{"id":121222,"date":"2026-11-02T10:24:46","date_gmt":"2026-11-02T02:24:46","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/121222.html"},"modified":"2026-11-02T10:24:46","modified_gmt":"2026-11-02T02:24:46","slug":"uva-792-program-modules","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/121222.html","title":{"rendered":"UVa 792 Program Modules"},"content":{"rendered":"

\u9898\u76ee\u63cf\u8ff0<\/h3>\n

\u7ed9\u5b9a\u4e00\u4e2a\u7a0b\u5e8f\u4e2d\u7684\u6240\u6709\u51fd\u6570\u53ca\u5176\u76f4\u63a5\u8c03\u7528\u5173\u7cfb，\u5b9a\u4e49\u5173\u7cfb A\u2192BA \\\\rightarrow B<\/span><\/span>A<\/span><\/span>\u2192<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u51fd\u6570 AA<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u76f4\u63a5\u8c03\u7528 BB<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span>，A\u21d2BA \\\\Rightarrow B<\/span><\/span>A<\/span><\/span>\u21d2<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u8868\u793a AA<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u53ef\u4f20\u9012\u5730\u8c03\u7528 BB<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span>（\u76f4\u63a5\u6216\u95f4\u63a5）\u3002\u5df2\u77e5 \u2192\\\\rightarrow<\/span><\/span>\u2192<\/span><\/span><\/span><\/span><\/span> \u662f \u21d2\\\\Rightarrow<\/span><\/span>\u21d2<\/span><\/span><\/span><\/span><\/span> \u7684\u5b50\u96c6，\u4e14 \u21d2\\\\Rightarrow<\/span><\/span>\u21d2<\/span><\/span><\/span><\/span><\/span> \u5177\u6709\u4f20\u9012\u6027\u3002
\n\u73b0\u9700\u8981\u5c06\u6240\u6709\u51fd\u6570\u5212\u5206\u4e3a\u82e5\u5e72\u6a21\u5757，\u6ee1\u8db3：<\/p>\n

  • \u82e5 A\u21d2BA \\\\Rightarrow B<\/span><\/span>A<\/span><\/span>\u21d2<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u4e14 B\u21d2AB \\\\Rightarrow A<\/span><\/span>B<\/span><\/span>\u21d2<\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>，\u5219 AA<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u4e0e BB<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u5fc5\u987b\u5728\u540c\u4e00\u6a21\u5757\u3002<\/li>\n
  • \u4efb\u610f\u4e24\u4e2a\u4e0d\u6ee1\u8db3\u4e0a\u8ff0\u6761\u4ef6\u7684\u51fd\u6570\u5fc5\u987b\u5206\u5c5e\u4e0d\u540c\u6a21\u5757\u3002<\/li>\n

    \u8981\u6c42\u8f93\u51fa\u6240\u6709\u6a21\u5757，\u6bcf\u4e2a\u6a21\u5757\u5185\u7684\u51fd\u6570\u540d\u6309\u5b57\u5178\u5e8f\u5347\u5e8f\u6392\u5217，\u6a21\u5757\u6309\u7b2c\u4e00\u4e2a\u5143\u7d20（\u6700\u5c0f\u51fd\u6570\u540d）\u7684\u5b57\u5178\u5e8f\u5347\u5e8f\u6392\u5217\u3002\u6bcf\u7ec4\u6570\u636e\u8f93\u51fa\u540e\u8ddf\u4e00\u4e2a\u7a7a\u884c\u3002<\/p>\n

    \u8f93\u5165\u683c\u5f0f<\/h3>\n

    \u8f93\u5165\u5305\u542b\u82e5\u5e72\u7ec4\u6570\u636e，\u6bcf\u7ec4\u6570\u636e\u4ee3\u8868\u4e00\u4e2a\u5f85\u6a21\u5757\u5316\u7684\u7a0b\u5e8f\u3002\u6bcf\u7ec4\u6570\u636e\u683c\u5f0f\u4e3a：<\/p>\n

    (Fun1 Fun11 … Fun1n1)(Fun2 Fun21 … Fun2n2)… (Funm Funm1 … Funmn m).<\/p>\n

    \u5176\u4e2d\u6bcf\u4e2a\u62ec\u53f7\u9879\u8868\u793a\u6e90\u51fd\u6570 FuniFun_i<\/span><\/span>F<\/span>u<\/span>n<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u76f4\u63a5\u8c03\u7528\u5176\u540e\u6240\u6709\u51fd\u6570 FunijFun_{ij}<\/span><\/span>F<\/span>u<\/span>n<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>（j=1..nij = 1..n_i<\/span><\/span>j<\/span><\/span>=<\/span><\/span><\/span><\/span>1..<\/span>n<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）\u3002
    \n\u51fd\u6570\u540d\u7531\u5b57\u6bcd\u7ec4\u6210，\u533a\u5206\u5927\u5c0f\u5199\u3002\u62ec\u53f7\u4e4b\u95f4\u3001\u51fd\u6570\u540d\u4e4b\u95f4\u53ef\u4ee5\u6709\u4efb\u610f\u6570\u91cf\u7684\u7a7a\u683c\u3001\u5236\u8868\u7b26\u6216\u6362\u884c\u3002
    \n\u6bcf\u7ec4\u6570\u636e\u4ee5\u53e5\u70b9 . \u7ed3\u5c3e，\u8f93\u5165\u6b63\u786e（\u6bcf\u4e2a\u51fd\u6570\u6070\u597d\u51fa\u73b0\u5728\u4e00\u4e2a\u9879\u7684\u5de6\u4fa7，\u540c\u4e00\u9879\u5185\u51fd\u6570\u540d\u4e92\u4e0d\u76f8\u540c）\u3002
    \n\u5982\u679c\u4e00\u7ec4\u6570\u636e\u4e0d\u542b\u4efb\u4f55\u62ec\u53f7，\u5219\u8868\u793a\u7a7a\u51fd\u6570\u96c6（\u4f8b\u5982\u4ec5\u4e00\u4e2a .）\u3002<\/p>\n

    \u8f93\u51fa\u683c\u5f0f<\/h3>\n

    \u5bf9\u4e8e\u6bcf\u7ec4\u6570\u636e，\u8f93\u51fa\u82e5\u5e72\u884c，\u6bcf\u884c\u4e00\u4e2a\u6a21\u5757\u5185\u7684\u51fd\u6570\u540d（\u5347\u5e8f\u6392\u5217，\u7a7a\u683c\u5206\u9694）\u3002
    \n\u6a21\u5757\u4e4b\u95f4\u6309\u5404\u81ea\u6700\u5c0f\u51fd\u6570\u540d\u7684\u5b57\u5178\u5e8f\u5347\u5e8f\u8f93\u51fa\u3002
    \n\u6bcf\u7ec4\u6570\u636e\u7684\u8f93\u51fa\u7ed3\u675f\u540e\u5fc5\u987b\u8f93\u51fa\u4e00\u4e2a\u7a7a\u884c（\u5373\u4f7f\u8be5\u7ec4\u6ca1\u6709\u51fd\u6570，\u4e5f\u8981\u8f93\u51fa\u4e00\u4e2a\u7a7a\u884c）\u3002<\/p>\n

    \u6837\u4f8b<\/h3>\n

    \u8f93\u5165<\/p>\n

    .<\/p>\n

    (a a) (a b) (b).<\/p>\n

    (a b c) (b a e) (c d)
    \n(d d) (e b).<\/p>\n

    \u8f93\u51fa<\/p>\n

    a
    \nb<\/p>\n

    a b e
    \nc
    \nd<\/p>\n

    \u9898\u76ee\u5206\u6790<\/h3>\n

    \u89c4\u5219 1\\\\texttt{1}<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span> \u548c\u89c4\u5219 2\\\\texttt{2}<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span> \u5171\u540c\u5b9a\u4e49\u4e86\u6a21\u5757\u7684\u5212\u5206\u6807\u51c6：\u82e5\u4e24\u4e2a\u51fd\u6570\u76f8\u4e92\u53ef\u8fbe（\u5373 A\u21d2BA \\\\Rightarrow B<\/span><\/span>A<\/span><\/span>\u21d2<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u4e14 B\u21d2AB \\\\Rightarrow A<\/span><\/span>B<\/span><\/span>\u21d2<\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>），\u5219\u5b83\u4eec\u5fc5\u987b\u5728\u540c\u4e00\u6a21\u5757；\u5426\u5219\u7edd\u5bf9\u4e0d\u80fd\u5728\u540c\u4e00\u6a21\u5757\u3002\u8fd9\u6b63\u662f\u6709\u5411\u56fe\u4e2d\u5f3a\u8fde\u901a\u5206\u91cf（Strongly\u00a0Connected\u00a0Component\\\\texttt{Strongly Connected Component}<\/span><\/span>Strongly\u00a0Connected\u00a0Component<\/span><\/span><\/span><\/span><\/span><\/span>, SCC\\\\texttt{SCC}<\/span><\/span>SCC<\/span><\/span><\/span><\/span><\/span><\/span>） \u7684\u5b9a\u4e49\u3002
    \n\u56e0\u6b64，\u5c06\u6bcf\u4e2a\u51fd\u6570\u770b\u4f5c\u8282\u70b9，\u76f4\u63a5\u8c03\u7528\u5173\u7cfb A\u2192BA \\\\rightarrow B<\/span><\/span>A<\/span><\/span>\u2192<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u770b\u4f5c\u4ece AA<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u5230 BB<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u7684\u6709\u5411\u8fb9，\u5219\u4e00\u4e2a\u6a21\u5757\u5373\u5bf9\u5e94\u4e00\u4e2a\u5f3a\u8fde\u901a\u5206\u91cf\u3002
    \n\u7531\u4e8e \u21d2\\\\Rightarrow<\/span><\/span>\u21d2<\/span><\/span><\/span><\/span><\/span> \u662f \u2192\\\\rightarrow<\/span><\/span>\u2192<\/span><\/span><\/span><\/span><\/span> \u7684\u4f20\u9012\u95ed\u5305，\u540c\u4e00\u5f3a\u8fde\u901a\u5206\u91cf\u5185\u7684\u4efb\u610f\u4e24\u4e2a\u8282\u70b9\u76f8\u4e92\u53ef\u8fbe，\u7b26\u5408\u89c4\u5219 1；\u4e0d\u540c\u5f3a\u8fde\u901a\u5206\u91cf\u4e4b\u95f4\u7684\u8282\u70b9\u4e0d\u5b58\u5728\u53cc\u5411\u53ef\u8fbe\u8def\u5f84，\u7b26\u5408\u89c4\u5219 2\\\\texttt{2}<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

    \u56e0\u6b64，\u95ee\u9898\u8f6c\u5316\u4e3a：\u7ed9\u5b9a\u6709\u5411\u56fe，\u6c42\u6240\u6709\u5f3a\u8fde\u901a\u5206\u91cf，\u5e76\u6309\u9898\u76ee\u8981\u6c42\u6392\u5e8f\u8f93\u51fa\u3002<\/p>\n

    \u89e3\u9898\u601d\u8def<\/h3>\n

    \u56fe\u6784\u5efa<\/h4>\n

    \u9996\u5148\u9700\u4ece\u8f93\u5165\u4e2d\u63d0\u53d6\u6bcf\u4e2a\u51fd\u6570\u53ca\u5176\u76f4\u63a5\u8c03\u7528\u5217\u8868\u3002\u8f93\u5165\u4e3a\u81ea\u7531\u683c\u5f0f，\u4f46\u4ee5\u53e5\u70b9 . \u5206\u9694\u6bcf\u7ec4\u6570\u636e\u3002
    \n\u6211\u4eec\u53ef\u4ee5\u5148\u8bfb\u5165\u6574\u4e2a\u6570\u636e\u96c6（\u76f4\u5230\u9047\u5230 .）\u4e3a\u4e00\u4e2a\u5b57\u7b26\u4e32，\u518d\u901a\u8fc7\u67e5\u627e\u62ec\u53f7 ( \u548c ) \u6765\u63d0\u53d6\u6bcf\u4e2a\u62ec\u53f7\u5185\u7684\u5185\u5bb9\u3002\u6bcf\u4e2a\u62ec\u53f7\u5185\u90e8\u662f\u4e00\u4e2a\u7a7a\u683c\u5206\u9694\u7684\u5355\u8bcd\u5e8f\u5217，\u7b2c\u4e00\u4e2a\u5355\u8bcd\u4e3a\u6e90\u51fd\u6570，\u5176\u4f59\u4e3a\u76ee\u6807\u51fd\u6570\u3002
    \n\u4e3a\u6bcf\u4e2a\u51fd\u6570\u5206\u914d\u552f\u4e00\u7f16\u53f7，\u5efa\u7acb\u90bb\u63a5\u8868\u3002<\/p>\n

    \u5f3a\u8fde\u901a\u5206\u91cf\u6c42\u89e3<\/h4>\n

    \u4f7f\u7528 Tarjan\\\\texttt{Tarjan}<\/span><\/span>Tarjan<\/span><\/span><\/span><\/span><\/span><\/span> \u7b97\u6cd5\u6c42 SCC\\\\texttt{SCC}<\/span><\/span>SCC<\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u8be5\u7b97\u6cd5\u901a\u8fc7\u4e00\u6b21\u6df1\u5ea6\u4f18\u5148\u641c\u7d22（DFS\\\\texttt{DFS}<\/span><\/span>DFS<\/span><\/span><\/span><\/span><\/span><\/span>），\u8bb0\u5f55\u6bcf\u4e2a\u8282\u70b9\u7684 dfn\\\\textit{dfn}<\/span><\/span>dfn<\/span><\/span><\/span><\/span><\/span><\/span>（\u8bbf\u95ee\u6b21\u5e8f）\u548c low\\\\textit{low}<\/span><\/span>low<\/span><\/span><\/span><\/span><\/span><\/span>（\u80fd\u56de\u6eaf\u5230\u7684\u6700\u65e9\u7956\u5148）\u3002\u5f53 dfn[u]=low[u]\\\\textit{dfn}[u] = \\\\textit{low}[u]<\/span><\/span>dfn<\/span><\/span>[<\/span>u<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>low<\/span><\/span>[<\/span>u<\/span>]<\/span><\/span><\/span><\/span><\/span> \u65f6，\u6808\u4e2d\u4ece\u6808\u9876\u5230 uu<\/span><\/span>u<\/span><\/span><\/span><\/span><\/span> \u7684\u6240\u6709\u8282\u70b9\u6784\u6210\u4e00\u4e2a\u5f3a\u8fde\u901a\u5206\u91cf\u3002
    \n\u590d\u6742\u5ea6\u4e3a O(V+E)O(V + E)<\/span><\/span>O<\/span>(<\/span>V<\/span><\/span>+<\/span><\/span><\/span><\/span>E<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d VV<\/span><\/span>V<\/span><\/span><\/span><\/span><\/span> \u4e3a\u51fd\u6570\u6570，EE<\/span><\/span>E<\/span><\/span><\/span><\/span><\/span> \u4e3a\u76f4\u63a5\u8c03\u7528\u8fb9\u6570\u3002<\/p>\n

    \u6392\u5e8f\u4e0e\u8f93\u51fa<\/h4>\n

    \u6bcf\u4e2a SCC\\\\texttt{SCC}<\/span><\/span>SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5185\u90e8\u51fd\u6570\u540d\u6309\u5b57\u5178\u5e8f\u6392\u5e8f，\u6574\u4e2a SCC\\\\texttt{SCC}<\/span><\/span>SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5217\u8868\u6309\u5176\u6700\u5c0f\u51fd\u6570\u540d\u7684\u5b57\u5178\u5e8f\u6392\u5e8f\u3002
    \n\u8f93\u51fa\u65f6，\u6bcf\u4e2a SCC\\\\texttt{SCC}<\/span><\/span>SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5360\u4e00\u884c，\u51fd\u6570\u540d\u7528\u7a7a\u683c\u5206\u9694，\u672b\u5c3e\u6362\u884c\u3002\u6bcf\u7ec4\u6570\u636e\u7ed3\u675f\u540e\u989d\u5916\u8f93\u51fa\u4e00\u4e2a\u7a7a\u884c\u3002<\/p>\n

    \u590d\u6742\u5ea6\u5206\u6790<\/h4>\n
      \n
    • \u89e3\u6790\u8f93\u5165：\u6bcf\u4e2a\u5b57\u7b26\u6216\u5355\u8bcd\u8bfb\u5165\u4e00\u6b21，\u65f6\u95f4\u590d\u6742\u5ea6 O(\u8f93\u5165\u603b\u957f\u5ea6)O(\\\\text{\u8f93\u5165\u603b\u957f\u5ea6})<\/span><\/span>O<\/span>(<\/span>\u8f93\u5165\u603b\u957f\u5ea6<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n
    • \u5efa\u56fe：\u6bcf\u4e2a\u62ec\u53f7\u9879\u5904\u7406\u4e00\u6b21，\u603b\u8fb9\u6570 EE<\/span><\/span>E<\/span><\/span><\/span><\/span><\/span>，\u65f6\u95f4\u590d\u6742\u5ea6 O(E)O(E)<\/span><\/span>O<\/span>(<\/span>E<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n
    • Tarjan\\\\texttt{Tarjan}<\/span><\/span>Tarjan<\/span><\/span><\/span><\/span><\/span><\/span>：O(V+E)O(V + E)<\/span><\/span>O<\/span>(<\/span>V<\/span><\/span>+<\/span><\/span><\/span><\/span>E<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n
    • \u6392\u5e8f：\u6bcf\u4e2a SCC\\\\texttt{SCC}<\/span><\/span>SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5185\u90e8\u6392\u5e8f，\u603b\u4ee3\u4ef7 O(\u2211kilog\u2061ki)\u2264O(Vlog\u2061V)O(\\\\sum k_i \\\\log k_i) \\\\le O(V \\\\log V)<\/span><\/span>O<\/span>(<\/span>\u2211<\/span><\/span>k<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>log<\/span><\/span><\/span>k<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>O<\/span>(<\/span>V<\/span><\/span>log<\/span><\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span><\/span>；\u5916\u90e8\u6392\u5e8f O(Clog\u2061C)O(C \\\\log C)<\/span><\/span>O<\/span>(<\/span>C<\/span><\/span>log<\/span><\/span><\/span>C<\/span>)<\/span><\/span><\/span><\/span><\/span>，CC<\/span><\/span>C<\/span><\/span><\/span><\/span><\/span> \u4e3a SCC\\\\texttt{SCC}<\/span><\/span>SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u6570\u91cf，C\u2264VC \\\\le V<\/span><\/span>C<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>V<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n
    • \u603b\u65f6\u95f4\u590d\u6742\u5ea6 O(V+E+Vlog\u2061V)O(V + E + V \\\\log V)<\/span><\/span>O<\/span>(<\/span>V<\/span><\/span>+<\/span><\/span><\/span><\/span>E<\/span><\/span>+<\/span><\/span><\/span><\/span>V<\/span><\/span>log<\/span><\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span><\/span>，\u7a7a\u95f4\u590d\u6742\u5ea6 O(V+E)O(V + E)<\/span><\/span>O<\/span>(<\/span>V<\/span><\/span>+<\/span><\/span><\/span><\/span>E<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n

      \u4ee3\u7801\u5b9e\u73b0<\/h3>\n

      \/\/ Program Modules<\/span>
      \n\/\/ UVa ID: 792<\/span>
      \n\/\/ Verdict: Accepted<\/span>
      \n\/\/ Submission Date: 2026-07-09<\/span>
      \n\/\/ UVa Run Time: 0.300s<\/span>
      \n\/\/<\/span>
      \n\/\/ \u7248\u6743\u6240\u6709（C）2026，\u90b1\u79cb\u3002metaphysis # yeah dot net<\/span><\/p>\n

      #<\/span>include<\/span> <bits\/stdc++.h><\/span><\/span>
      \nusing<\/span> namespace<\/span> std;<\/span><\/p>\n

      vector<<\/span>string><\/span> splitByWhitespace<\/span>(<\/span>const<\/span> string&<\/span> s)<\/span> {<\/span>
      \n vector<<\/span>string><\/span> tokens;<\/span>
      \n stringstream ss<\/span>(<\/span>s)<\/span>;<\/span>
      \n string token;<\/span>
      \n while<\/span> (<\/span>ss >><\/span> token)<\/span> tokens.<\/span>push_back<\/span>(<\/span>token)<\/span>;<\/span>
      \n return<\/span> tokens;<\/span>
      \n}<\/span><\/p>\n

      int<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
      \n ios::<\/span>sync_with_stdio<\/span>(<\/span>false<\/span>)<\/span>;<\/span>
      \n cin.<\/span>tie<\/span>(<\/span>nullptr<\/span>)<\/span>;<\/span>
      \n string data,<\/span> token;<\/span>
      \n while<\/span> (<\/span>cin >><\/span> token)<\/span> {<\/span>
      \n data =<\/span> token;<\/span>
      \n while<\/span> (<\/span>1<\/span>)<\/span> {<\/span>
      \n if<\/span> (<\/span>token.<\/span>back<\/span>(<\/span>)<\/span> ==<\/span> '.'<\/span>)<\/span> break<\/span>;<\/span>
      \n cin >><\/span> token;<\/span>
      \n data +=<\/span> ' '<\/span> +<\/span> token;<\/span>
      \n }<\/span>
      \n vector<<\/span>string><\/span> names;<\/span>
      \n unordered_map<<\/span>string,<\/span> int<\/span>><\/span> idMap;<\/span>
      \n vector<<\/span>vector<<\/span>int<\/span>>><\/span> g;<\/span>
      \n auto<\/span> getNode =<\/span> [<\/span>&<\/span>]<\/span>(<\/span>const<\/span> string&<\/span> name)<\/span> -><\/span> int<\/span> {<\/span>
      \n auto<\/span> it =<\/span> idMap.<\/span>find<\/span>(<\/span>name)<\/span>;<\/span>
      \n if<\/span> (<\/span>it !=<\/span> idMap.<\/span>end<\/span>(<\/span>)<\/span>)<\/span> return<\/span> it-><\/span>second;<\/span>
      \n int<\/span> newId =<\/span> (<\/span>int<\/span>)<\/span>names.<\/span>size<\/span>(<\/span>)<\/span>;<\/span>
      \n idMap[<\/span>name]<\/span> =<\/span> newId;<\/span>
      \n names.<\/span>push_back<\/span>(<\/span>name)<\/span>;<\/span>
      \n g.<\/span>push_back<\/span>(<\/span>{<\/span>}<\/span>)<\/span>;<\/span>
      \n return<\/span> newId;<\/span>
      \n }<\/span>;<\/span>
      \n size_t pos =<\/span> 0<\/span>;<\/span>
      \n while<\/span> (<\/span>true<\/span>)<\/span> {<\/span>
      \n size_t left =<\/span> data.<\/span>find<\/span>(<\/span>'('<\/span>,<\/span> pos)<\/span>;<\/span>
      \n if<\/span> (<\/span>left ==<\/span> string::<\/span>npos)<\/span> break<\/span>;<\/span>
      \n size_t right =<\/span> data.<\/span>find<\/span>(<\/span>')'<\/span>,<\/span> left +<\/span> 1<\/span>)<\/span>;<\/span>
      \n string inner =<\/span> data.<\/span>substr<\/span>(<\/span>left +<\/span> 1<\/span>,<\/span> right –<\/span> left –<\/span> 1<\/span>)<\/span>;<\/span>
      \n vector<<\/span>string><\/span> tokens =<\/span> splitByWhitespace<\/span>(<\/span>inner)<\/span>;<\/span>
      \n if<\/span> (<\/span>tokens.<\/span>empty<\/span>(<\/span>)<\/span>)<\/span> {<\/span>
      \n pos =<\/span> right +<\/span> 1<\/span>;<\/span>
      \n continue<\/span>;<\/span>
      \n }<\/span>
      \n int<\/span> srcId =<\/span> getNode<\/span>(<\/span>tokens[<\/span>0<\/span>]<\/span>)<\/span>;<\/span>
      \n for<\/span> (<\/span>size_t i =<\/span> 1<\/span>;<\/span> i <<\/span> tokens.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> {<\/span>
      \n int<\/span> tId =<\/span> getNode<\/span>(<\/span>tokens[<\/span>i]<\/span>)<\/span>;<\/span>
      \n g[<\/span>srcId]<\/span>.<\/span>push_back<\/span>(<\/span>tId)<\/span>;<\/span>
      \n }<\/span>
      \n pos =<\/span> right +<\/span> 1<\/span>;<\/span>
      \n }<\/span>
      \n int<\/span> n =<\/span> names.<\/span>size<\/span>(<\/span>)<\/span>;<\/span>
      \n vector<<\/span>int<\/span>><\/span> dfn<\/span>(<\/span>n,<\/span> 0<\/span>)<\/span>,<\/span> low<\/span>(<\/span>n,<\/span> 0<\/span>)<\/span>,<\/span> sccId<\/span>(<\/span>n,<\/span> –<\/span>1<\/span>)<\/span>,<\/span> stk;<\/span>
      \n vector<<\/span>char<\/span>><\/span> inStack<\/span>(<\/span>n,<\/span> 0<\/span>)<\/span>;<\/span>
      \n int<\/span> timer =<\/span> 0<\/span>,<\/span> sccCnt =<\/span> 0<\/span>;<\/span>
      \n function<<\/span>void<\/span>(<\/span>int<\/span>)<\/span>><\/span> tarjan =<\/span> [<\/span>&<\/span>]<\/span>(<\/span>int<\/span> u)<\/span> {<\/span>
      \n dfn[<\/span>u]<\/span> =<\/span> low[<\/span>u]<\/span> =<\/span> ++<\/span>timer;<\/span>
      \n stk.<\/span>push_back<\/span>(<\/span>u)<\/span>;<\/span>
      \n inStack[<\/span>u]<\/span> =<\/span> 1<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> v :<\/span> g[<\/span>u]<\/span>)<\/span> {<\/span>
      \n if<\/span> (<\/span>!<\/span>dfn[<\/span>v]<\/span>)<\/span> {<\/span>
      \n tarjan<\/span>(<\/span>v)<\/span>;<\/span>
      \n low[<\/span>u]<\/span> =<\/span> min<\/span>(<\/span>low[<\/span>u]<\/span>,<\/span> low[<\/span>v]<\/span>)<\/span>;<\/span>
      \n }<\/span> else<\/span> if<\/span> (<\/span>inStack[<\/span>v]<\/span>)<\/span> {<\/span>
      \n low[<\/span>u]<\/span> =<\/span> min<\/span>(<\/span>low[<\/span>u]<\/span>,<\/span> dfn[<\/span>v]<\/span>)<\/span>;<\/span>
      \n }<\/span>
      \n }<\/span>
      \n if<\/span> (<\/span>low[<\/span>u]<\/span> ==<\/span> dfn[<\/span>u]<\/span>)<\/span> {<\/span>
      \n ++<\/span>sccCnt;<\/span>
      \n while<\/span> (<\/span>true<\/span>)<\/span> {<\/span>
      \n int<\/span> v =<\/span> stk.<\/span>back<\/span>(<\/span>)<\/span>;<\/span> stk.<\/span>pop_back<\/span>(<\/span>)<\/span>;<\/span>
      \n inStack[<\/span>v]<\/span> =<\/span> 0<\/span>;<\/span>
      \n sccId[<\/span>v]<\/span> =<\/span> sccCnt;<\/span>
      \n if<\/span> (<\/span>v ==<\/span> u)<\/span> break<\/span>;<\/span>
      \n }<\/span>
      \n }<\/span>
      \n }<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> if<\/span> (<\/span>!<\/span>dfn[<\/span>i]<\/span>)<\/span> tarjan<\/span>(<\/span>i)<\/span>;<\/span>
      \n vector<<\/span>vector<<\/span>string>><\/span> sccNodes<\/span>(<\/span>sccCnt +<\/span> 1<\/span>)<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> sccNodes[<\/span>sccId[<\/span>i]<\/span>]<\/span>.<\/span>push_back<\/span>(<\/span>names[<\/span>i]<\/span>)<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <=<\/span> sccCnt;<\/span> ++<\/span>i)<\/span> sort<\/span>(<\/span>sccNodes[<\/span>i]<\/span>.<\/span>begin<\/span>(<\/span>)<\/span>,<\/span> sccNodes[<\/span>i]<\/span>.<\/span>end<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
      \n vector<<\/span>int<\/span>><\/span> order<\/span>(<\/span>sccCnt)<\/span>;<\/span>
      \n iota<\/span>(<\/span>order.<\/span>begin<\/span>(<\/span>)<\/span>,<\/span> order.<\/span>end<\/span>(<\/span>)<\/span>,<\/span> 1<\/span>)<\/span>;<\/span>
      \n sort<\/span>(<\/span>order.<\/span>begin<\/span>(<\/span>)<\/span>,<\/span> order.<\/span>end<\/span>(<\/span>)<\/span>,<\/span> [<\/span>&<\/span>]<\/span>(<\/span>int<\/span> a,<\/span> int<\/span> b)<\/span> {<\/span>
      \n return<\/span> sccNodes[<\/span>a]<\/span>[<\/span>0<\/span>]<\/span> <<\/span> sccNodes[<\/span>b]<\/span>[<\/span>0<\/span>]<\/span>;<\/span>
      \n }<\/span>)<\/span>;<\/span>
      \n for<\/span> (<\/span>int<\/span> idx :<\/span> order)<\/span> {<\/span>
      \n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> (<\/span>int<\/span>)<\/span>sccNodes[<\/span>idx]<\/span>.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>j)<\/span> {<\/span>
      \n if<\/span> (<\/span>j)<\/span> cout <<<\/span> ' '<\/span>;<\/span>
      \n cout <<<\/span> sccNodes[<\/span>idx]<\/span>[<\/span>j]<\/span>;<\/span>
      \n }<\/span>
      \n cout <<<\/span> '\\\\n'<\/span>;<\/span>
      \n }<\/span>
      \n cout <<<\/span> '\\\\n'<\/span>;<\/span>
      \n }<\/span>
      \n return<\/span> 0<\/span>;<\/span>
      \n}<\/span><\/p>\n

      \u603b\u7ed3<\/h3>\n

      \u672c\u9898\u672c\u8d28\u662f\u56fe\u8bba\u4e2d\u7684\u5f3a\u8fde\u901a\u5206\u91cf\u6c42\u89e3，\u76f4\u63a5\u5e94\u7528 Tarjan\\\\texttt{Tarjan}<\/span><\/span>Tarjan<\/span><\/span><\/span><\/span><\/span><\/span> \u7b97\u6cd5\u5373\u53ef\u3002
      \n\u5173\u952e\u70b9\u5728\u4e8e\u6b63\u786e\u89e3\u6790\u8f93\u5165\u683c\u5f0f，\u5c06\u81ea\u7531\u683c\u5f0f\u7684\u62ec\u53f7\u8868\u8fbe\u5f0f\u8f6c\u5316\u4e3a\u6709\u5411\u56fe\u3002
      \n\u8f93\u51fa\u90e8\u5206\u9700\u6ce8\u610f\u6392\u5e8f\u89c4\u5219（\u6a21\u5757\u5185\u5347\u5e8f\u3001\u6a21\u5757\u95f4\u6309\u6700\u5c0f\u5143\u7d20\u5347\u5e8f）\u548c\u6bcf\u7ec4\u6570\u636e\u540e\u7684\u7a7a\u884c\u3002
      \n\u6b64\u9898\u63d0\u9192\u6211\u4eec，\u590d\u6742\u95ee\u9898\u5f80\u5f80\u80fd\u5f52\u7ed3\u4e3a\u7ecf\u5178\u7b97\u6cd5，\u53ea\u8981\u51c6\u786e\u5efa\u6a21，\u5b9e\u73b0\u5e76\u4e0d\u56f0\u96be\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

      \u9898\u76ee\u63cf\u8ff0
      \n\u7ed9\u5b9a\u4e00\u4e2a\u7a0b\u5e8f\u4e2d\u7684\u6240\u6709\u51fd\u6570\u53ca\u5176\u76f4\u63a5\u8c03\u7528\u5173\u7cfb，\u5b9a\u4e49\u5173\u7cfb A\u2192BA \\\\rightarrow BA\u2192B \u8868\u793a\u51fd\u6570 AAA \u76f4\u63a5\u8c03\u7528 BBB，A\u21d2BA \\\\Rightarrow BA\u21d2B \u8868\u793a AAA \u53ef\u4f20\u9012\u5730\u8c03\u7528 BBB（\u76f4\u63a5\u6216\u95f4\u63a5）\u3002\u5df2\u77e5 \u2192\\\\rightarrow\u2192 \u662f \u21d2\\\\Rightarrow\u21d2 \u7684\u5b50\u96c6，\u4e14 \u21d2\\\\Rightarrow\u21d2 \u5177\u6709\u4f20\u9012\u6027\u3002
      \n\u73b0\u9700\u8981\u5c06\u6240\u6709\u51fd\u6570\u5212\u5206\u4e3a\u82e5\u5e72\u6a21\u5757，\u6ee1\u8db3&#<\/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":[55,427,4405],"topic":[],"class_list":["post-121222","post","type-post","status-publish","format-standard","hentry","category-server","tag-c","tag-427","tag-4405"],"yoast_head":"\nUVa 792 Program Modules - \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\/121222.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"UVa 792 Program Modules - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u9898\u76ee\u63cf\u8ff0 \u7ed9\u5b9a\u4e00\u4e2a\u7a0b\u5e8f\u4e2d\u7684\u6240\u6709\u51fd\u6570\u53ca\u5176\u76f4\u63a5\u8c03\u7528\u5173\u7cfb，\u5b9a\u4e49\u5173\u7cfb A\u2192BA \\rightarrow BA\u2192B \u8868\u793a\u51fd\u6570 AAA \u76f4\u63a5\u8c03\u7528 BBB，A\u21d2BA \\Rightarrow BA\u21d2B \u8868\u793a AAA \u53ef\u4f20\u9012\u5730\u8c03\u7528 BBB（\u76f4\u63a5\u6216\u95f4\u63a5）\u3002\u5df2\u77e5 \u2192\\rightarrow\u2192 \u662f \u21d2\\Rightarrow\u21d2 \u7684\u5b50\u96c6，\u4e14 \u21d2\\Rightarrow\u21d2 \u5177\u6709\u4f20\u9012\u6027\u3002 \u73b0\u9700\u8981\u5c06\u6240\u6709\u51fd\u6570\u5212\u5206\u4e3a\u82e5\u5e72\u6a21\u5757，\u6ee1\u8db3&#\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/121222.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-11-02T02:24:46+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/121222.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/121222.html\",\"name\":\"UVa 792 Program Modules - 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