{"id":1077,"date":"2021-04-19T23:21:03","date_gmt":"2021-04-19T15:21:03","guid":{"rendered":"http:\/\/www.zyhcoding.club\/?p=1077"},"modified":"2021-04-20T21:09:54","modified_gmt":"2021-04-20T13:09:54","slug":"cf710f-string-set-queries","status":"publish","type":"post","link":"http:\/\/www.zyhcoding.club\/index.php\/2021\/04\/19\/cf710f-string-set-queries\/","title":{"rendered":"CF710F String Set Queries"},"content":{"rendered":"

CF710F String Set Queries AC\u81ea\u52a8\u673a+\u4e8c\u8fdb\u5236\u5206\u7ec4<\/a><\/h3>\n

\u9898\u610f\uff1a\u8f93\u5165n\u8868\u793a\u64cd\u4f5c\u6570\uff0c\u67093\u79cd\u64cd\u4f5c\u3002\u8bbe\u8ba1\u4e00\u4e2a\u5b57\u7b26\u4e32\u96c6\u5408\uff0c
\n1 x \u5728\u96c6\u5408\u4e2d\u63d2\u5165\u5b57\u7b26\u4e32x
\n2 x \u5728\u96c6\u5408\u4e2d\u5220\u9664\u5b57\u7b26\u4e32x(\u4fdd\u8bc1\u5220\u9664\u4e4b\u524dx\u5b58\u5728)
\n3 x \u8be2\u95ee\u5f53\u524d\u96c6\u5408\u4e2d\u5b57\u7b26\u4e32\u5728x\u4e2d\u51fa\u73b0\u6b21\u6570(\u8ba1\u7b97\u91cd\u590d)
\n\u5f3a\u5236\u5728\u7ebf\uff0c\\sum x_{i} <= 3e5<\/code>
\n\u591a\u5b57\u7b26\u4e32\u5339\u914d\uff0cAC\u81ea\u52a8\u673a\uff0c\u4f46AC\u81ea\u52a8\u673a\u4e0d\u652f\u6301\u5728\u7ebf\u6dfb\u52a0\u4e0e\u5220\u9664\u5b57\u7b26\u4e32\uff0c\u6240\u4ee5\u4f7f\u7528\u4e8c\u8fdb\u5236\u5206\u7ec4\uff0c\u5e76\u4e14\u521b\u5efa\u4e24\u7ec4AC\u81ea\u52a8\u673a\u3002\u81ea\u52a8\u673a\u7ec4A\u7528\u6765\u5b58\u653e\u5df2\u7ecf\u6dfb\u52a0\u7684\u5b57\u7b26\u4e32\uff0cB\u7528\u6765\u5b58\u653e\u5df2\u7ecf\u5220\u9664\u7684\u5b57\u7b26\u4e32\uff0cA-B\u5c31\u662f\u7b54\u6848\u3002
\n\u4e8c\u8fdb\u5236\u5206\u7ec4\uff0c\u5373\u5171\u521b\u5efalogn\u7ec4\u81ea\u52a8\u673a\uff0c\u7f16\u53f7\u4f9d\u6b21\u4e3a0,1,2\u00b7\u00b7\u00b7 \u6bcf\u6b21\u57280\u53f7\u81ea\u52a8\u673a\u63d2\u5165\u4e00\u4e2a\u5b57\u7b26\u4e32\uff0c\u82e50\u53f7\u81ea\u52a8\u673a\u672c\u6765\u5c31\u5b58\u5728\uff0c\u90a3\u4e48\u5c31\u628a0\u53f7\u548c1\u53f7\u5408\u5e76\uff0c0\u53f7\u81ea\u52a8\u673a\u6b64\u65f6\u5df2\u9500\u6bc1\uff0c\u82e51\u53f7\u5b58\u5728\uff0c\u5219\u7ee7\u7eed\u5408\u5e76\u00b7\u00b7\u00b7\uff0c\u53ef\u4ee5\u60f3\u5230i<\/code>\u53f7\u81ea\u52a8\u673a\u662f\u75312^i<\/code>\u4e2a\u5b57\u7b26\u4e32\u6784\u5efa\u6210\u7684\uff0c\u6240\u4ee5\u53ea\u9700\u8981nlogn<\/code>\u4e2a\u81ea\u52a8\u673a\u5c31\u53ef\u6536\u7eb3n<\/code>\u4e2a\u5b57\u7b26\u4e32\uff0c\u4e14\u540c\u4e00\u65f6\u523b\u6bcf\u4e2a\u5b57\u7b26\u4e32\u6700\u591a\u5b58\u5728\u4e8e\u4e00\u4e2a\u81ea\u52a8\u673a\u4e2d\u3002\u6bcf\u4e2a\u5b57\u7b26\u4e32\u6700\u591a\u4f1a\u88ab\u5408\u5e76logn<\/code>\u6b21\uff0c\u6bcf\u6b21\u63d2\u5165\u5b8c\u6210\u540e\uff0c\u5c31build\u4e00\u4e0b\uff0c\u6bcf\u4e2a\u5b57\u7b26\u4e32\u6700\u591a\u88abbuild\u4e5f\u662flogn<\/code>\u6b21\u3002\u7136\u540e\u8be2\u95ee\u65f6\uff0c\u628a\u6bcd\u4e32\u5728\u6bcf\u4e2a\u81ea\u52a8\u673a\u4e0a\u90fd\u8dd1\u4e00\u904d\uff0c\u4e5f\u662flogn<\/code>\u6b21\uff0c\u6700\u7ec8\u5e73\u5747\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(logn)<\/code>\u3002<\/p>\n

\u4ee3\u7801\u5b9e\u73b0<\/h6>\n

\u8fd9\u91cc\u9762\u6700\u96be\u5b9e\u73b0\u7684\u5c31\u662f\u5408\u5e76\u4e24\u4e2a\u81ea\u52a8\u673a\u8fd9\u90e8\u5206\uff0c\u56e0\u4e3aAC\u81ea\u52a8\u673a\u662f\u5728Trie\u6811\u4e0a\u5efa\u7acb\u8d77\u6765\u7684\uff0c\u4f46\u5e76\u4e0d\u5b8c\u5168\u662fTrie\u6811\uff0c\u6bcf\u4e2a\u7ed3\u70b9\u7684\u67d0\u4e2a\u5b69\u5b50\u7ed3\u70b9\u53ef\u80fd\u662f\u5b9e\u9645\u5b58\u5728\u7684\uff0c\u5373\u5b58\u5728\u5b57\u7b26\u4e32\u7ecf\u8fc7\u5176\u5b69\u5b50\u7ed3\u70b9\uff0c\u4f46\u4e5f\u53ef\u80fd\u662f\u8be5\u5b69\u5b50\u7ed3\u70b9\u4e0d\u5b58\u5728\uff0c\u800c\u4e3a\u4e86\u5339\u914d\u52a0\u901f\u8be5\u5b69\u5b50\u7ed3\u70b9\u4e5f\u4f1a\u6709\u503c\uff0c\u6307\u5411\u4e00\u4e2a\u5b58\u5728\u7684\u7ed3\u70b9\uff0c\u4e5f\u5c31\u662f\u8bf4AC\u81ea\u52a8\u673a\u7684Trie\u6811\u4e2d\u5305\u542b\u4e24\u7c7b\u7ed3\u70b9\uff1a\u4e00\u4e2a\u662f\u5728\u63d2\u5165\u5b57\u7b26\u4e32\u65f6\u5efa\u7acb\u7684\u5b9e\u7ed3\u70b9\uff0c\u4e00\u4e2a\u662f\u5728AC\u81ea\u52a8\u673a\u7684build<\/code>\u64cd\u4f5c\u4e2d\u5efa\u7acb\u7684\u865a\u7ed3\u70b9\uff0c\u7528\u6765\u52a0\u901f\u5339\u914d<\/strong>\u3002\u5408\u5e76\u4e24\u4e2a\u81ea\u52a8\u673a\u65f6\u662f\u4e0d\u8003\u8651\u865a\u7ed3\u70b9\u7684\uff0c\u6240\u4ee5\u5728\u63d2\u5165\u5b57\u7b26\u4e32\u65f6\u8981\u5bf9Trie\u6811\u4e2d\u7684\u7ed3\u70b9\u8fdb\u884c\u865a\u5b9e\u6807\u8bb0\uff0c\u4fbf\u4e8e\u5408\u5e76\u65f6\u4f7f\u7528\u3002<\/p>\n

\n

\u65b0\u5f00\u53d1\u7684AC\u81ea\u52a8\u673a\u7684\u6027\u8d28\uff1a\u5f53\u4f7f\u7528\u6bcd\u4e32\u626b\u63cfAC\u81ea\u52a8\u673a\u65f6\uff0c\u626b\u63cf\u5230\u67d0\u4e2a\u7ed3\u70b9\uff0c\u5728fail\u6811\u4e2d\u4ece\u8be5\u7ed3\u70b9\u4e00\u76f4\u5230\u6839\u7ed3\u70b9\u7684\u8def\u5f84\u4e2d\uff0c\u7ec8\u7ed3\u70b9\u7684\u4e2a\u6570\u5c31\u662f\u81ea\u52a8\u673a\u4e2d\u5b57\u7b26\u4e32\u7684\u51fa\u73b0\u6b21\u6570\uff0c\u8fd9\u4e2a\u6b21\u6570\u4ec5\u4ec5\u662f\u8be5\u7ed3\u70b9\u7684\u8d21\u732e\uff0c\u6240\u6709\u626b\u63cf\u5230\u7684\u7ed3\u70b9\u7684\u8d21\u732e\u52a0\u8d77\u6765\u5c31\u662f\u6240\u6709\u6a21\u677f\u4e32\u5728\u6bcd\u4e32\u4e2d\u7684\u51fa\u73b0\u6b21\u6570<\/strong><\/p>\n<\/blockquote>\n

#include <bits\/stdc++.h>\n\nusing namespace std;\n\nconst int maxn = 1e5+5;\n\n\/\/ AC\u81ea\u52a8\u673a\u5305\u88c5\u6210\u4e00\u4e2a\u7ed3\u6784\u4f53  Trie\u4e3aTrie\u6811\uff0cfail\u8868\u793afail\u5931\u914d\u6307\u9488\uff0ccnt\u8868\u793a\u7ed3\u70b9\u4f7f\u7528\u4e2a\u6570\uff0cend\u8868\u793a\u6709\u591a\u5c11\u4e2a\u5b57\u7b26\u4e32\u7ec8\u7ed3\u4e8e\u6b64\u7ed3\u70b9\nstruct AC_auto {\n    int Trie[maxn][27], fail[maxn], cnt, val[maxn], end[maxn]; \/\/val\u8868\u793a\u67d0\u4e2a\u7ed3\u70b9\u7684\u6743\u503c\uff0c\u5373\u6bcd\u4e32\u626b\u63cf\u81ea\u52a8\u673a\u8fc7\u7a0b\u4e2d\u626b\u63cf\u5230\u8be5\u7ed3\u70b9\uff0c\u5bf9\u7b54\u6848\u6240\u8d21\u732e\u7684\u6743\u503c\n    \/\/ val[i]\u7684\u503c\u7b49\u4e8efail\u6811\u4e2d\u4ece\u8be5\u7ed3\u70b9\u5230\u6839\u8282\u70b9\u7684\u8def\u5f84\u4e0aend\u4e4b\u548c\n    bool mk[maxn][27];                             \/\/ mk\u5bf9\u5e94\u4e8etrie\u6811\uff0c\u8868\u793a\u67d0\u7ed3\u70b9\u7684\u67d0\u4e2a\u5b69\u5b50\u7ed3\u70b9\u662f\u5426\u4e3a\u771f\u7ed3\u70b9\n    void insert(char *s, int len) {\n        int root = 0;\n        for (int i=1; i<=len; i++) {\n            if (!mk[root][s[i]-'a'+1]) {\n                Trie[root][s[i]-'a'+1] = ++cnt;\n                mk[root][s[i]-'a'+1] = true;\n            }\n            root = Trie[root][s[i]-'a'+1];\n        }\n        end[root] += 1;\n        return;\n    }\n    void build() {\n        queue<int> q;\n        for (int i=0; i<=cnt; i++)  val[i] = end[i];\n        for (int i=1; i<27; i++) {\n            fail[Trie[0][i]] = 0;\n            if (mk[0][i])\n                q.push(Trie[0][i]);\n        }\n        while (!q.empty()) {\n            int tmp = q.front();    q.pop();\n            val[tmp] += val[fail[tmp]];\n            for (int i=1; i<27; i++) {\n                if (mk[tmp][i]) {\n                    fail[Trie[tmp][i]] = Trie[fail[tmp]][i];\n                    q.push(Trie[tmp][i]);\n                }else   Trie[tmp][i] = Trie[fail[tmp]][i];\n            }\n        }\n        return;\n    }\n    int query(char *s, int len) {\n        int ans = 0, root = 0;\n        for (int i=1; i<=len; i++) {\n            root = Trie[root][s[i]-'a'+1];\n            ans += val[root];\n        }\n        return ans;\n    }\n    \/\/ AC\u81ea\u52a8\u673a\u9500\u6bc1\uff0c\u628a\u6bcf\u4e2a\u5b9e\u7ed3\u70b9\u7684\u5b69\u5b50\u7ed3\u70b9\u6307\u5411\u7684\u503c\u90fd\u8d4b0\uff0c\u6bcf\u4e2a\u5b9e\u7ed3\u70b9\u7684\u5404\u4e2a\u5c5e\u6027(fail, end, val)\u90fd\u8d4b0\u5373\u53ef\n    void destory() {\n        for (int i=0; i<=cnt; i++){\n            for (int j=1; j<27; j++)\n                Trie[i][j] = 0, mk[i][j] = false;\n            fail[i] = 0;\n            val[i] = 0;\n            end[i] = 0;\n        }\n        cnt = 0;\n        return;\n    }\n};\nstruct zyh{\n    struct AC_auto ACAM[19];\n    bool vis[20];                \/\/ vis[i]=true\u8868\u793ai\u53f7\u81ea\u52a8\u673a\u5b58\u5728\n    void insert(char *s, int len) {\n        ACAM[0].insert(s, len);\n        if (!vis[0]) {\n            ACAM[0].build();\n            vis[0] = true;\n            return;\n        }\n        int i=0;\n        for ( ; ; i++) {\n            if (!vis[i+1])    break;\n            merge(ACAM[i], ACAM[i+1]);\n            vis[i] = false;\n            ACAM[i].destory();\n        }\n        merge(ACAM[i], ACAM[i+1]);\n        ACAM[i].destory();\n        ACAM[i+1].build();\n        vis[i] = false, vis[i+1] = true;\n        return;\n    }\n    int query(char *s, int len) {\n        int ans = 0;\n        for (int i=0; i<19; i++) if (vis[i])\n            ans += ACAM[i].query(s, len);\n        return ans;\n    }\n    \/\/ \u5408\u5e76\u4e24\u7ec4\u81ea\u52a8\u673a\uff0c\u628ax\u52a0\u5230y\u4e0a\uff0cx\u662f\u4e0d\u53d8\u7684\n    void merge(const struct AC_auto &x, struct AC_auto &y) {\n        dfs(x, y, 0, 0);\n        return;\n    }\n    void dfs(const struct AC_auto &x, struct AC_auto &y, int a, int b) {\n        for (int i=1; i<27; i++)    if (x.mk[a][i]){\n            if (!y.mk[b][i]) {\n                y.Trie[b][i] = ++y.cnt;\n                y.mk[b][i] = true;\n            }\n            y.end[y.Trie[b][i]] += x.end[x.Trie[a][i]];\n            dfs(x, y, x.Trie[a][i], y.Trie[b][i]);\n        }\n        return;\n    }\n}A, B;\nint m, t, len;\nchar s[300005];\n\nint main () {\n    scanf ("%d", &m);\n    while (m--) {\n        scanf ("%d %s", &t, s+1);\n        len = strlen(s+1);\n        if (t==1)   A.insert(s, len);\n        else if (t==2)  B.insert(s, len);\n        else {\n            printf ("%d\\n", A.query(s, len) - B.query(s, len));\n            \/\/cout << A.query(s, len) - B.query(s, len) << endl;\n            fflush(stdout);\n        }\n    }\n    return 0;\n}<\/code><\/pre>\n
\u4f7f\u7528fflush(stdout)<\/code>\u8bed\u53e5\u53ef\u4ee5\u5f3a\u5236\u628a\u7f13\u5b58\u533a\u7684\u5185\u5bb9\u8f93\u51fa\uff0c\u800c\u4e0d\u662f\u628a\u6240\u6709\u8f93\u5165\u90fd\u8bfb\u5b8c\u4e4b\u540e\u624d\u5f00\u59cb\u8f93\u51fa\uff0c\u8fd9\u6837\u5c31\u4f1a\u8fbe\u5230\u5f3a\u5236\u5728\u7ebf\u7684\u76ee\u7684\u3002cout<\/code>\u8bed\u53e5\u5728\u6267\u884c\u5b8c\u6210\u540e\u4f1a\u81ea\u52a8\u68c0\u67e5\u4e00\u6b21\u7f13\u51b2\u533a\uff0c\u4f7f\u7528cout<\/code>\u5c31\u4e0d\u9700\u8981\u4f7f\u7528fflush(stdout)<\/code>\u4e86<\/p>\n","protected":false},"excerpt":{"rendered":"
CF710F String Set Queries AC\u81ea\u52a8\u673a+\u4e8c\u8fdb\u5236\u5206\u7ec4 \u9898\u610f\uff1a\u8f93\u5165n\u8868\u793a\u64cd\u4f5c\u6570\uff0c […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[11],"tags":[70],"_links":{"self":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/1077"}],"collection":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/comments?post=1077"}],"version-history":[{"count":26,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/1077\/revisions"}],"predecessor-version":[{"id":1079,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/1077\/revisions\/1079"}],"wp:attachment":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/media?parent=1077"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/categories?post=1077"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/tags?post=1077"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}