}\) 的旅行

SELECT *
FROM pgr_withPoints(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
  driving_side => 'r', details => true);
 seq | path_seq | start_pid | end_pid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        -1 |      -6 |   -1 |    1 |  0.4 |        0
   2 |        2 |        -1 |      -6 |    5 |    1 |    1 |      0.4
   3 |        3 |        -1 |      -6 |    6 |    4 |  0.7 |      1.4
   4 |        4 |        -1 |      -6 |   -6 |   -1 |    0 |      2.1
   5 |        1 |        -1 |      -3 |   -1 |    1 |  0.4 |        0
   6 |        2 |        -1 |      -3 |    5 |    1 |    1 |      0.4
   7 |        3 |        -1 |      -3 |    6 |    4 |  0.7 |      1.4
   8 |        4 |        -1 |      -3 |   -6 |    4 |  0.3 |      2.1
   9 |        5 |        -1 |      -3 |    7 |   10 |    1 |      2.4
  10 |        6 |        -1 |      -3 |    8 |   12 |  0.6 |      3.4
  11 |        7 |        -1 |      -3 |   -3 |   -1 |    0 |        4
  12 |        1 |        -1 |      -2 |   -1 |    1 |  0.4 |        0
  13 |        2 |        -1 |      -2 |    5 |    1 |    1 |      0.4
  14 |        3 |        -1 |      -2 |    6 |    4 |  0.7 |      1.4
  15 |        4 |        -1 |      -2 |   -6 |    4 |  0.3 |      2.1
  16 |        5 |        -1 |      -2 |    7 |    8 |    1 |      2.4
  17 |        6 |        -1 |      -2 |   11 |    9 |    1 |      3.4
  18 |        7 |        -1 |      -2 |   16 |   15 |  0.4 |      4.4
  19 |        8 |        -1 |      -2 |   -2 |   -1 |    0 |      4.8
  20 |        1 |        -1 |      10 |   -1 |    1 |  0.4 |        0
  21 |        2 |        -1 |      10 |    5 |    1 |    1 |      0.4
  22 |        3 |        -1 |      10 |    6 |    4 |  0.7 |      1.4
  23 |        4 |        -1 |      10 |   -6 |    4 |  0.3 |      2.1
  24 |        5 |        -1 |      10 |    7 |    8 |    1 |      2.4
  25 |        6 |        -1 |      10 |   11 |    9 |    1 |      3.4
  26 |        7 |        -1 |      10 |   16 |   16 |    1 |      4.4
  27 |        8 |        -1 |      10 |   15 |    3 |    1 |      5.4
  28 |        9 |        -1 |      10 |   10 |   -1 |    0 |      6.4
  29 |        1 |        -1 |      11 |   -1 |    1 |  0.4 |        0
  30 |        2 |        -1 |      11 |    5 |    1 |    1 |      0.4
  31 |        3 |        -1 |      11 |    6 |    4 |  0.7 |      1.4
  32 |        4 |        -1 |      11 |   -6 |    4 |  0.3 |      2.1
  33 |        5 |        -1 |      11 |    7 |    8 |    1 |      2.4
  34 |        6 |        -1 |      11 |   11 |   -1 |    0 |      3.4
  35 |        1 |         5 |      -6 |    5 |    1 |    1 |        0
  36 |        2 |         5 |      -6 |    6 |    4 |  0.7 |        1
  37 |        3 |         5 |      -6 |   -6 |   -1 |    0 |      1.7
  38 |        1 |         5 |      -3 |    5 |    1 |    1 |        0
  39 |        2 |         5 |      -3 |    6 |    4 |  0.7 |        1
  40 |        3 |         5 |      -3 |   -6 |    4 |  0.3 |      1.7
  41 |        4 |         5 |      -3 |    7 |   10 |    1 |        2
  42 |        5 |         5 |      -3 |    8 |   12 |  0.6 |        3
  43 |        6 |         5 |      -3 |   -3 |   -1 |    0 |      3.6
  44 |        1 |         5 |      -2 |    5 |    1 |    1 |        0
  45 |        2 |         5 |      -2 |    6 |    4 |  0.7 |        1
  46 |        3 |         5 |      -2 |   -6 |    4 |  0.3 |      1.7
  47 |        4 |         5 |      -2 |    7 |    8 |    1 |        2
  48 |        5 |         5 |      -2 |   11 |    9 |    1 |        3
  49 |        6 |         5 |      -2 |   16 |   15 |  0.4 |        4
  50 |        7 |         5 |      -2 |   -2 |   -1 |    0 |      4.4
  51 |        1 |         5 |      10 |    5 |    1 |    1 |        0
  52 |        2 |         5 |      10 |    6 |    4 |  0.7 |        1
  53 |        3 |         5 |      10 |   -6 |    4 |  0.3 |      1.7
  54 |        4 |         5 |      10 |    7 |    8 |    1 |        2
  55 |        5 |         5 |      10 |   11 |    9 |    1 |        3
  56 |        6 |         5 |      10 |   16 |   16 |    1 |        4
  57 |        7 |         5 |      10 |   15 |    3 |    1 |        5
  58 |        8 |         5 |      10 |   10 |   -1 |    0 |        6
  59 |        1 |         5 |      11 |    5 |    1 |    1 |        0
  60 |        2 |         5 |      11 |    6 |    4 |  0.7 |        1
  61 |        3 |         5 |      11 |   -6 |    4 |  0.3 |      1.7
  62 |        4 |         5 |      11 |    7 |    8 |    1 |        2
  63 |        5 |         5 |      11 |   11 |   -1 |    0 |        3
(63 rows)

从前方超车或右侧行驶来访。

对于点 \(6\) 和顶点 \(11\)

SELECT (start_pid || ' -> ' || end_pid ||' at ' || path_seq || 'th step')::TEXT AS path_at,
  CASE WHEN edge = -1 THEN ' visits'
      ELSE ' passes in front of'
  END as status,
  CASE WHEN node < 0 THEN 'Point'
      ELSE 'Vertex'
  END as is_a,
  abs(node) as id
FROM pgr_withPoints(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
  driving_side => 'r', details => true)
WHERE node IN (-6, 11);
       path_at        |       status        |  is_a  | id
----------------------+---------------------+--------+----
 -1 -> -6 at 4th step |  visits             | Point  |  6
 -1 -> -3 at 4th step |  passes in front of | Point  |  6
 -1 -> -2 at 4th step |  passes in front of | Point  |  6
 -1 -> -2 at 6th step |  passes in front of | Vertex | 11
 -1 -> 10 at 4th step |  passes in front of | Point  |  6
 -1 -> 10 at 6th step |  passes in front of | Vertex | 11
 -1 -> 11 at 4th step |  passes in front of | Point  |  6
 -1 -> 11 at 6th step |  visits             | Vertex | 11
 5 -> -6 at 3th step  |  visits             | Point  |  6
 5 -> -3 at 3th step  |  passes in front of | Point  |  6
 5 -> -2 at 3th step  |  passes in front of | Point  |  6
 5 -> -2 at 5th step  |  passes in front of | Vertex | 11
 5 -> 10 at 3th step  |  passes in front of | Point  |  6
 5 -> 10 at 5th step  |  passes in front of | Vertex | 11
 5 -> 11 at 3th step  |  passes in front of | Point  |  6
 5 -> 11 at 5th step  |  visits             | Vertex | 11
(16 rows)

从前方超车或以左侧驾驶方式行驶。

对于点 \(6\) 和顶点 \(11\)

SELECT (start_pid || ' => ' || end_pid ||' at ' || path_seq || 'th step')::TEXT AS path_at,
  CASE WHEN edge = -1 THEN ' visits'
      ELSE ' passes in front of'
  END as status,
  CASE WHEN node < 0 THEN 'Point'
        ELSE 'Vertex'
    END as is_a,
    abs(node) as id
FROM pgr_withPoints(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  'SELECT pid, edge_id, fraction, side from pointsOfInterest',
  ARRAY[5, -1], ARRAY[-2, -3, -6, 10, 11],
  driving_side => 'l', details => true)
WHERE node IN (-6, 11);
       path_at        |       status        |  is_a  | id
----------------------+---------------------+--------+----
 -1 => -6 at 3th step |  visits             | Point  |  6
 -1 => -3 at 3th step |  passes in front of | Point  |  6
 -1 => -2 at 3th step |  passes in front of | Point  |  6
 -1 => -2 at 5th step |  passes in front of | Vertex | 11
 -1 => 10 at 3th step |  passes in front of | Point  |  6
 -1 => 10 at 5th step |  passes in front of | Vertex | 11
 -1 => 11 at 3th step |  passes in front of | Point  |  6
 -1 => 11 at 5th step |  visits             | Vertex | 11
 5 => -6 at 4th step  |  visits             | Point  |  6
 5 => -3 at 4th step  |  passes in front of | Point  |  6
 5 => -2 at 4th step  |  passes in front of | Point  |  6
 5 => -2 at 6th step  |  passes in front of | Vertex | 11
 5 => 10 at 4th step  |  passes in front of | Point  |  6
 5 => 10 at 6th step  |  passes in front of | Vertex | 11
 5 => 11 at 4th step  |  passes in front of | Point  |  6
 5 => 11 at 6th step  |  visits             | Vertex | 11
(16 rows)

另请参阅

索引和表格