全点对最短路径¶
本文介绍全点对最短路径算法，并演示如何用 GQL 实现该算法。
算法介绍¶
全点对最短路径用于计算图中任意两点之间的最短距离。
该过程将算法逻辑封装为可复用过程，可直接在图数据上执行并输出结果。
更多信息，请参见全点对最短路径。
数据模型¶
为了在 GQL 中实现全点对最短路径算法，使用以下数据模型创建图类型：
- 实体由类型为
Node的点表示，点属性包括id和rating。 - 实体间关系由类型为
Link的边表示，边属性包括weight。
该图类型的完整定义，请参见准备图数据。
过程实现¶
为了计算全点对最短路径结果，创建一个过程。
关于该过程的更多信息，请参见过程实现。下文将介绍该过程的关键组成部分及其工作原理。
该过程接受以下输入参数：
- 该过程不需要输入参数。
此外，在过程内部定义了以下变量：
| 变量名 | 变量类型 | 描述 |
|---|---|---|
vertex_ids |
全局 SumAgg 聚合值变量 | Floyd-Warshall 枢轴迭代所用的所有点 ID 列表。 |
inf |
原始值变量 | 不可达点对的无穷大哨兵值。 |
k_idx |
原始值变量 | 当前枢轴在 vertex_ids 中的索引。 |
mid_id |
原始值变量 | Floyd-Warshall 松弛中当前枢轴点 ID。 |
k_row |
全局 SumAgg 聚合值变量 | 当前枢轴行的全局 {点 ID → 距枢轴距离} 映射。 |
dist |
点绑定 SumAgg 聚合值变量 | 每点到所有其他点的 {目标 ID → 最短距离} 映射。 |
result_table |
表变量 | 存储 (src_id, dst_id, dist) 三元组的输出表。 |
以下步骤概述了该过程的逻辑：
- 将所有点 ID 收集到
vertex_ids；用直接边权初始化每点的dist映射，不可达点对设为无穷大。 - 将每个点作为 Floyd-Warshall 枢轴（
mid_id）依次迭代，将枢轴的距离行加载到k_row。 - 对每对点 (i, j)，通过枢轴松弛：
dist[i][j] = min(dist[i][j], dist[i][mid] + k_row[j])。 - 导出所有可达的（src_id、dst_id、distance）三元组并返回。
操作步骤¶
在悦数图管理的控制台中，按顺序执行以下代码块。首次使用时，先按准备算法示例数据确认操作位置和目录挂载。
1. 准备图数据¶
-
创建一个与数据模型匹配的图类型。
''' CREATE GRAPH TYPE IF NOT EXISTS all_pairs_shortest_path_graph_type AS { NODE Node (LABEL Node {id INT PRIMARY KEY, rating INT}), EDGE Link (Node)-[LABEL Link {weight INT, MULTIEDGE KEY()}]->(Node) } ''' -
下载以下 CSV 文件，保留文件名，保存到部署目录下的
examples/algorithms/all_pairs_shortest_path/：查看 CSV 内容
all_pairs_shortest_path_node.csvid,rating 1,0 2,2 3,1 4,0 5,0 6,2 7,1 8,2 9,0 10,1 11,0 12,2 13,1 14,1 15,0 16,2 17,0 18,1 19,2 20,0 21,2 22,1 23,0 24,1all_pairs_shortest_path_edge.csvsrc_id,dst_id,weight 1,2,4 1,3,2 1,4,7 1,5,9 2,3,1 2,4,6 2,5,5 2,6,2 3,4,3 3,5,4 3,6,8 4,6,2 4,7,6 4,8,5 5,6,4 5,8,7 5,9,6 6,8,1 6,9,5 6,10,6 7,9,2 7,10,9 8,9,3 8,11,6 8,12,4 9,10,4 9,12,7 9,13,2 10,12,1 10,13,8 10,14,4 11,12,2 11,14,5 11,15,7 12,14,3 12,15,6 12,16,5 13,15,2 13,16,7 14,15,4 14,17,8 14,18,2 15,16,1 15,18,5 15,19,3 16,18,3 16,19,6 17,18,2 17,20,7 17,21,5 18,19,4 18,21,9 18,22,6 19,21,1 19,22,5 20,21,3 20,23,6 20,24,8 21,22,2 21,23,4 21,24,7 22,24,4 23,24,1 -
基于图类型创建临时图，并将数据文件加载到临时图中。
CREATE TEMPORARY GRAPH IF NOT EXISTS #all_pairs_shortest_path_graph TYPED all_pairs_shortest_path_graph_type''' USE #all_pairs_shortest_path_graph IMPORT INTO GRAPH { NODE (v@Node {id: id, rating: rating}) FROM DATAFILE { PATH: "file:///examples/algorithms/all_pairs_shortest_path/all_pairs_shortest_path_node.csv", FORMAT: "CSV", DELIMITER: ',' }, EDGE (id: src_id)-[e@Link {weight: weight}]->(id: dst_id) FROM DATAFILE { PATH: "file:///examples/algorithms/all_pairs_shortest_path/all_pairs_shortest_path_edge.csv", FORMAT: "CSV", DELIMITER: ',' } } '''导入成功后，在控制台执行以下查询核对点数：
''' USE #all_pairs_shortest_path_graph MATCH (n) RETURN count(n) AS node_count '''node_count应为24。点数不符时，先按文件问题排查检查文件和导入结果。
2. 创建过程¶
创建实现全点对最短路径算法的过程。关于该过程的更多信息，请参见过程实现。
'''
CREATE OR REPLACE PROCEDURE all_pairs_shortest_path()
RETURNS (source_id INT64, target_id INT64, distance DOUBLE)
COMMENT "Compute the classical Floyd-Warshall all-pairs shortest-path distance matrix on a directed weighted graph whose vertex primary key is id and edge weight property is weight. Unreachable pairs are returned as inf. The graph must not contain a negative cycle."
AS {
VALUE vertex_ids ListAgg<INT64>
VALUE inf DOUBLE = 1000000000000000000.0
VALUE k_idx INT64 = 0
VALUE mid_id INT64 = 0
VALUE k_row MapAgg<INT64, MinAgg<DOUBLE>>
NODE VALUE dist MapAgg<INT64, MinAgg<DOUBLE>>
TABLE result_table TYPED TABLE {
source_id INT64,
target_id INT64,
distance DOUBLE
}
MATCH (n)
PER NODE (n) {
SET @vertex_ids += n.id
SET n.@dist.clear()
SET n.@dist += TUPLE(n.id, 0.0)
}
MATCH (s)-[e]->(t)
PER PATH {
SET s.@dist += TUPLE(t.id, CAST(e.weight AS DOUBLE))
}
WHILE k_idx < @vertex_ids.size() THEN {
SET mid_id = @vertex_ids[k_idx]
SET k_idx = k_idx + 1
SET @k_row.clear()
MATCH (k)
WHERE k.id = mid_id
PER NODE (k) {
VALUE row_idx INT64 = 0
WHILE row_idx < k.@dist.size() THEN {
SET @k_row += TUPLE((k.@dist[row_idx])._0, (k.@dist[row_idx])._1)
SET row_idx = row_idx + 1
}
}
MATCH (s)
WHERE s.@dist.contains_key(mid_id)
PER NODE (s) {
VALUE via_k DOUBLE = 0.0
VALUE row_idx INT64 = 0
VALUE row_size INT64 = 0
VALUE target_id INT64 = 0
VALUE candidate DOUBLE = 0.0
SET via_k = s.@dist.get(mid_id)
SET row_size = CAST(@k_row.size() AS INT64)
WHILE row_idx < row_size THEN {
SET target_id = (@k_row[row_idx])._0
SET candidate = via_k + (@k_row[row_idx])._1
IF s.@dist.contains_key(target_id) = false OR candidate < s.@dist.get(target_id) THEN {
SET s.@dist += TUPLE(target_id, candidate)
}
SET row_idx = row_idx + 1
}
}
}
MATCH (s)
PER NODE (s) {
VALUE idx INT64 = 0
VALUE target_id INT64 = 0
WHILE idx < @vertex_ids.size() THEN {
SET target_id = @vertex_ids[idx]
IF s.@dist.contains_key(target_id) THEN {
EXPORT s.id, target_id, s.@dist.get(target_id) INTO result_table
}
ELSE {
EXPORT s.id, target_id, inf INTO result_table
}
SET idx = idx + 1
}
}
FOR r IN result_table
RETURN
r.source_id AS source_id,
r.target_id AS target_id,
r.distance AS distance
ORDER BY source_id ASC, target_id ASC
}
'''
3. 调用过程¶
计算所有点对的最短路径距离，每行返回起点、终点和距离。
USE #all_pairs_shortest_path_graph CALL all_pairs_shortest_path() RETURN source_id, target_id, distance
返回：
展开查看返回
+-----------+-----------+----------+
| source_id | target_id | distance |
+-----------+-----------+----------+
| 1 | 1 | 0.0 |
| 1 | 2 | 4.0 |
| 1 | 3 | 2.0 |
| 1 | 4 | 5.0 |
| 1 | 5 | 6.0 |
| 1 | 6 | 6.0 |
| 1 | 7 | 11.0 |
| 1 | 8 | 7.0 |
| 1 | 9 | 10.0 |
| 1 | 10 | 12.0 |
| 1 | 11 | 13.0 |
| 1 | 12 | 11.0 |
| 1 | 13 | 12.0 |
| 1 | 14 | 14.0 |
| 1 | 15 | 14.0 |
| 1 | 16 | 15.0 |
| 1 | 17 | 22.0 |
| 1 | 18 | 16.0 |
| 1 | 19 | 17.0 |
| 1 | 20 | 29.0 |
| 1 | 21 | 18.0 |
| 1 | 22 | 20.0 |
| 1 | 23 | 22.0 |
| 1 | 24 | 23.0 |
| 2 | 1 | 1e+18 |
| 2 | 2 | 0.0 |
| 2 | 3 | 1.0 |
| 2 | 4 | 4.0 |
| 2 | 5 | 5.0 |
| 2 | 6 | 2.0 |
| 2 | 7 | 10.0 |
| 2 | 8 | 3.0 |
| 2 | 9 | 6.0 |
| 2 | 10 | 8.0 |
| 2 | 11 | 9.0 |
| 2 | 12 | 7.0 |
| 2 | 13 | 8.0 |
| 2 | 14 | 10.0 |
| 2 | 15 | 10.0 |
| 2 | 16 | 11.0 |
| 2 | 17 | 18.0 |
| 2 | 18 | 12.0 |
| 2 | 19 | 13.0 |
| 2 | 20 | 25.0 |
| 2 | 21 | 14.0 |
| 2 | 22 | 16.0 |
| 2 | 23 | 18.0 |
| 2 | 24 | 19.0 |
| 3 | 1 | 1e+18 |
| 3 | 2 | 1e+18 |
| 3 | 3 | 0.0 |
| 3 | 4 | 3.0 |
| 3 | 5 | 4.0 |
| 3 | 6 | 5.0 |
| 3 | 7 | 9.0 |
| 3 | 8 | 6.0 |
| 3 | 9 | 9.0 |
| 3 | 10 | 11.0 |
| 3 | 11 | 12.0 |
| 3 | 12 | 10.0 |
| 3 | 13 | 11.0 |
| 3 | 14 | 13.0 |
| 3 | 15 | 13.0 |
| 3 | 16 | 14.0 |
| 3 | 17 | 21.0 |
| 3 | 18 | 15.0 |
| 3 | 19 | 16.0 |
| 3 | 20 | 28.0 |
| 3 | 21 | 17.0 |
| 3 | 22 | 19.0 |
| 3 | 23 | 21.0 |
| 3 | 24 | 22.0 |
| 4 | 1 | 1e+18 |
| 4 | 2 | 1e+18 |
| 4 | 3 | 1e+18 |
| 4 | 4 | 0.0 |
| 4 | 5 | 1e+18 |
| 4 | 6 | 2.0 |
| 4 | 7 | 6.0 |
| 4 | 8 | 3.0 |
| 4 | 9 | 6.0 |
| 4 | 10 | 8.0 |
| 4 | 11 | 9.0 |
| 4 | 12 | 7.0 |
| 4 | 13 | 8.0 |
| 4 | 14 | 10.0 |
| 4 | 15 | 10.0 |
| 4 | 16 | 11.0 |
| 4 | 17 | 18.0 |
| 4 | 18 | 12.0 |
| 4 | 19 | 13.0 |
| 4 | 20 | 25.0 |
| 4 | 21 | 14.0 |
| 4 | 22 | 16.0 |
| 4 | 23 | 18.0 |
| 4 | 24 | 19.0 |
| 5 | 1 | 1e+18 |
| 5 | 2 | 1e+18 |
| 5 | 3 | 1e+18 |
| 5 | 4 | 1e+18 |
| 5 | 5 | 0.0 |
| 5 | 6 | 4.0 |
| 5 | 7 | 1e+18 |
| 5 | 8 | 5.0 |
| 5 | 9 | 6.0 |
| 5 | 10 | 10.0 |
| 5 | 11 | 11.0 |
| 5 | 12 | 9.0 |
| 5 | 13 | 8.0 |
| 5 | 14 | 12.0 |
| 5 | 15 | 10.0 |
| 5 | 16 | 11.0 |
| 5 | 17 | 20.0 |
| 5 | 18 | 14.0 |
| 5 | 19 | 13.0 |
| 5 | 20 | 27.0 |
| 5 | 21 | 14.0 |
| 5 | 22 | 16.0 |
| 5 | 23 | 18.0 |
| 5 | 24 | 19.0 |
| 6 | 1 | 1e+18 |
| 6 | 2 | 1e+18 |
| 6 | 3 | 1e+18 |
| 6 | 4 | 1e+18 |
| 6 | 5 | 1e+18 |
| 6 | 6 | 0.0 |
| 6 | 7 | 1e+18 |
| 6 | 8 | 1.0 |
| 6 | 9 | 4.0 |
| 6 | 10 | 6.0 |
| 6 | 11 | 7.0 |
| 6 | 12 | 5.0 |
| 6 | 13 | 6.0 |
| 6 | 14 | 8.0 |
| 6 | 15 | 8.0 |
| 6 | 16 | 9.0 |
| 6 | 17 | 16.0 |
| 6 | 18 | 10.0 |
| 6 | 19 | 11.0 |
| 6 | 20 | 23.0 |
| 6 | 21 | 12.0 |
| 6 | 22 | 14.0 |
| 6 | 23 | 16.0 |
| 6 | 24 | 17.0 |
| 7 | 1 | 1e+18 |
| 7 | 2 | 1e+18 |
| 7 | 3 | 1e+18 |
| 7 | 4 | 1e+18 |
| 7 | 5 | 1e+18 |
| 7 | 6 | 1e+18 |
| 7 | 7 | 0.0 |
| 7 | 8 | 1e+18 |
| 7 | 9 | 2.0 |
| 7 | 10 | 6.0 |
| 7 | 11 | 1e+18 |
| 7 | 12 | 7.0 |
| 7 | 13 | 4.0 |
| 7 | 14 | 10.0 |
| 7 | 15 | 6.0 |
| 7 | 16 | 7.0 |
| 7 | 17 | 18.0 |
| 7 | 18 | 10.0 |
| 7 | 19 | 9.0 |
| 7 | 20 | 25.0 |
| 7 | 21 | 10.0 |
| 7 | 22 | 12.0 |
| 7 | 23 | 14.0 |
| 7 | 24 | 15.0 |
| 8 | 1 | 1e+18 |
| 8 | 2 | 1e+18 |
| 8 | 3 | 1e+18 |
| 8 | 4 | 1e+18 |
| 8 | 5 | 1e+18 |
| 8 | 6 | 1e+18 |
| 8 | 7 | 1e+18 |
| 8 | 8 | 0.0 |
| 8 | 9 | 3.0 |
| 8 | 10 | 7.0 |
| 8 | 11 | 6.0 |
| 8 | 12 | 4.0 |
| 8 | 13 | 5.0 |
| 8 | 14 | 7.0 |
| 8 | 15 | 7.0 |
| 8 | 16 | 8.0 |
| 8 | 17 | 15.0 |
| 8 | 18 | 9.0 |
| 8 | 19 | 10.0 |
| 8 | 20 | 22.0 |
| 8 | 21 | 11.0 |
| 8 | 22 | 13.0 |
| 8 | 23 | 15.0 |
| 8 | 24 | 16.0 |
| 9 | 1 | 1e+18 |
| 9 | 2 | 1e+18 |
| 9 | 3 | 1e+18 |
| 9 | 4 | 1e+18 |
| 9 | 5 | 1e+18 |
| 9 | 6 | 1e+18 |
| 9 | 7 | 1e+18 |
| 9 | 8 | 1e+18 |
| 9 | 9 | 0.0 |
| 9 | 10 | 4.0 |
| 9 | 11 | 1e+18 |
| 9 | 12 | 5.0 |
| 9 | 13 | 2.0 |
| 9 | 14 | 8.0 |
| 9 | 15 | 4.0 |
| 9 | 16 | 5.0 |
| 9 | 17 | 16.0 |
| 9 | 18 | 8.0 |
| 9 | 19 | 7.0 |
| 9 | 20 | 23.0 |
| 9 | 21 | 8.0 |
| 9 | 22 | 10.0 |
| 9 | 23 | 12.0 |
| 9 | 24 | 13.0 |
| 10 | 1 | 1e+18 |
| 10 | 2 | 1e+18 |
| 10 | 3 | 1e+18 |
| 10 | 4 | 1e+18 |
| 10 | 5 | 1e+18 |
| 10 | 6 | 1e+18 |
| 10 | 7 | 1e+18 |
| 10 | 8 | 1e+18 |
| 10 | 9 | 1e+18 |
| 10 | 10 | 0.0 |
| 10 | 11 | 1e+18 |
| 10 | 12 | 1.0 |
| 10 | 13 | 8.0 |
| 10 | 14 | 4.0 |
| 10 | 15 | 7.0 |
| 10 | 16 | 6.0 |
| 10 | 17 | 12.0 |
| 10 | 18 | 6.0 |
| 10 | 19 | 10.0 |
| 10 | 20 | 19.0 |
| 10 | 21 | 11.0 |
| 10 | 22 | 12.0 |
| 10 | 23 | 15.0 |
| 10 | 24 | 16.0 |
| 11 | 1 | 1e+18 |
| 11 | 2 | 1e+18 |
| 11 | 3 | 1e+18 |
| 11 | 4 | 1e+18 |
| 11 | 5 | 1e+18 |
| 11 | 6 | 1e+18 |
| 11 | 7 | 1e+18 |
| 11 | 8 | 1e+18 |
| 11 | 9 | 1e+18 |
| 11 | 10 | 1e+18 |
| 11 | 11 | 0.0 |
| 11 | 12 | 2.0 |
| 11 | 13 | 1e+18 |
| 11 | 14 | 5.0 |
| 11 | 15 | 7.0 |
| 11 | 16 | 7.0 |
| 11 | 17 | 13.0 |
| 11 | 18 | 7.0 |
| 11 | 19 | 10.0 |
| 11 | 20 | 20.0 |
| 11 | 21 | 11.0 |
| 11 | 22 | 13.0 |
| 11 | 23 | 15.0 |
| 11 | 24 | 16.0 |
| 12 | 1 | 1e+18 |
| 12 | 2 | 1e+18 |
| 12 | 3 | 1e+18 |
| 12 | 4 | 1e+18 |
| 12 | 5 | 1e+18 |
| 12 | 6 | 1e+18 |
| 12 | 7 | 1e+18 |
| 12 | 8 | 1e+18 |
| 12 | 9 | 1e+18 |
| 12 | 10 | 1e+18 |
| 12 | 11 | 1e+18 |
| 12 | 12 | 0.0 |
| 12 | 13 | 1e+18 |
| 12 | 14 | 3.0 |
| 12 | 15 | 6.0 |
| 12 | 16 | 5.0 |
| 12 | 17 | 11.0 |
| 12 | 18 | 5.0 |
| 12 | 19 | 9.0 |
| 12 | 20 | 18.0 |
| 12 | 21 | 10.0 |
| 12 | 22 | 11.0 |
| 12 | 23 | 14.0 |
| 12 | 24 | 15.0 |
| 13 | 1 | 1e+18 |
| 13 | 2 | 1e+18 |
| 13 | 3 | 1e+18 |
| 13 | 4 | 1e+18 |
| 13 | 5 | 1e+18 |
| 13 | 6 | 1e+18 |
| 13 | 7 | 1e+18 |
| 13 | 8 | 1e+18 |
| 13 | 9 | 1e+18 |
| 13 | 10 | 1e+18 |
| 13 | 11 | 1e+18 |
| 13 | 12 | 1e+18 |
| 13 | 13 | 0.0 |
| 13 | 14 | 1e+18 |
| 13 | 15 | 2.0 |
| 13 | 16 | 3.0 |
| 13 | 17 | 1e+18 |
| 13 | 18 | 6.0 |
| 13 | 19 | 5.0 |
| 13 | 20 | 1e+18 |
| 13 | 21 | 6.0 |
| 13 | 22 | 8.0 |
| 13 | 23 | 10.0 |
| 13 | 24 | 11.0 |
| 14 | 1 | 1e+18 |
| 14 | 2 | 1e+18 |
| 14 | 3 | 1e+18 |
| 14 | 4 | 1e+18 |
| 14 | 5 | 1e+18 |
| 14 | 6 | 1e+18 |
| 14 | 7 | 1e+18 |
| 14 | 8 | 1e+18 |
| 14 | 9 | 1e+18 |
| 14 | 10 | 1e+18 |
| 14 | 11 | 1e+18 |
| 14 | 12 | 1e+18 |
| 14 | 13 | 1e+18 |
| 14 | 14 | 0.0 |
| 14 | 15 | 4.0 |
| 14 | 16 | 5.0 |
| 14 | 17 | 8.0 |
| 14 | 18 | 2.0 |
| 14 | 19 | 6.0 |
| 14 | 20 | 15.0 |
| 14 | 21 | 7.0 |
| 14 | 22 | 8.0 |
| 14 | 23 | 11.0 |
| 14 | 24 | 12.0 |
| 15 | 1 | 1e+18 |
| 15 | 2 | 1e+18 |
| 15 | 3 | 1e+18 |
| 15 | 4 | 1e+18 |
| 15 | 5 | 1e+18 |
| 15 | 6 | 1e+18 |
| 15 | 7 | 1e+18 |
| 15 | 8 | 1e+18 |
| 15 | 9 | 1e+18 |
| 15 | 10 | 1e+18 |
| 15 | 11 | 1e+18 |
| 15 | 12 | 1e+18 |
| 15 | 13 | 1e+18 |
| 15 | 14 | 1e+18 |
| 15 | 15 | 0.0 |
| 15 | 16 | 1.0 |
| 15 | 17 | 1e+18 |
| 15 | 18 | 4.0 |
| 15 | 19 | 3.0 |
| 15 | 20 | 1e+18 |
| 15 | 21 | 4.0 |
| 15 | 22 | 6.0 |
| 15 | 23 | 8.0 |
| 15 | 24 | 9.0 |
| 16 | 1 | 1e+18 |
| 16 | 2 | 1e+18 |
| 16 | 3 | 1e+18 |
| 16 | 4 | 1e+18 |
| 16 | 5 | 1e+18 |
| 16 | 6 | 1e+18 |
| 16 | 7 | 1e+18 |
| 16 | 8 | 1e+18 |
| 16 | 9 | 1e+18 |
| 16 | 10 | 1e+18 |
| 16 | 11 | 1e+18 |
| 16 | 12 | 1e+18 |
| 16 | 13 | 1e+18 |
| 16 | 14 | 1e+18 |
| 16 | 15 | 1e+18 |
| 16 | 16 | 0.0 |
| 16 | 17 | 1e+18 |
| 16 | 18 | 3.0 |
| 16 | 19 | 6.0 |
| 16 | 20 | 1e+18 |
| 16 | 21 | 7.0 |
| 16 | 22 | 9.0 |
| 16 | 23 | 11.0 |
| 16 | 24 | 12.0 |
| 17 | 1 | 1e+18 |
| 17 | 2 | 1e+18 |
| 17 | 3 | 1e+18 |
| 17 | 4 | 1e+18 |
| 17 | 5 | 1e+18 |
| 17 | 6 | 1e+18 |
| 17 | 7 | 1e+18 |
| 17 | 8 | 1e+18 |
| 17 | 9 | 1e+18 |
| 17 | 10 | 1e+18 |
| 17 | 11 | 1e+18 |
| 17 | 12 | 1e+18 |
| 17 | 13 | 1e+18 |
| 17 | 14 | 1e+18 |
| 17 | 15 | 1e+18 |
| 17 | 16 | 1e+18 |
| 17 | 17 | 0.0 |
| 17 | 18 | 2.0 |
| 17 | 19 | 6.0 |
| 17 | 20 | 7.0 |
| 17 | 21 | 5.0 |
| 17 | 22 | 7.0 |
| 17 | 23 | 9.0 |
| 17 | 24 | 10.0 |
| 18 | 1 | 1e+18 |
| 18 | 2 | 1e+18 |
| 18 | 3 | 1e+18 |
| 18 | 4 | 1e+18 |
| 18 | 5 | 1e+18 |
| 18 | 6 | 1e+18 |
| 18 | 7 | 1e+18 |
| 18 | 8 | 1e+18 |
| 18 | 9 | 1e+18 |
| 18 | 10 | 1e+18 |
| 18 | 11 | 1e+18 |
| 18 | 12 | 1e+18 |
| 18 | 13 | 1e+18 |
| 18 | 14 | 1e+18 |
| 18 | 15 | 1e+18 |
| 18 | 16 | 1e+18 |
| 18 | 17 | 1e+18 |
| 18 | 18 | 0.0 |
| 18 | 19 | 4.0 |
| 18 | 20 | 1e+18 |
| 18 | 21 | 5.0 |
| 18 | 22 | 6.0 |
| 18 | 23 | 9.0 |
| 18 | 24 | 10.0 |
| 19 | 1 | 1e+18 |
| 19 | 2 | 1e+18 |
| 19 | 3 | 1e+18 |
| 19 | 4 | 1e+18 |
| 19 | 5 | 1e+18 |
| 19 | 6 | 1e+18 |
| 19 | 7 | 1e+18 |
| 19 | 8 | 1e+18 |
| 19 | 9 | 1e+18 |
| 19 | 10 | 1e+18 |
| 19 | 11 | 1e+18 |
| 19 | 12 | 1e+18 |
| 19 | 13 | 1e+18 |
| 19 | 14 | 1e+18 |
| 19 | 15 | 1e+18 |
| 19 | 16 | 1e+18 |
| 19 | 17 | 1e+18 |
| 19 | 18 | 1e+18 |
| 19 | 19 | 0.0 |
| 19 | 20 | 1e+18 |
| 19 | 21 | 1.0 |
| 19 | 22 | 3.0 |
| 19 | 23 | 5.0 |
| 19 | 24 | 6.0 |
| 20 | 1 | 1e+18 |
| 20 | 2 | 1e+18 |
| 20 | 3 | 1e+18 |
| 20 | 4 | 1e+18 |
| 20 | 5 | 1e+18 |
| 20 | 6 | 1e+18 |
| 20 | 7 | 1e+18 |
| 20 | 8 | 1e+18 |
| 20 | 9 | 1e+18 |
| 20 | 10 | 1e+18 |
| 20 | 11 | 1e+18 |
| 20 | 12 | 1e+18 |
| 20 | 13 | 1e+18 |
| 20 | 14 | 1e+18 |
| 20 | 15 | 1e+18 |
| 20 | 16 | 1e+18 |
| 20 | 17 | 1e+18 |
| 20 | 18 | 1e+18 |
| 20 | 19 | 1e+18 |
| 20 | 20 | 0.0 |
| 20 | 21 | 3.0 |
| 20 | 22 | 5.0 |
| 20 | 23 | 6.0 |
| 20 | 24 | 7.0 |
| 21 | 1 | 1e+18 |
| 21 | 2 | 1e+18 |
| 21 | 3 | 1e+18 |
| 21 | 4 | 1e+18 |
| 21 | 5 | 1e+18 |
| 21 | 6 | 1e+18 |
| 21 | 7 | 1e+18 |
| 21 | 8 | 1e+18 |
| 21 | 9 | 1e+18 |
| 21 | 10 | 1e+18 |
| 21 | 11 | 1e+18 |
| 21 | 12 | 1e+18 |
| 21 | 13 | 1e+18 |
| 21 | 14 | 1e+18 |
| 21 | 15 | 1e+18 |
| 21 | 16 | 1e+18 |
| 21 | 17 | 1e+18 |
| 21 | 18 | 1e+18 |
| 21 | 19 | 1e+18 |
| 21 | 20 | 1e+18 |
| 21 | 21 | 0.0 |
| 21 | 22 | 2.0 |
| 21 | 23 | 4.0 |
| 21 | 24 | 5.0 |
| 22 | 1 | 1e+18 |
| 22 | 2 | 1e+18 |
| 22 | 3 | 1e+18 |
| 22 | 4 | 1e+18 |
| 22 | 5 | 1e+18 |
| 22 | 6 | 1e+18 |
| 22 | 7 | 1e+18 |
| 22 | 8 | 1e+18 |
| 22 | 9 | 1e+18 |
| 22 | 10 | 1e+18 |
| 22 | 11 | 1e+18 |
| 22 | 12 | 1e+18 |
| 22 | 13 | 1e+18 |
| 22 | 14 | 1e+18 |
| 22 | 15 | 1e+18 |
| 22 | 16 | 1e+18 |
| 22 | 17 | 1e+18 |
| 22 | 18 | 1e+18 |
| 22 | 19 | 1e+18 |
| 22 | 20 | 1e+18 |
| 22 | 21 | 1e+18 |
| 22 | 22 | 0.0 |
| 22 | 23 | 1e+18 |
| 22 | 24 | 4.0 |
| 23 | 1 | 1e+18 |
| 23 | 2 | 1e+18 |
| 23 | 3 | 1e+18 |
| 23 | 4 | 1e+18 |
| 23 | 5 | 1e+18 |
| 23 | 6 | 1e+18 |
| 23 | 7 | 1e+18 |
| 23 | 8 | 1e+18 |
| 23 | 9 | 1e+18 |
| 23 | 10 | 1e+18 |
| 23 | 11 | 1e+18 |
| 23 | 12 | 1e+18 |
| 23 | 13 | 1e+18 |
| 23 | 14 | 1e+18 |
| 23 | 15 | 1e+18 |
| 23 | 16 | 1e+18 |
| 23 | 17 | 1e+18 |
| 23 | 18 | 1e+18 |
| 23 | 19 | 1e+18 |
| 23 | 20 | 1e+18 |
| 23 | 21 | 1e+18 |
| 23 | 22 | 1e+18 |
| 23 | 23 | 0.0 |
| 23 | 24 | 1.0 |
| 24 | 1 | 1e+18 |
| 24 | 2 | 1e+18 |
| 24 | 3 | 1e+18 |
| 24 | 4 | 1e+18 |
| 24 | 5 | 1e+18 |
| 24 | 6 | 1e+18 |
| 24 | 7 | 1e+18 |
| 24 | 8 | 1e+18 |
| 24 | 9 | 1e+18 |
| 24 | 10 | 1e+18 |
| 24 | 11 | 1e+18 |
| 24 | 12 | 1e+18 |
| 24 | 13 | 1e+18 |
| 24 | 14 | 1e+18 |
| 24 | 15 | 1e+18 |
| 24 | 16 | 1e+18 |
| 24 | 17 | 1e+18 |
| 24 | 18 | 1e+18 |
| 24 | 19 | 1e+18 |
| 24 | 20 | 1e+18 |
| 24 | 21 | 1e+18 |
| 24 | 22 | 1e+18 |
| 24 | 23 | 1e+18 |
| 24 | 24 | 0.0 |
+-----------+-----------+----------+
保存结果到文件或图中
如需将返回的结果保存为 CSV 文件或写入图，请参见 EXPORT。导出字段应与返回列及目标属性对应。