{"id":103927,"date":"2026-09-11T14:57:04","date_gmt":"2026-09-11T06:57:04","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/103927.html"},"modified":"2026-09-11T14:57:04","modified_gmt":"2026-09-11T06:57:04","slug":"%e5%af%bc%e8%88%aa-app-%e6%98%af%e6%80%8e%e4%b9%88%e7%ae%97%e5%87%ba%e6%9c%80%e7%9f%ad%e8%b7%af%e5%be%84%e7%9a%84%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/103927.html","title":{"rendered":"\u5bfc\u822a App \u662f\u600e\u4e48\u7b97\u51fa\u6700\u77ed\u8def\u5f84\u7684\uff1f"},"content":{"rendered":"

\u5bfc\u822a App \u662f\u600e\u4e48\u7b97\u51fa\u6700\u77ed\u8def\u5f84\u7684？<\/h2>\n

\u4f60\u5728\u5bfc\u822a\u91cc\u8f93\u5165\u76ee\u7684\u5730，\u51e0\u767e\u6beb\u79d2\u5185\u5b83\u5c31\u7ed9\u51fa\u8def\u7ebf\u2014\u2014\u80cc\u540e\u662f\u51e0\u5341\u4e07\u4e2a\u8def\u53e3\u8282\u70b9\u3001\u4e0a\u767e\u4e07\u6761\u9053\u8def\u7684\u56fe\u641c\u7d22\u3002\u8fd9\u4e2a"\u77ac\u95f4\u7b97\u6700\u77ed\u8def"\u7684\u7b97\u6cd5\u53eb Dijkstra，1956 \u5e74\u7531\u8377\u5170\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6 Edsger Dijkstra \u7528 20 \u5206\u949f\u8bbe\u8ba1\u51fa\u6765\u3002\u4eca\u5929\u8bb2\u900f\u5b83\u3002<\/p>\n

\u4e00\u3001\u628a\u5730\u56fe\u53d8\u6210"\u56fe"<\/h3>\n

\u8def\u5f84\u89c4\u5212\u7684\u7b2c\u4e00\u6b65\u662f\u5efa\u6a21：\u8def\u53e3 = \u8282\u70b9，\u9053\u8def = \u8fb9，\u8ddd\u79bb\/\u65f6\u95f4 = \u8fb9\u6743\u3002\u4e8e\u662f"\u627e\u6700\u5feb\u8def\u7ebf"\u53d8\u6210\u56fe\u8bba\u95ee\u9898：\u6c42\u4e24\u70b9\u95f4\u7684\u6700\u77ed\u8def\u5f84\u3002<\/p>\n

\u4e8c\u3001Dijkstra \u7684\u6838\u5fc3\u601d\u60f3：\u8d2a\u5fc3\u6269\u5c55<\/h3>\n

\u7b97\u6cd5\u601d\u8def\u975e\u5e38\u76f4\u89c2\u2014\u2014\u4ece\u8d77\u70b9\u5411\u5916"\u6269\u6563"，\u6bcf\u6b21\u9009\u5f53\u524d\u6700\u8fd1\u7684\u672a\u8bbf\u95ee\u8282\u70b9：<\/p>\n

  • \u8d77\u70b9\u8ddd\u79bb\u8bbe\u4e3a 0，\u5176\u4ed6\u8bbe\u4e3a\u65e0\u7a77<\/li>\n
  • \u4ece\u672a\u8bbf\u95ee\u8282\u70b9\u4e2d\u9009\u8ddd\u79bb\u6700\u5c0f\u7684\u90a3\u4e2a（\u8fd9\u5c31\u662f"\u8d2a\u5fc3"）<\/li>\n
  • \u7528\u5b83\u66f4\u65b0\u90bb\u5c45\u7684\u8ddd\u79bb（\u677e\u5f1b\u64cd\u4f5c：dist[v] = min(dist[v], dist[u] + w)）<\/li>\n
  • \u91cd\u590d\u76f4\u5230\u6240\u6709\u70b9\u8bbf\u95ee\u5b8c<\/li>\n

    \u4e3a\u4ec0\u4e48\u8d2a\u5fc3\u662f\u5bf9\u7684？ \u56e0\u4e3a\u6240\u6709\u8fb9\u6743\u975e\u8d1f\u2014\u2014\u5f53\u67d0\u4e2a\u8282\u70b9\u7684\u8ddd\u79bb\u662f\u5f53\u524d\u6700\u5c0f\u65f6，\u4e0d\u53ef\u80fd\u518d\u6709\u66f4\u77ed\u7684\u8def\u5f84\u7ed5\u8fc7\u5176\u4ed6\u8282\u70b9\u5230\u8fbe\u5b83\u3002\u8fd9\u4e2a"\u975e\u8d1f\u6743"\u524d\u63d0\u662f Dijkstra \u6210\u7acb\u7684\u5173\u952e\u3002<\/p>\n

    \u4e09\u3001\u4e3a\u4ec0\u4e48\u7528\u4f18\u5148\u961f\u5217？<\/h3>\n

    \u6734\u7d20\u5b9e\u73b0\u6bcf\u8f6e\u90fd\u8981"\u626b\u63cf\u6240\u6709\u70b9\u627e\u6700\u5c0f"\u2014\u2014O(V\u00b2)\u3002\u7528**\u4f18\u5148\u961f\u5217（\u6700\u5c0f\u5806）**\u628a"\u627e\u6700\u5c0f"\u964d\u5230 O(log V)，\u603b\u590d\u6742\u5ea6 O(E log V)\u3002\u8fd9\u5c31\u662f\u5bfc\u822a\u80fd\u5b9e\u65f6\u8ba1\u7b97\u7684\u539f\u56e0\u3002<\/p>\n

    \u56db\u3001\u4ee3\u7801\u6f14\u793a：\u624b\u5199 Dijkstra<\/h3>\n

    import<\/span> heapq<\/p>\n

    graph =<\/span> {<\/span>
    \n 'A'<\/span>:<\/span> {<\/span>'B'<\/span>:<\/span> 4<\/span>,<\/span> 'C'<\/span>:<\/span> 2<\/span>}<\/span>,<\/span>
    \n 'B'<\/span>:<\/span> {<\/span>'C'<\/span>:<\/span> 5<\/span>,<\/span> 'D'<\/span>:<\/span> 10<\/span>}<\/span>,<\/span>
    \n 'C'<\/span>:<\/span> {<\/span>'E'<\/span>:<\/span> 3<\/span>}<\/span>,<\/span>
    \n 'D'<\/span>:<\/span> {<\/span>'F'<\/span>:<\/span> 11<\/span>}<\/span>,<\/span>
    \n 'E'<\/span>:<\/span> {<\/span>'D'<\/span>:<\/span> 4<\/span>}<\/span>,<\/span>
    \n 'F'<\/span>:<\/span> {<\/span>}<\/span>,<\/span>
    \n}<\/span><\/p>\n

    def<\/span> dijkstra<\/span>(<\/span>graph,<\/span> start)<\/span>:<\/span>
    \n dist =<\/span> {<\/span>n:<\/span> float<\/span>(<\/span>'inf'<\/span>)<\/span> for<\/span> n in<\/span> graph}<\/span>
    \n dist[<\/span>start]<\/span> =<\/span> 0<\/span>
    \n pq =<\/span> [<\/span>(<\/span>0<\/span>,<\/span> start)<\/span>]<\/span> # \u6700\u5c0f\u5806：(\u8ddd\u79bb, \u8282\u70b9)<\/span>
    \n while<\/span> pq:<\/span>
    \n d,<\/span> u =<\/span> heapq.<\/span>heappop(<\/span>pq)<\/span>
    \n if<\/span> d ><\/span> dist[<\/span>u]<\/span>:<\/span> # \u8fc7\u671f\u6761\u76ee，\u8df3\u8fc7<\/span>
    \n continue<\/span>
    \n for<\/span> v,<\/span> w in<\/span> graph[<\/span>u]<\/span>.<\/span>items(<\/span>)<\/span>:<\/span>
    \n if<\/span> d +<\/span> w <<\/span> dist[<\/span>v]<\/span>:<\/span> # \u677e\u5f1b<\/span>
    \n dist[<\/span>v]<\/span> =<\/span> d +<\/span> w
    \n heapq.<\/span>heappush(<\/span>pq,<\/span> (<\/span>d +<\/span> w,<\/span> v)<\/span>)<\/span>
    \n return<\/span> dist<\/p>\n

    d =<\/span> dijkstra(<\/span>graph,<\/span> 'A'<\/span>)<\/span>
    \nprint<\/span>(<\/span>"\u4ece A \u51fa\u53d1\u5230\u5404\u70b9\u6700\u77ed\u8ddd\u79bb:"<\/span>)<\/span>
    \nfor<\/span> k,<\/span> v in<\/span> d.<\/span>items(<\/span>)<\/span>:<\/span>
    \n print<\/span>(<\/span>f" A -> <\/span>{<\/span>k}<\/span><\/span>: <\/span>{<\/span>v}<\/span><\/span>"<\/span><\/span>)<\/span><\/p>\n

    \u8fd0\u884c\u8f93\u51fa：<\/p>\n

    \u4ece A \u51fa\u53d1\u5230\u5404\u70b9\u6700\u77ed\u8ddd\u79bb:
    \n A -> A: 0
    \n A -> B: 4
    \n A -> C: 2
    \n A -> D: 9
    \n A -> E: 5
    \n A -> F: 20<\/p>\n

    \u6ce8\u610f A\u2192D：\u76f4\u8fbe\u6ca1\u6709\u8fb9，\u7ed5\u9053 A\u2192C\u2192E\u2192D \u5f97\u5230 2+3+4=9，\u6bd4 A\u2192B\u2192D（4+10=14）\u66f4\u77ed\u2014\u2014\u7b97\u6cd5\u81ea\u52a8\u627e\u5230\u4e86\u6700\u4f18\u7ed5\u884c\u65b9\u6848\u3002\u5bfc\u822a App \u5904\u7406\u7684\u662f\u767e\u4e07\u8282\u70b9\u7684\u653e\u5927\u7248，\u539f\u7406\u5b8c\u5168\u4e00\u6837\u3002<\/p>\n

    \u4e94\u3001\u907f\u5751\u6e05\u5355<\/h3>\n
  • \u8fb9\u6743\u5fc5\u987b\u975e\u8d1f：\u6709\u8d1f\u6743\u8fb9\u8981\u7528 Bellman-Ford（Dijkstra \u4f1a\u5931\u6548）<\/li>\n
  • \u4f18\u5148\u961f\u5217\u8981\u5904\u7406"\u8fc7\u671f\u6761\u76ee"：\u8282\u70b9\u8ddd\u79bb\u66f4\u65b0\u540e，\u5806\u91cc\u4f1a\u6709\u65e7\u8bb0\u5f55，\u5f39\u51fa\u65f6\u6bd4\u5bf9\u8df3\u8fc7<\/li>\n
  • \u5b9e\u9645\u5bfc\u822a\u8981\u4f18\u5316：A* \u7b97\u6cd5\u52a0\u542f\u53d1\u5f0f（\u7528\u76f4\u7ebf\u8ddd\u79bb\u5f15\u5bfc\u641c\u7d22\u65b9\u5411），\u628a\u641c\u7d22\u7a7a\u95f4\u4ece"\u5168\u56fe"\u538b\u5230"\u76ee\u6807\u65b9\u5411\u7684\u9525\u5f62\u533a\u57df"<\/li>\n
  • \u52a8\u6001\u8def\u51b5\u8981\u91cd\u65b0\u7b97：\u5b9e\u65f6\u8def\u51b5\u6539\u53d8\u8fb9\u6743，\u9700\u8981\u589e\u91cf\u66f4\u65b0\u6216\u5206\u5c42\u56fe（\u5982 Contraction Hierarchies）<\/li>\n
  • \u4e0d\u53ea\u662f\u8ddd\u79bb：\u771f\u5b9e\u5bfc\u822a\u4f18\u5316\u7684\u662f"\u65f6\u95f4"（\u542b\u7ea2\u7eff\u706f\u3001\u62e5\u5835），\u8fb9\u6743\u5b9a\u4e49\u51b3\u5b9a\u7ed3\u679c<\/li>\n

    \u516d\u3001\u60f3\u7cfb\u7edf\u5b66\u56fe\u7b97\u6cd5？<\/h3>\n

    \u672c\u6587\u7cbe\u9009\u81ea ima \u77e5\u8bc6\u53f7\u3010Kruptos\u3011\u300a\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u8be6\u89e3\u300b\u8ba2\u9605\u5e93（\u7b2c 075 \u671f\u56fe\u7684\u8868\u793a\u3001\u7b2c 077 \u671f BFS\u3001\u7b2c 079 \u671f Dijkstra\u3001\u7b2c 080 \u671f Bellman-Ford \u7b49 100 \u671f\u7cfb\u7edf\u6559\u7a0b，\u4ece\u6570\u7ec4\u3001\u94fe\u8868\u3001\u6811\u5230\u6392\u5e8f\u3001\u52a8\u6001\u89c4\u5212\u4e0e\u56fe\u8bba，\u6bcf\u671f\u914d\u53ef\u8fd0\u884c\u4ee3\u7801）\u3002<\/p>\n

    📚 \u5b8c\u6574\u7cfb\u5217 100 \u671f + \u914d\u5957\u4ee3\u7801，\u5df2\u5728 ima \u77e5\u8bc6\u53f7\u53d1\u5e03<\/p>\n

    \u672c\u6587\u53ea\u662f\u7cfb\u5217\u7684\u4e00\u4e2a\u5207\u7247\u3002\u5b8c\u6574\u7cfb\u5217（100 \u671f\u7cfb\u7edf\u6559\u7a0b + \u6bcf\u671f\u53ef\u8fd0\u884c\u4ee3\u7801）\u5728 ima \u77e5\u8bc6\u53f7\u3010Kruptos\u3011\u6301\u7eed\u66f4\u65b0\u4e2d：<\/p>\n

      \n
    • 🗂 68+ \u6280\u672f\u77e5\u8bc6\u5e93：\u4fe1\u53f7\u4e0e\u7cfb\u7edf\u3001SDR \u8f6f\u4ef6\u65e0\u7ebf\u7535\u3001\u6570\u5b57\u4fe1\u53f7\u5904\u7406\u3001\u64cd\u4f5c\u7cfb\u7edf\u3001AI Agent\u3001\u5927\u6a21\u578b\u5fae\u8c03\u2026\u2026\u51e0\u4e4e\u8986\u76d6\u5168\u90e8\u8f6f\u786c\u4ef6\u6280\u672f\u6808<\/li>\n
    • 🧠 8 \u6b3e AI \u6280\u80fd：\u7cfb\u5217\u751f\u4ea7\u3001\u77e5\u8bc6\u5e93\u7ba1\u7406\u3001CMMI \u53d7\u7ba1\u5f00\u53d1\u3001\u81ea\u8fdb\u5316 Agent \u7b49，\u5df2\u5728 ima \u6280\u80fd\u5e7f\u573a\u4e0a\u67b6，\u5373\u88c5\u5373\u7528<\/li>\n
    • \u2705 \u5168\u90e8\u514d\u8d39\u8ba2\u9605，\u540e\u7eed\u66f4\u65b0\u81ea\u52a8\u63a8\u9001<\/li>\n<\/ul>\n

      🔍 \u8ba2\u9605\u65b9\u5f0f：\u6253\u5f00 ima（\u817e\u8baf\u667a\u80fd\u5de5\u4f5c\u53f0）\u2192 \u641c\u7d22\u300cKruptos\u300d\u2192 \u4e00\u952e\u8ba2\u9605\u3002\u6216\u5728 ima \u5185\u76f4\u63a5\u641c\u7d22\u300a\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u8be6\u89e3\u300b\u7b49\u77e5\u8bc6\u5e93\u540d\u79f0\u3002<\/p>\n

      💬 \u4f60\u9762\u8bd5\u9047\u5230\u8fc7\u56fe\u7b97\u6cd5\u9898\u5417？A* \u7528\u8fc7\u5417？\u8bc4\u8bba\u533a\u804a\u804a\u2014\u2014\u60f3\u770b Bellman-Ford \u8fd8\u662f A*，\u70b9\u8d5e\u9ad8\u7684\u5b89\u6392\u3002<\/p>\n

      \n

      \u4f5c\u8005：Kruptos（\u897f\u7535\u6bd5\u4e1a，13 \u5e74\u65e0\u7ebf\u901a\u4fe1\/DSP\/\u5d4c\u5165\u5f0f\u79d1\u7814）｜\u539f\u521b\u5185\u5bb9，\u8f6c\u8f7d\u6ce8\u660e\u51fa\u5904<\/p>\n","protected":false},"excerpt":{"rendered":"

      \u5bfc\u822a App \u662f\u600e\u4e48\u7b97\u51fa\u6700\u77ed\u8def\u5f84\u7684？\u4f60\u5728\u5bfc\u822a\u91cc\u8f93\u5165\u76ee\u7684\u5730，\u51e0\u767e\u6beb\u79d2\u5185\u5b83\u5c31\u7ed9\u51fa\u8def\u7ebf\u2014\u2014\u80cc\u540e\u662f\u51e0\u5341\u4e07\u4e2a\u8def\u53e3\u8282\u70b9\u3001\u4e0a\u767e\u4e07\u6761\u9053\u8def\u7684\u56fe\u641c\u7d22\u3002\u8fd9\u4e2a\\”\u77ac\u95f4\u7b97\u6700\u77ed\u8def\\”\u7684\u7b97\u6cd5\u53eb Dijkstra，1956 \u5e74\u7531\u8377\u5170\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6 Edsger Dijkstra \u7528 20 \u5206\u949f\u8bbe\u8ba1\u51fa\u6765\u3002\u4eca\u5929\u8bb2\u900f\u5b83\u3002\u4e00\u3001\u628a\u5730\u56fe\u53d8\u6210\\”\u56fe\\”
      \n\u8def\u5f84\u89c4\u5212\u7684\u7b2c\u4e00\u6b65\u662f\u5efa\u6a21：\u8def\u53e3 \u8282\u70b9，\u9053\u8def \u8fb9，\u8ddd\u79bb\/\u65f6\u95f4 \u8fb9\u6743\u3002\u4e8e\u662f\\”\u627e\u6700\u5feb\u8def\u7ebf\\”\u53d8\u6210\u56fe\u8bba<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11653,50,207,427],"topic":[],"class_list":["post-103927","post","type-post","status-publish","format-standard","hentry","category-server","tag-11653","tag-50","tag-207","tag-427"],"yoast_head":"\n\u5bfc\u822a App \u662f\u600e\u4e48\u7b97\u51fa\u6700\u77ed\u8def\u5f84\u7684\uff1f - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/103927.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u5bfc\u822a App \u662f\u600e\u4e48\u7b97\u51fa\u6700\u77ed\u8def\u5f84\u7684\uff1f - 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