{"id":837,"date":"2023-11-09T21:07:45","date_gmt":"2023-11-09T13:07:45","guid":{"rendered":"http:\/\/ggapa.net:81\/?p=837"},"modified":"2023-11-09T23:45:50","modified_gmt":"2023-11-09T15:45:50","slug":"lca-%e9%97%ae%e9%a2%98%e7%9a%84%e4%b8%8d%e5%90%8c%e8%a7%a3%e6%b3%95","status":"publish","type":"post","link":"http:\/\/ggapa.net:81\/2023\/11\/09\/lca-%e9%97%ae%e9%a2%98%e7%9a%84%e4%b8%8d%e5%90%8c%e8%a7%a3%e6%b3%95\/","title":{"rendered":"LCA \u95ee\u9898\u7684\u4e0d\u540c\u89e3\u6cd5"},"content":{"rendered":"

0 \u5e8f<\/h1>\n

\u4e3a\u4e86\u5f3a\u5316\u7b14\u8005\u5bf9LCA\u7684\u7406\u89e3\uff0c\u6545\u4f5c\u6b64\u6587\u3002<\/p>\n

1 DFS\u5e8f\u6c42LCA<\/h1>\n

1.1 \u7b97\u6cd5\u4ecb\u7ecd<\/h2>\n

\u8003\u8651\u6811\u4e0a\u7684\u4e24\u4e2a\u8282\u70b9 $u$, $v$ \u548c\u5176\u7956\u5148 $d$\uff0c\u6211\u4eec\u4e4b\u6240\u4ee5\u4f7f\u7528\u6b27\u62c9\u5e8f\u6c42\u89e3 LCA \u662f\u56e0\u4e3a\u5728\u6b27\u62c9\u5e8f\u4e2d $d$ \u4e00\u5b9a\u5728 $u,v$ \u4e4b\u95f4\u51fa\u73b0\u3002\u4f46\u5bf9\u4e8e DFS \u5e8f\u6765\u8bf4\uff0c$d$ \u4e00\u5b9a\u5728 $u,v$ \u4e4b\u524d\u51fa\u73b0\u3002<\/p>\n

\u4ee4 $u$ \u7684 DFN \u5c0f\u4e8e $v$\uff0c\u4e14 $u\\ne v$ \u3002<\/p>\n

\u5f53 $u\uff0cv$ \u6ca1\u6709\u7956\u5148\u5173\u7cfb\u65f6\u3002\u5728 DFN \u4e2d\u6700\u5148\u51fa\u73b0\u7684\u662f $d$ \uff0c\u5176\u6b21\u662f $u$\uff0c\u6700\u540e\u662f $v$ \u3002\u8bbe $v'$ \u662f $d$ \u7684\u513f\u5b50\u3002\u6839\u636e DFS \u7684\u7279\u6027\u53ef\u77e5\uff0c$v'$ \u5728 $u\\sim v$ \u7684 DFN \u5e8f\u4e4b\u95f4\u3002<\/p>\n

\u8fd9\u610f\u5473\u7740\u6211\u4eec\u53ea\u9700\u8981\u6c42\u51fa $u \\sim v$ \u7684 DFS \u5e8f\u4e4b\u95f4\u6df1\u5ea6\u6700\u5c0f\u7684\u4e00\u4e2a\u8282\u70b9\uff0c\u90a3\u4e48\u4ed6\u7684\u7236\u4eb2\u4fbf\u662f\u6211\u4eec\u82e6\u82e6\u5bfb\u627e\u7684 LCA\u3002<\/p>\n

\u5982\u4f55\u4fdd\u8bc1\u8fd9\u4e2a\u65b9\u6cd5\u7684\u6b63\u786e\u6027\uff1f\u5728 $u\\sim v$ \u7684 DFS \u5e8f\u4e4b\u95f4\uff0c$d$ \u4e00\u5b9a\u4e0d\u4f1a\u5b58\u5728\uff0c\u800c $d$ \u7684\u513f\u5b50\u4e00\u5b9a\u5b58\u5728\u3002<\/p>\n

\u5f53 $u, v$ \u5b58\u5728\u7956\u5148\u5173\u7cfb\uff0c\u8fd9\u66f4\u5bb9\u6613\u5224\u65ad\u4e86\uff0c\u6839\u636e\u5b9a\u4e49\uff0c $u$ \u4e00\u5b9a\u662f $v$ \u7684\u7956\u5148\u3002\u67e5\u8be2\u7684\u5e8f\u5217\u7531 $[dfn_u,dfn_v]$ \u53d8\u6210 $[dfn_u+1,dfn_v]$ \u3002\u4e3a\u4ec0\u4e48\u8981 "$+1$"\uff1f\u6839\u636e\u4e0a\u4e00\u79cd\u60c5\u51b5\u53ef\u77e5\uff0c\u6b64\u65f6\u7684\u7956\u5148\u662f $u$ \uff0c\u4f46\u6b64\u65f6\u6df1\u5ea6\u6700\u5c0f\u7684\u8282\u70b9\u4e00\u5b9a\u662f $u$\uff0c\u5982\u679c\u5728\u8fd9\u65f6\u53d6\u5b83\u7684\u7236\u4eb2\uff0c\u5f88\u660e\u663e\u4e0d\u662f\u6211\u4eec\u8981\u627e\u7684\u6b63\u786e\u7b54\u6848\u3002<\/p>\n

\u5f88\u663e\u7136\uff0c\u5f53$u\uff0cv$ \u6ca1\u6709\u7956\u5148\u5173\u7cfb\u65f6\uff0c $u$ \u4e00\u5b9a\u4e0d\u7b49\u4e8e $d'$ \uff0c\u6240\u4ee5\u521a\u521a\u63d0\u51fa\u7684\u7ed3\u8bba\u9002\u7528 $u$ \u7684 DFN \u5c0f\u4e8e $v$\uff0c\u4e14 $u\\ne v$ \u6240\u6709\u7684\u60c5\u51b5\u3002<\/p>\n

\u82e5 $u=v$ \u65f6\uff0c\u5b83\u4eec\u7684 LCA \u4e00\u5b9a\u662f $u$ \uff0c\u8fd9\u662f\u552f\u4e00\u4e00\u79cd\u9700\u8981\u7279\u5224\u7684\u60c5\u51b5\u3002<\/p>\n

\u7efc\u4e0a\u6240\u8ff0\uff0c\u82e5 $u\\ne v$ \uff0c$u,v$ \u7684 LCA \u662f $[dfn_u,dfn_v]$ \u4e2d\u6df1\u5ea6\u6700\u5c0f\u7684\u70b9\u7684\u7236\u4eb2\uff0c\u82e5 $u=v$ \u65f6\uff0c$u,v$ \u7684 LCA \u662f $u$\u3002<\/p>\n

1.2\u7b97\u6cd5\u5b9e\u73b0<\/h2>\n

\u53ef\u4ee5\u901a\u8fc7 ST \u8868\u6765\u67e5\u8be2 $[dfn_u,dfn_v]$ \u4e2d\u6df1\u5ea6\u6700\u5c0f\u7684\u70b9\u3002\u65f6\u95f4\u590d\u6742\u5ea6 $O(nlogn)$ \u3002<\/p>\n

\u4ee5\u4e0b\u662f\u6a21\u677f\u9898\u76ee P3379 <\/a> \u7684\u4ee3\u7801\uff1a<\/p>\n

\/\/ P3379 \u3010\u6a21\u677f\u3011\u6700\u8fd1\u516c\u5171\u7956\u5148\uff08LCA\uff09\n\/\/ https:\/\/www.luogu.com.cn\/problem\/P3379\n\/\/ 2023-11-09 21:40\n#include <iostream>\n#include <vector>\n#include <cmath>\nusing namespace std;\nconst int maxn = 500000 + 5;\n\nint n, m, s;\nvector<int> G[maxn];\nint dfn[maxn], mi[20][maxn];\n\nint get(int x, int y) {\n    return dfn[x] < dfn[y] ? x : y;\n}\n\nvoid dfs(int x, int f) {\n    dfn[x] = ++dfn[0]; mi[0][dfn[x]] = f;\n    for(auto to : G[x]) if(to != f) dfs(to, x);\n}\n\nint lca(int x, int y) {\n    if(x == y) return x;\n    if((x = dfn[x]) > (y = dfn[y])) swap(x, y);\n    int d = log2(y - x++);\n    return get(mi[d][x], mi[d][y - (1 << d) + 1]);\n}\n\nint main() {\n    ios::sync_with_stdio(0);\n    cin.tie(0);\n    cout.tie(0);\n    \/\/ freopen("AKIOI.in", "r", stdin);\n    \/\/ freopen("AKIOI.out", "w", stdout);\n    cin >> n >> m >> s;\n    for(int i = 1, u, v; i < n; i++)  {\n        cin >> u >> v;\n        G[u].push_back(v); G[v].push_back(u);\n    }\n    dfs(s, 0);\n    for(int i = 1; i <= log2(n); i++) for(int j = 1; j + (1 << i) - 1 <= n; j++) \n        mi[i][j] = get(mi[i - 1][j], mi[i - 1][j + (1 << i - 1)]);\n    while(m--) {\n        int x, y;\n        cin >> x >> y;\n        cout << lca(x, y) << "\\n";\n    }\n    return 0;\n}\n\n\/*\n\u7f16\u7a0b\u8bed\u8a00\nC++14 (GCC 9)\n\u4ee3\u7801\u957f\u5ea6\n1.25KB\n\u7528\u65f6\n1.64s\n\u5185\u5b58\n77.61MB\nGGapa\n\n\u6240\u5c5e\u9898\u76ee\nP3379 \u3010\u6a21\u677f\u3011\u6700\u8fd1\u516c\u5171\u7956\u5148\uff08LCA\uff09\n\u8bc4\u6d4b\u72b6\u6001\nAccepted\n\u8bc4\u6d4b\u5206\u6570\n100\n\u63d0\u4ea4\u65f6\u95f4\n2023-11-09 22:02:41\n*\/<\/code><\/pre>\n
2 \u6811\u94fe\u5256\u5206 LCA<\/h1>\n
2.1 \u7b97\u6cd5\u4ecb\u7ecd<\/h2>\n
\u5bf9\u4e8e\u4e00\u4e2a\u7236\u8282\u70b9\u7684\u6240\u6709\u513f\u5b50\u6765\u8bf4\uff0c\u5728\u5b83\u4eec\u4e4b\u95f4\u5b50\u6811\u5927\u5c0f\u6700\u5927\u7684\u4fbf\u662f\u91cd\u513f\u5b50<\/strong>($hson$)\uff0c\u5176\u4f59\u7684\u513f\u5b50\u662f\u8f7b\u513f\u5b50<\/strong>\u3002\u6211\u4eec\u53ef\u4ee5\u5bf9\u4e00\u68f5\u6811\u4e0a\u6240\u6709\u7684\u975e\u53f6\u5b50\u8282\u70b9\u8fdb\u884c\u64cd\u4f5c\uff0c\u6c42\u51fa\u4ed6\u4eec\u7684\u91cd\u513f\u5b50\u3002\u4ece\u4e00\u4e2a\u8282\u70b9 $u$ \u51fa\u53d1\uff0c\u6bcf\u6b21\u9012\u5f52\u5230\u4e0b\u4e00\u4e2a\u91cd\u513f\u5b50\u76f4\u5230\u53f6\u5b50\u8282\u70b9\u672a\u77e5\uff0c\u53ef\u5f97\u4e00\u4e2a\u9012\u5f52\u51fd\u6570 $f(x)=f(hson_x)$ \u3002\u5728\u9012\u5f52\u7684\u8fc7\u7a0b\u4e2d\u8bbf\u95ee\u5230\u7684\u8282\u70b9\u53ef\u4ee5\u8fde\u6210\u4e00\u6761\u94fe\uff0c\u8fd9\u6761\u94fe\u4fbf\u662f\u91cd\u94fe\u3002\u6bcf\u6761\u91cd\u94fe\u7684\u51fa\u53d1\u70b9\u88ab\u79f0\u4e3a $top$ \u3002<\/p>\n
\u8003\u8651\u6811\u4e0a\u7684\u4e24\u4e2a\u8282\u70b9 $u$, $v$ \u548c\u5176\u7956\u5148 $d$\uff0c<\/p>\n
    \n
  1. \u82e5 $top_u = top_v$ \u8fd9\u8bf4\u660e $u,v$ \u5728\u4e00\u6761\u91cd\u94fe\u4e0a\uff0c$u,v$ \u4e00\u5b9a\u5b58\u5728\u7956\u5148\u5173\u7cfb\uff0c\u6b64\u65f6 $u,v$ \u4e2d\u6df1\u5ea6\u8f83\u5c0f\u7684\u8282\u70b9\u4fbf\u662f\u4ed6\u4eec\u7684 LCA\u3002<\/li>\n
  2. \u5426\u5219\uff0c\u9700\u8981\u628a\u6df1\u5ea6\u8f83\u5927\u7684\u8282\u70b9\u8df3\u5230\u8fd9\u6761\u91cd\u94fe\u7684\u9876\u7aef\u3002\u5e76\u91cd\u590d\u6267\u884c\u64cd\u4f5c1\u3002<\/li>\n<\/ol>\n
    \u4e3a\u4ec0\u4e48\u4e0d\u80fd\u540c\u65f6\u5c06 $u, v$  \u4e0a\u8df3\uff1f\u4ee4 $u$ \u7684\u6df1\u5ea6\u5927\u4e8e $v$ \u56e0\u4e3a\u6709\u65f6\u6df1\u5ea6\u8f83\u5927\u7684\u8282\u70b9\u7684 $top$ \u4fbf\u662f $v$ \u6240\u5728\u7684\u91cd\u94fe\uff0c\u6bcf\u8df3\u4e00\u6b21\u90fd\u4f1a\u4f7f\u5b83\u79bb\u5f00\u5f53\u524d\u7684\u91cd\u94fe\u3002\u8fd9\u65f6 $v$ \u5f80\u4e0a\u8df3\u5c31\u4e0d\u80fd\u8fbe\u6210\u6761\u4ef6\uff0c\u6548\u7387\u4f4e\u4e0b\u3002<\/p>\n
    \u65f6\u95f4\u590d\u6742\u5ea6 $O(n\\log n)$<\/p>\n
    2.2 \u7b97\u6cd5\u5b9e\u73b0<\/h2>\n
    \u9700\u8981\u8fdb\u884c\u4e24\u6b21\u9012\u5f52\uff0c\u7b2c\u4e00\u6b21\u9012\u5f52\u6c42\u51fa\u6bcf\u4e2a\u975e\u53f6\u5b50\u8282\u70b9\u7684\u91cd\u513f\u5b50\uff1b\u7b2c\u4e8c\u6b21\u5faa\u73af\u6c42\u51fa $top$\uff0c\u4e5f\u5c31\u662f\u91cd\u94fe\u3002<\/p>\n
    \u4ee5\u4e0b\u662f\u6a21\u677f\u9898\u76ee P3379 <\/a> \u7684\u4ee3\u7801\uff1a<\/p>\n
    \/\/ P3379 \u3010\u6a21\u677f\u3011\u6700\u8fd1\u516c\u5171\u7956\u5148\uff08LCA\uff09\n\/\/ https:\/\/www.luogu.com.cn\/problem\/P3379\n\/\/ 2023-11-09 20:41\n#include <iostream>\n#include <vector>\nusing namespace std;\nconst int maxn = 500000 + 5;\n\nint n, m, s; \nvector<int> G[maxn];\nint si[maxn], top[maxn], hson[maxn], fa[maxn], dep[maxn];\n\nvoid dfs1(int x, int f) {\n    si[x] = 1; dep[x] = dep[f] + 1; fa[x] = f;\n    for(auto to : G[x]) {\n        if(to == f) continue;\n        dfs1(to, x);\n        si[x] += si[to];\n        if(si[to] > si[hson[x]]) hson[x] = to;\n    }\n}\n\nvoid dfs2(int x, int tp) {\n    top[x] = tp;\n    if(!hson[x]) return ;\n    dfs2(hson[x], tp);\n    for(auto to : G[x]) {\n        if(to == fa[x] || to == hson[x]) continue;\n         dfs2(to, to);       \n    }\n}\n\nint lca(int x, int y) {\n    while(top[x] != top[y]) {\n        if(dep[top[x]] < dep[top[y]]) swap(x, y);   \n        x = fa[top[x]];\n    }\n    return (dep[x] < dep[y] ? x : y);\n}\n\nint main() {\n    ios::sync_with_stdio(0);\n    cin.tie(0);\n    cout.tie(0);\n    \/\/ freopen("AKIOI.in", "r", stdin);\n    \/\/ freopen("AKIOI.out", "w", stdout);\n    cin >> n >> m >> s;\n    for(int i = 1, u, v; i < n; i++) {\n        cin >> u >> v;\n        G[u].push_back(v);\n        G[v].push_back(u);\n    }\n    dfs1(s, 0);\n    dfs2(s, s);\n    while(m--) {\n        int x, y;\n        cin >> x >> y;\n        cout << lca(x, y) << "\\n";\n    }\n    return 0;\n}\n\n\/*\n\u7f16\u7a0b\u8bed\u8a00\nC++14 (GCC 9)\n\u4ee3\u7801\u957f\u5ea6\n1.37KB\n\u7528\u65f6\n1.86s\n\u5185\u5b58\n55.85MB\nGGapa\n\n\u6240\u5c5e\u9898\u76ee\nP3379 \u3010\u6a21\u677f\u3011\u6700\u8fd1\u516c\u5171\u7956\u5148\uff08LCA\uff09\n\u8bc4\u6d4b\u72b6\u6001\nAccepted\n\u8bc4\u6d4b\u5206\u6570\n100\n\u63d0\u4ea4\u65f6\u95f4\n2023-11-09 21:04:30\n*\/<\/code><\/pre>\n
    3 \u500d\u589e LCA<\/h1>\n
    3.1 \u7b97\u6cd5\u4ecb\u7ecd<\/h2>\n
    \u76f8\u5bf9\u4e8e\u66b4\u529b\u7b97\u6cd5\uff0c\u500d\u589e LCA \u51cf\u5c11\u4e86\u5411\u4e0a\u8df3\u7684\u6b21\u6570\uff0c\u5982\u4f55\u51cf\u5c11\uff1f\u6bcf\u6b21\u4ece\u5927\u5230\u5c0f\u5c1d\u8bd5\u8df3 $2^i$ \u4e2a\u8282\u70b9\uff0c\u76f4\u5230\u5230\u8fbe\u76ee\u7684\u5730\u3002<\/p>\n
    \u4e3a\u4e86\u65b9\u4fbf\u8df3\uff0c\u9700\u8981\u8bb0\u5f55\u6bcf\u4e00\u4e2a\u8282\u70b9 $2^i$ \u7ea7\u7684\u7956\u5148\u3002<\/p>\n
    \u8003\u8651\u6811\u4e0a\u7684\u4e24\u4e2a\u8282\u70b9 $u$, $v$\uff0c\u9700\u8981\u5148\u4f7f $dep_u=dep_v$<\/p>\n
    \u63a5\u7740\uff0c\u4e24\u4e2a\u8282\u70b9\u540c\u65f6\u5f80\u4e0a\u8df3\uff0c\u76f4\u5230$fa{vi}=fa<\/em>{ui}$\u4e3a\u6b62\uff0c\u6b64\u65f6 $fau$ \u4fbf\u662f $u,v$ \u7684 LCA\u3002\u6709\u4e00\u70b9\u9700\u8981\u6ce8\u610f\uff0c\u8981\u8df3\u5230 $fa<\/em>{ui}=fa_{vi}$ \u800c\u4e0d\u662f $u=v$ \u662f\u4e3a\u4e86\u9632\u6b62\u8df3\u8fc7\u4e86\uff0c\u627e\u5230\u7684\u662f\u4ed6\u4eec\u7684\u516c\u5171\u7956\u5148\uff0c\u800c\u4e0d\u662f LCA\u3002<\/p>\n
    \u65f6\u95f4\u590d\u6742\u5ea6$O(n\\log n)$<\/p>\n
    3.2 \u7b97\u6cd5\u5b9e\u73b0<\/h2>\n
    \u4ee5\u4e0b\u662f\u6a21\u677f\u9898\u76ee P3379 <\/a> \u7684\u4ee3\u7801\uff1a<\/p>\n
    \/\/ P3379 \u3010\u6a21\u677f\u3011\u6700\u8fd1\u516c\u5171\u7956\u5148\uff08LCA\uff09\n\/\/ https:\/\/www.luogu.com.cn\/problem\/P3379\n#include <iostream>\n#include <vector>\n#include <algorithm>\n#include <cstring>\nusing namespace std;\nconst int maxn = 500000 + 5;\nconst int maxk = 21; \/\/ log2(maxn) + 1\n\nint fa[maxk][maxn];\nint depth[maxn];\nvector<int> vec[maxn];\n\nvoid dfs(int x, int f)\n{\n    fa[0][x] = f;\n    depth[x] = depth[f] + 1;\n    for (int i = 1; i < maxk; i++)\n    {\n        fa[i][x] = fa[i - 1][fa[i - 1][x]];\n    }\n    for (auto to : vec[x])\n    {\n        if (to == f)\n            continue;\n        dfs(to, x);\n    }\n}\n\nint LCA(int x, int y)\n{\n    if (depth[x] < depth[y])\n        swap(x, y);\n    for (int i = maxk - 1; i >= 0; i--)\n    {\n        if (depth[fa[i][x]] >= depth[y])\n            x = fa[i][x];\n    }\n    if (x == y)\n        return x;\n    for (int i = maxk - 1; i >= 0; i--)\n    {\n        if (fa[i][x] != fa[i][y])\n        {\n            x = fa[i][x];\n            y = fa[i][y];\n        }\n    }\n    return fa[0][x];\n}\n\nint main()\n{\n    ios::sync_with_stdio(0);\n    cin.tie(0);\n    cout.tie(0);\n    int n, m, s;\n    scanf("%d%d%d", &n, &m, &s);\n    for (int i = 1, x, y; i < n; i++)\n    {\n        scanf("%d%d", &x, &y);\n        vec[x].push_back(y);\n        vec[y].push_back(x);\n    }\n    dfs(s, 0);\n    for (int i = 0; i < m; i++)\n    {\n        int a, b;\n        scanf("%d%d", &a, &b);\n        cout << LCA(a, b) << endl;\n    }\n    return 0;\n}\n\/*\n\u7f16\u7a0b\u8bed\u8a00\nC++14 (GCC 9) O2\n\u4ee3\u7801\u957f\u5ea6\n1.43KB\n\u7528\u65f6\n5.53s\n\u5185\u5b58\n90.44MB\nGGapa\n\n\u6240\u5c5e\u9898\u76ee\nP3379 \u3010\u6a21\u677f\u3011\u6700\u8fd1\u516c\u5171\u7956\u5148\uff08LCA\uff09\n\u8bc4\u6d4b\u72b6\u6001\nAccepted\n\u8bc4\u6d4b\u5206\u6570\n100\n\u63d0\u4ea4\u65f6\u95f4\n2023-07-31 15:39:45\n*\/<\/code><\/pre>\n
    \u500d\u589e\u7684\u5e38\u6570\u5f88\u5927\uff0c\u6240\u4ee5\u8bf4\u82b1\u4e86\u63a5\u8fd1 5s\u3002<\/p>\n
    4 \u5404\u79cd LCA \u7b97\u6cd5\u7684\u5bf9\u6bd4<\/h1>\n
      \n
    • \n
      \u9884\u5904\u7406\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u76f8\u540c\uff0c\u5e38\u6570\u500d\u589e\u6700\u5927\u3002<\/p>\n<\/li>\n
    • \n
      \u5355\u6b21\u67e5\u8be2\u590d\u6742\u5ea6\uff1aDFS \u5e8f $<$ \u6811\u94fe\u5256\u5206 $=$ \u500d\u589e<\/p>\n<\/li>\n
    • \n
      \u5355\u6b21\u67e5\u8be2\u5e38\u6570\u5927\u5c0f\uff1a\u6811\u94fe\u5256\u5206 $<$ DFS \u5e8f $<$ \u500d\u589e<\/p>\n<\/li>\n
    • \n
      \u4e2a\u4eba\u8ba4\u4e3a DFS \u5e8f\u4ee3\u7801\u96be\u6613\u7a0b\u5ea6\u8f83\u4f4e\u3002<\/p>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"
      0 \u5e8f \u4e3a\u4e86\u5f3a\u5316\u7b14\u8005\u5bf9LCA\u7684\u7406\u89e3\uff0c\u6545\u4f5c\u6b64\u6587\u3002 1 DFS\u5e8f\u6c42LCA 1.1 \u7b97\u6cd5\u4ecb\u7ecd \u8003\u8651\u6811\u4e0a\u7684\u4e24\u4e2a\u8282\u70b9 $ […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[29],"_links":{"self":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/837"}],"collection":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/comments?post=837"}],"version-history":[{"count":2,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/837\/revisions"}],"predecessor-version":[{"id":844,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/837\/revisions\/844"}],"wp:attachment":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/media?parent=837"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/categories?post=837"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/tags?post=837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}