{"id":198149,"date":"2024-05-10T00:07:18","date_gmt":"2024-05-09T16:07:18","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/198149.html"},"modified":"2024-05-10T00:07:26","modified_gmt":"2024-05-09T16:07:26","slug":"%e5%a6%82%e4%bd%95%e7%94%a8-sql-%e5%ae%9e%e7%8e%b0-dijkstra-%e7%9a%84%e6%9c%80%e7%9f%ad%e8%b7%af%e5%be%84%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/198149.html","title":{"rendered":"\u5982\u4f55\u7528 SQL \u5b9e\u73b0 Dijkstra \u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5"},"content":{"rendered":"

\"\u5982\u4f55\u7528<\/p>\n

\u7528SQL\u5b9e\u73b0Dijkstra\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5<\/strong> \u53ef\u4ee5\u901a\u8fc7\u4e00\u7cfb\u5217\u7684\u8868\u64cd\u4f5c\u6765\u5b8c\u6210\u3002\u9996\u5148\u3001\u6211\u4eec\u9700\u8981\u4e00\u5f20\u5b58\u50a8\u56fe\u8282\u70b9\u95f4\u8fb9\u548c\u6743\u91cd\u4fe1\u606f\u7684\u8868\uff0c\u5176\u6b21\u3001\u521b\u5efa\u4e00\u4e2a\u8868\u7528\u4e8e\u5b58\u50a8\u5df2\u786e\u5b9a\u6700\u77ed\u8def\u5f84\u7684\u8282\u70b9\uff0c\u6700\u540e\u3001\u5229\u7528\u8fed\u4ee3\u67e5\u8be2\u6765\u6a21\u62df\u7b97\u6cd5\u4e2d\u7684\u677e\u5f1b\u64cd\u4f5c\u3002<\/p>\n<\/p>\n

Dijkstra\u7b97\u6cd5\u662f\u4e00\u79cd\u8d2a\u5fc3\u7b97\u6cd5\uff0c\u5b83\u7528\u4e8e\u5bfb\u627e\u56fe\u4e2d\u67d0\u4e2a\u8282\u70b9\u5230\u5176\u4ed6\u6240\u6709\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u3002\u5b83\u7684\u57fa\u672c\u601d\u60f3\u662f\u5148\u5c06\u8d77\u59cb\u8282\u70b9\u7684\u8ddd\u79bb\u8bbe\u7f6e\u4e3a0\uff0c\u5176\u4f59\u6240\u6709\u8282\u70b9\u8bbe\u7f6e\u4e3a\u65e0\u7a77\u5927\uff0c\u7136\u540e\u901a\u8fc7\u4e0d\u65ad\u9009\u62e9\u6700\u5c0f\u8ddd\u79bb\u8282\u70b9\u5e76\u8fdb\u884c\u8ddd\u79bb\u66f4\u65b0\u6765\u627e\u5230\u6700\u77ed\u8def\u5f84\u3002\u5728SQL\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u9012\u5f52\u67e5\u8be2\u6765\u5b9e\u73b0\u8fd9\u4e00\u8fc7\u7a0b\uff0c\u6bcf\u6b21\u67e5\u8be2\u9009\u62e9\u4e00\u4e2a\u6700\u77ed\u8ddd\u79bb\u8282\u70b9\uff0c\u5e76\u66f4\u65b0\u4e0e\u4e4b\u76f8\u90bb\u8282\u70b9\u7684\u8ddd\u79bb\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u521b\u5efa\u56fe\u7ed3\u6784\u8868<\/h3>\n<\/p>\n

\u5728\u4f7f\u7528SQL\u5b9e\u73b0Dijkstra\u7b97\u6cd5\u4e4b\u524d\uff0c\u9700\u8981\u6709\u4e00\u4e2a\u56fe\u7684\u8868\u793a\u3002\u901a\u5e38\uff0c\u8fd9\u53ef\u4ee5\u901a\u8fc7\u4e24\u5f20\u8868\u6765\u5b9e\u73b0\uff1a\u8282\u70b9\u8868\u548c\u8fb9\u8868\u3002\u8282\u70b9\u8868\u4ee3\u8868\u56fe\u4e2d\u7684\u6240\u6709\u8282\u70b9\uff0c\u8fb9\u8868\u5219\u8868\u793a\u8282\u70b9\u4e4b\u95f4\u7684\u8fde\u901a\u5173\u7cfb\u548c\u6bcf\u6761\u8fb9\u7684\u6743\u91cd\u3002<\/p>\n<\/p>\n

CREATE TABLE Nodes (<\/p>\n
    node_id INT PRIMARY KEY<\/p>\n
);<\/p>\n
CREATE TABLE Edges (<\/p>\n
    source_node_id INT,<\/p>\n
    target_node_id INT,<\/p>\n
    weight INT,<\/p>\n
    PRIMARY KEY (source_node_id, target_node_id),<\/p>\n
    FOREIGN KEY (source_node_id) REFERENCES Nodes(node_id),<\/p>\n
    FOREIGN KEY (target_node_id) REFERENCES Nodes(node_id)<\/p>\n
);<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e8c\u3001\u521d\u59cb\u5316\u8282\u70b9\u8ddd\u79bb\u548c\u524d\u9a71\u8282\u70b9\u8868<\/h3>\n<\/p>\n
\u5728Dijkstra\u7b97\u6cd5\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u8bb0\u5f55\u6bcf\u4e2a\u8282\u70b9\u7684\u5f53\u524d\u6700\u77ed\u8ddd\u79bb\u548c\u5230\u8fbe\u8be5\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u7684\u524d\u9a71\u8282\u70b9\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u521b\u5efa\u4e00\u4e2a\u540d\u4e3aNodeStatus<\/code>\u7684\u8868\u6765\u5b9e\u73b0\u3002<\/p>\n<\/p>\n
CREATE TABLE NodeStatus (<\/p>\n
    node_id INT,<\/p>\n
    distance INT,<\/p>\n
    predecessor INT,<\/p>\n
    visited BOOLEAN DEFAULT false,<\/p>\n
    PRIMARY KEY (node_id),<\/p>\n
    FOREIGN KEY (node_id) REFERENCES Nodes(node_id)<\/p>\n
);<\/p>\n
-- \u521d\u59cb\u5316\u6240\u6709\u8282\u70b9\u7684\u8ddd\u79bb\u4e3a\u65e0\u7a77\u5927\uff0c\u524d\u9a71\u8282\u70b9\u4e3aNULL<\/p>\n
UPDATE NodeStatus<\/p>\n
SET distance = 2147483647, -- \u7528\u4e00\u4e2a\u8db3\u591f\u5927\u7684\u6570\u4ee3\u8868\u65e0\u7a77\u5927<\/p>\n
    predecessor = NULL,<\/p>\n
    visited = false;<\/p>\n
-- \u8bbe\u7f6e\u8d77\u70b9\u8282\u70b9\u7684\u8ddd\u79bb\u4e3a0<\/p>\n
UPDATE NodeStatus<\/p>\n
SET distance = 0<\/p>\n
WHERE node_id = [\u8d77\u70b9\u8282\u70b9ID];<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e09\u3001\u6267\u884cDijkstra\u7b97\u6cd5<\/h3>\n<\/p>\n
Dijkstra\u7b97\u6cd5\u7684\u6838\u5fc3\u662f\u8fed\u4ee3\u8fc7\u7a0b\uff0cSQL\u4e2d\u53ef\u4ee5\u4f7f\u7528\u9012\u5f52\u67e5\u8be2\u5faa\u73af\u5b9e\u73b0\u3002<\/p>\n<\/p>\n
WITH RECURSIVE Dijkstra AS (<\/p>\n
    SELECT *<\/p>\n
    FROM NodeStatus<\/p>\n
    WHERE visited = false<\/p>\n
    ORDER BY distance ASC<\/p>\n
    LIMIT 1<\/p>\n
    UNION ALL<\/p>\n
    SELECT ns.*<\/p>\n
    FROM NodeStatus ns<\/p>\n
    INNER JOIN Dijkstra d ON ns.node_id = d.node_id<\/p>\n
    INNER JOIN Edges e ON ns.node_id = e.source_node_id<\/p>\n
    INNER JOIN NodeStatus ns2 ON ns2.node_id = e.target_node_id AND ns2.visited = false<\/p>\n
    SET ns2.distance = CASE<\/p>\n
        WHEN ns2.distance > ns.distance + e.weight THEN ns.distance + e.weight<\/p>\n
        ELSE ns2.distance<\/p>\n
    END,<\/p>\n
    ns2.predecessor = CASE<\/p>\n
        WHEN ns2.distance > ns.distance + e.weight THEN ns.node_id<\/p>\n
        ELSE ns2.predecessor<\/p>\n
    END,<\/p>\n
    ns.visited = true<\/p>\n
    WHERE ns2.distance > ns.distance + e.weight<\/p>\n
)<\/p>\n
SELECT *<\/p>\n
FROM Dijkstra;<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u6bb5SQL\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528 WITH RECURSIVE<\/code> \u5173\u952e\u5b57\u542f\u52a8\u4e00\u4e2a\u9012\u5f52\u67e5\u8be2\u3002\u9996\u5148\uff0c\u6211\u4eec\u4eceNodeStatus<\/code>\u4e2d\u9009\u51fa\u5f53\u524d\u672a\u8bbf\u95ee\u4e14\u8ddd\u79bb\u6700\u5c0f\u7684\u8282\u70b9\u4f5c\u4e3a\u8d77\u70b9\u3002\u7136\u540e\uff0c\u6839\u636e\u8fd9\u4e2a\u8282\u70b9\u7684\u4fe1\u606f\uff0c\u6211\u4eec\u66f4\u65b0\u4e0e\u5176\u76f8\u90bb\u7684\u8282\u70b9\u7684distance<\/code>\u548cpredecessor<\/code>\uff0c\u540c\u65f6\u6807\u8bb0\u8be5\u8282\u70b9\u4e3a\u5df2\u8bbf\u95ee\u3002\u5728\u66f4\u65b0\u76f8\u90bb\u8282\u70b9\u7684distance<\/code>\u65f6\uff0c\u6211\u4eec\u671f\u671b\u8fd9\u4e2a\u8ddd\u79bb\u5c0f\u4e8e\u5f53\u524d\u8bb0\u5f55\u7684distance<\/code>\u3002<\/p>\n<\/p>\n
\u56db\u3001\u63d0\u53d6\u6700\u77ed\u8def\u5f84<\/h3>\n<\/p>\n
\u6700\u540e\uff0c\u5728\u8fd0\u884c\u5b8cDijkstra\u7b97\u6cd5\u540e\uff0c\u6211\u4eec\u9700\u8981\u63d0\u53d6\u6700\u77ed\u8def\u5f84\uff0c\u8fd9\u53ef\u4ee5\u901a\u8fc7\u524d\u9a71\u8282\u70b9\u6765\u56de\u6eaf\u3002<\/p>\n<\/p>\n
WITH RECURSIVE ShortestPath(node_id, path, distance) AS (<\/p>\n
    SELECT node_id, CAST(node_id AS CHAR(10000)), distance<\/p>\n
    FROM NodeStatus<\/p>\n
    WHERE node_id = [\u76ee\u6807\u8282\u70b9ID] AND visited = true<\/p>\n
    UNION ALL<\/p>\n
    SELECT ns.node_id, CONCAT(sp.path, '->', ns.node_id), ns.distance<\/p>\n
    FROM NodeStatus ns<\/p>\n
    INNER JOIN ShortestPath sp ON ns.node_id = sp.predecessor<\/p>\n
)<\/p>\n
SELECT *<\/p>\n
FROM ShortestPath<\/p>\n
WHERE node_id = [\u8d77\u70b9\u8282\u70b9ID];<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u9012\u5f52\u67e5\u8be2\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u9009\u62e9\u76ee\u6807\u8282\u70b9\uff0c\u5e76\u6784\u5efa\u4e00\u4e2a\u5305\u542b\u5355\u4e2a\u8282\u70b9\u7684\u8def\u5f84\u3002\u7136\u540e\uff0c\u6211\u4eec\u6cbf\u7740\u524d\u9a71\u8282\u70b9\u9006\u5411\u8ffd\u6eaf\uff0c\u76f4\u5230\u5230\u8fbe\u8d77\u70b9\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u51fa\u4e00\u6761\u4ece\u76ee\u6807\u8282\u70b9\u5230\u8d77\u70b9\u7684\u6700\u77ed\u8def\u5f84\u3002<\/p>\n<\/p>\n
\u901a\u8fc7\u4ee5\u4e0a\u6b65\u9aa4\uff0c\u6211\u4eec\u4e0d\u4ec5\u5b9e\u73b0\u4e86\u7528SQL\u6765\u6a21\u62dfDijkstra\u7b97\u6cd5\u7684\u64cd\u4f5c\uff0c\u8fd8\u80fd\u591f\u63d0\u53d6\u51fa\u5177\u4f53\u7684\u6700\u77ed\u8def\u5f84\u3002\u6b64\u8fc7\u7a0b\u9700\u8981\u6ce8\u610f\u7ec6\u8282\u7684\u5904\u7406\uff0c\u6bd4\u5982\u65e0\u7a77\u5927\u7684\u8868\u793a\u65b9\u6cd5\u3001\u9012\u5f52\u67e5\u8be2\u7684\u7ec8\u6b62\u6761\u4ef6\u3001\u4ee5\u53ca\u8def\u5f84\u7684\u6b63\u786e\u62fc\u63a5\u3002\u7528SQL\u5b9e\u73b0Dijkstra\u7b97\u6cd5\uff0c\u5f3a\u8c03\u7684\u662fSQL\u5728\u5904\u7406\u56fe\u6570\u636e\u3001\u9012\u5f52\u903b\u8f91\u53ca\u5176\u5b83\u590d\u6742\u7b97\u6cd5\u4e0a\u7684\u7075\u6d3b\u6027\u548c\u5a01\u529b\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
\u5982\u4f55\u4f7f\u7528 SQL\u7f16\u5199Dijkstra\u7b97\u6cd5\u5b9e\u73b0\u56fe\u7684\u6700\u77ed\u8def\u5f84\u641c\u7d22\uff1f<\/strong><\/p>\n
    \n
  • \u95ee\u9898\uff1aDijkstra\u7b97\u6cd5\u662f\u7528\u4e8e\u56fe\u7684\u6700\u77ed\u8def\u5f84\u641c\u7d22\u7684\u7ecf\u5178\u7b97\u6cd5\u4e4b\u4e00\uff0c\u4f46\u662f\u5982\u4f55\u4f7f\u7528SQL\u7f16\u5199Dijkstra\u7b97\u6cd5\u5462\uff1f<\/li>\n<\/ul>\n
    \u56de\u7b54\uff1a\u5728SQL\u4e2d\u5b9e\u73b0Dijkstra\u7b97\u6cd5\u53ef\u4ee5\u4f7f\u7528\u9012\u5f52\u67e5\u8be2\uff08Recursive Query\uff09\u6765\u5b9e\u73b0\u3002\u9996\u5148\uff0c\u9700\u8981\u5c06\u56fe\u7684\u8282\u70b9\u548c\u8fb9\u5efa\u6a21\u4e3a\u6570\u636e\u5e93\u4e2d\u7684\u8868\u3002\u8282\u70b9\u8868\u5305\u542b\u8282\u70b9\u7684\u552f\u4e00\u6807\u8bc6\u7b26\u548c\u5176\u4ed6\u5c5e\u6027\uff0c\u8fb9\u8868\u5305\u542b\u8d77\u59cb\u8282\u70b9\u3001\u7ed3\u675f\u8282\u70b9\u548c\u8fb9\u7684\u6743\u91cd\u5c5e\u6027\u3002<\/p>\n
    \u5728\u9012\u5f52\u67e5\u8be2\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u4e24\u4e2a\u4e34\u65f6\u8868\uff1a\u8ddd\u79bb\u8868\uff08Distance Table\uff09\u548c\u8def\u5f84\u8868\uff08Path Table\uff09\u3002\u8ddd\u79bb\u8868\u7528\u4e8e\u8bb0\u5f55\u6bcf\u4e2a\u8282\u70b9\u5230\u8d77\u59cb\u8282\u70b9\u7684\u6700\u77ed\u8ddd\u79bb\uff0c\u8def\u5f84\u8868\u7528\u4e8e\u8bb0\u5f55\u6bcf\u4e2a\u8282\u70b9\u5230\u8d77\u59cb\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u3002<\/p>\n
    \u7136\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e0b\u5217SQL\u8bed\u53e5\u6765\u5b9e\u73b0Dijkstra\u7b97\u6cd5\uff1a<\/p>\n
    WITH RECURSIVE Distances AS (\n  SELECT start_node, 0 AS distance, ARRAY[start_node] AS path\n  FROM edges\n  WHERE start_node = <start_node>\n  \n  UNION ALL\n  \n  SELECT e.end_node, d.distance + e.weight AS distance, d.path || e.end_node\n  FROM edges e, Distances d\n  WHERE d.end_node = e.start_node\n  AND NOT e.end_node = ANY(d.path)\n)\nSELECT DISTINCT ON (end_node) end_node, distance, path\nFROM Distances\nORDER BY end_node, distance;\n<\/code><\/pre>\n
    \u5728\u4e0a\u8ff0SQL\u8bed\u53e5\u4e2d\uff0c<start_node><\/code>\u8868\u793a\u8d77\u59cb\u8282\u70b9\u7684\u552f\u4e00\u6807\u8bc6\u7b26\u3002\u8be5\u9012\u5f52\u67e5\u8be2\u4f1a\u9010\u6b65\u8ba1\u7b97\u6bcf\u4e2a\u8282\u70b9\u5230\u8d77\u59cb\u8282\u70b9\u7684\u6700\u77ed\u8ddd\u79bb\uff0c\u5e76\u8bb0\u5f55\u6700\u77ed\u8def\u5f84\u3002\u6700\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u8def\u5f84\u8868\u4e2d\u68c0\u7d22\u51fa\u6bcf\u4e2a\u8282\u70b9\u5230\u8d77\u59cb\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u3002<\/p>\n
    \u8bf7\u6ce8\u610f\uff0c\u4e0a\u8ff0SQL\u8bed\u53e5\u4ec5\u9002\u7528\u4e8e\u57fa\u672c\u7684Dijkstra\u7b97\u6cd5\u3002\u5982\u679c\u56fe\u4e2d\u5b58\u5728\u8d1f\u6743\u91cd\u7684\u8fb9\uff0c\u5219\u9700\u8981\u4f7f\u7528\u5176\u4ed6\u7b97\u6cd5\uff0c\u5982Bellman-Ford\u7b97\u6cd5\u3002<\/p>\n
    \u5982\u4f55\u5904\u7406\u56fe\u4e2d\u5b58\u5728\u8d1f\u6743\u91cd\u7684\u8fb9\u65f6\u4f7f\u7528SQL\u5b9e\u73b0\u6700\u77ed\u8def\u5f84\u641c\u7d22\uff1f<\/strong><\/p>\n
      \n
    • \u95ee\u9898\uff1aDijkstra\u7b97\u6cd5\u5728\u56fe\u4e2d\u5b58\u5728\u8d1f\u6743\u91cd\u7684\u8fb9\u65f6\u65e0\u6cd5\u6b63\u786e\u5de5\u4f5c\uff0c\u90a3\u4e48\u5982\u4f55\u4f7f\u7528SQL\u5b9e\u73b0\u6700\u77ed\u8def\u5f84\u641c\u7d22\u65f6\u5904\u7406\u8fd9\u79cd\u60c5\u51b5\u5462\uff1f<\/li>\n<\/ul>\n
      \u56de\u7b54\uff1aDijkstra\u7b97\u6cd5\u5bf9\u4e8e\u56fe\u4e2d\u5b58\u5728\u8d1f\u6743\u91cd\u7684\u8fb9\u65e0\u6cd5\u6b63\u786e\u8fd0\u884c\uff0c\u56e0\u4e3a\u5b83\u5047\u8bbe\u6240\u6709\u8fb9\u7684\u6743\u91cd\u90fd\u4e3a\u975e\u8d1f\u6570\u3002\u5982\u679c\u56fe\u4e2d\u5b58\u5728\u8d1f\u6743\u91cd\u7684\u8fb9\uff0c\u53ef\u4ee5\u9009\u62e9\u4f7f\u7528\u5176\u4ed6\u7b97\u6cd5\uff0c\u5982Bellman-Ford\u7b97\u6cd5\u3002<\/p>\n
      Bellman-Ford\u7b97\u6cd5\u662f\u4e00\u79cd\u7528\u4e8e\u89e3\u51b3\u542b\u6709\u8d1f\u6743\u91cd\u8fb9\u7684\u56fe\u7684\u6700\u77ed\u8def\u5f84\u95ee\u9898\u7684\u7ecf\u5178\u7b97\u6cd5\u3002\u5728SQL\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u8fed\u4ee3\u67e5\u8be2\uff08Iterative Query\uff09\u6765\u5b9e\u73b0Bellman-Ford\u7b97\u6cd5\u3002<\/p>\n
      \u8fed\u4ee3\u67e5\u8be2\uff08Iterative Query\uff09\u662f\u4e00\u79cd\u9010\u6b65\u8fed\u4ee3\u8ba1\u7b97\u7684\u67e5\u8be2\u65b9\u5f0f\uff0c\u5728\u6bcf\u4e00\u6b21\u8fed\u4ee3\u4e2d\u66f4\u65b0\u8ddd\u79bb\u8868\uff08Distance Table\uff09\uff0c\u76f4\u5230\u4e0d\u518d\u6709\u66f4\u65b0\u4e3a\u6b62\u3002\u5728\u6bcf\u4e00\u6b21\u8fed\u4ee3\u4e2d\uff0c\u90fd\u4f1a\u68c0\u67e5\u6bcf\u6761\u8fb9\uff0c\u5982\u679c\u5b58\u5728\u6bd4\u5f53\u524d\u6700\u77ed\u8ddd\u79bb\u66f4\u77ed\u7684\u8def\u5f84\uff0c\u5219\u66f4\u65b0\u8ddd\u79bb\u8868\u3002<\/p>\n
      \u4e0b\u9762\u662f\u4f7f\u7528SQL\u5b9e\u73b0Bellman-Ford\u7b97\u6cd5\u7684\u793a\u4f8b\uff1a<\/p>\n
      CREATE OR REPLACE FUNCTION bellman_ford(start_node INT) RETURNS TABLE (\n  end_node INT,\n  distance INT,\n  path INT[]\n)\nAS $$\nDECLARE\n  max_iter INT := (SELECT COUNT(*) FROM nodes) - 1;\nBEGIN\n  CREATE TEMPORARY TABLE distances (\n    node INT,\n    distance INT,\n    path INT[]\n  );\n\n  INSERT INTO distances\n  SELECT node_id, CASE WHEN node_id = start_node THEN 0 ELSE 99999999 END, ARRAY[node_id]\n  FROM nodes;\n\n  FOR i IN 1..max_iter LOOP\n    INSERT INTO distances\n    SELECT\n      e.end_node,\n      LEAST(d.distance + e.weight, distances.distance),\n      CASE\n        WHEN d.distance + e.weight < distances.distance THEN d.path || e.end_node\n        ELSE distances.path\n      END\n    FROM edges e\n    JOIN distances d ON d.node = e.start_node;\n  END LOOP;\n\n  RETURN QUERY\n  SELECT distinct on (end_node) node, distance, path\n  FROM distances\n  ORDER BY end_node, distance;\nEND;\n$$ LANGUAGE plpgsql;\n<\/code><\/pre>\n
      \u5728\u4e0a\u8ff0SQL\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u7f16\u5199\u4e86\u4e00\u4e2a\u540d\u4e3abellman_ford<\/code>\u7684\u51fd\u6570\uff0c\u8be5\u51fd\u6570\u4f7f\u7528Bellman-Ford\u7b97\u6cd5\u8ba1\u7b97\u6700\u77ed\u8def\u5f84\u3002\u51fd\u6570\u63a5\u53d7\u4e00\u4e2a\u8d77\u59cb\u8282\u70b9\u7684\u53c2\u6570\uff0c\u5e76\u8fd4\u56de\u5305\u542b\u7ec8\u6b62\u8282\u70b9\u3001\u6700\u77ed\u8ddd\u79bb\u548c\u6700\u77ed\u8def\u5f84\u7684\u7ed3\u679c\u96c6\u3002<\/p>\n
      \u5982\u4f55\u5728SQL\u4e2d\u5b9e\u73b0Dijkstra\u7b97\u6cd5\u4ee5\u627e\u5230\u591a\u4e2a\u6700\u77ed\u8def\u5f84\uff1f<\/strong><\/p>\n
        \n
      • \u95ee\u9898\uff1aDijkstra\u7b97\u6cd5\u901a\u5e38\u53ea\u8fd4\u56de\u5355\u4e00\u6700\u77ed\u8def\u5f84\uff0c\u4f46\u662f\u6709\u65f6\u6211\u4eec\u53ef\u80fd\u5e0c\u671b\u627e\u5230\u56fe\u4e2d\u6240\u6709\u5177\u6709\u6700\u77ed\u8ddd\u79bb\u7684\u8def\u5f84\u3002\u5982\u4f55\u5728SQL\u4e2d\u5b9e\u73b0Dijkstra\u7b97\u6cd5\u4ee5\u627e\u5230\u591a\u4e2a\u6700\u77ed\u8def\u5f84\u5462\uff1f<\/li>\n<\/ul>\n
        \u56de\u7b54\uff1aDijkstra\u7b97\u6cd5\u7684\u7ecf\u5178\u5b9e\u73b0\u901a\u5e38\u53ea\u8fd4\u56de\u4e00\u6761\u6700\u77ed\u8def\u5f84\u3002\u7136\u800c\uff0c\u5982\u679c\u6211\u4eec\u60f3\u627e\u5230\u56fe\u4e2d\u6240\u6709\u5177\u6709\u6700\u77ed\u8ddd\u79bb\u7684\u8def\u5f84\uff0c\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e9b\u4fee\u6539\u6765\u5b9e\u73b0\u3002<\/p>\n
        \u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u9012\u5f52\u67e5\u8be2\uff08Recursive Query\uff09\u6765\u8ba1\u7b97\u6240\u6709\u7684\u6700\u77ed\u8def\u5f84\u3002\u5728\u6bcf\u4e00\u6b21\u9012\u5f52\u67e5\u8be2\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u8003\u8651\u6240\u6709\u7b49\u4e8e\u5f53\u524d\u6700\u77ed\u8ddd\u79bb\u7684\u8def\u5f84\uff0c\u5e76\u5c06\u5b83\u4eec\u6dfb\u52a0\u5230\u7ed3\u679c\u96c6\u4e2d\u3002<\/p>\n
        \u4ee5\u4e0b\u662f\u4e00\u4e2a\u4f7f\u7528SQL\u5b9e\u73b0Dijkstra\u7b97\u6cd5\u8fd4\u56de\u6240\u6709\u6700\u77ed\u8def\u5f84\u7684\u793a\u4f8b\uff1a<\/p>\n
        WITH RECURSIVE Distances AS (\n  SELECT start_node, 0 AS distance, ARRAY[start_node] AS path\n  FROM edges\n  WHERE start_node = <start_node>\n  \n  UNION ALL\n  \n  SELECT e.end_node, d.distance + e.weight AS distance, d.path || e.end_node\n  FROM edges e, Distances d\n  WHERE d.end_node = e.start_node\n  AND NOT e.end_node = ANY(d.path)\n),\nShortestPaths AS (\n  SELECT end_node, distance, path\n  FROM Distances\n  WHERE distance = (SELECT MIN(distance) FROM Distances)\n)\nSELECT end_node, distance, path\nFROM ShortestPaths;\n<\/code><\/pre>\n
        \u4e0a\u8ff0SQL\u8bed\u53e5\u4e2d\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u4e00\u4e2a\u540d\u4e3aShortestPaths<\/code>\u7684\u4e34\u65f6\u8868\uff0c\u7528\u4e8e\u5b58\u50a8\u6240\u6709\u5177\u6709\u6700\u77ed\u8ddd\u79bb\u7684\u8def\u5f84\u3002\u5728\u9012\u5f52\u67e5\u8be2\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7\u5c06distance<\/code>\u7b49\u4e8e\u6700\u5c0f\u8ddd\u79bb\u7684\u8def\u5f84\u6dfb\u52a0\u5230ShortestPaths<\/code>\u8868\u4e2d\uff0c\u5b9e\u73b0\u4e86\u627e\u5230\u6240\u6709\u6700\u77ed\u8def\u5f84\u7684\u529f\u80fd\u3002<\/p>\n
        \u8bf7\u6ce8\u610f\uff0c\u8fd9\u79cd\u65b9\u6cd5\u53ef\u80fd\u4f1a\u4ea7\u751f\u5927\u91cf\u7684\u7ed3\u679c\uff0c\u5f53\u56fe\u975e\u5e38\u5927\u5e76\u4e14\u5b58\u5728\u8bb8\u591a\u5177\u6709\u76f8\u540c\u6700\u77ed\u8ddd\u79bb\u7684\u8def\u5f84\u65f6\uff0c\u53ef\u80fd\u4f1a\u5bfc\u81f4\u6027\u80fd\u95ee\u9898\u3002\u56e0\u6b64\uff0c\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5982\u679c\u53ea\u9700\u8981\u51e0\u6761\u6700\u77ed\u8def\u5f84\uff0c\u53ef\u4ee5\u4f7f\u7528\u5176\u4ed6\u65b9\u6cd5\u6765\u9650\u5236\u7ed3\u679c\u96c6\u7684\u5927\u5c0f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u7528SQL\u5b9e\u73b0Dijkstra\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5 \u53ef\u4ee5\u901a\u8fc7\u4e00\u7cfb\u5217\u7684\u8868\u64cd\u4f5c\u6765\u5b8c\u6210\u3002\u9996\u5148\u3001\u6211\u4eec\u9700\u8981\u4e00\u5f20\u5b58\u50a8\u56fe\u8282\u70b9\u95f4\u8fb9\u548c\u6743 […]","protected":false},"author":3,"featured_media":198157,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/198149"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=198149"}],"version-history":[{"count":0,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/198149\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/198157"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=198149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=198149"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=198149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}