{"id":787,"date":"2026-04-21T01:06:57","date_gmt":"2026-04-20T17:06:57","guid":{"rendered":"http:\/\/wordpress.fangt.online\/?p=787"},"modified":"2026-04-25T01:01:25","modified_gmt":"2026-04-24T17:01:25","slug":"%e7%b4%a0%e6%95%b0%e7%ad%9b-2-%e6%ac%a7%e6%8b%89%e7%ad%9b%ef%bc%88%e7%ba%bf%e6%80%a7%e7%ad%9b%ef%bc%89%e5%af%b9%e6%af%94","status":"publish","type":"post","link":"http:\/\/wordpress.fangt.online\/index.php\/2026\/04\/21\/%e7%b4%a0%e6%95%b0%e7%ad%9b-2-%e6%ac%a7%e6%8b%89%e7%ad%9b%ef%bc%88%e7%ba%bf%e6%80%a7%e7%ad%9b%ef%bc%89%e5%af%b9%e6%af%94\/","title":{"rendered":"\u7d20\u6570\u7b5b\uff1a\u6b27\u62c9\u7b5b"},"content":{"rendered":"\n

\u6b27\u62c9\u7b5b\u662f\u57c3\u6c0f\u7b5b\u7684\u4f18\u5316\u7248\u672c\uff0c\u6838\u5fc3\u601d\u60f3\u662f\u6bcf\u4e2a\u5408\u6570\u53ea\u88ab\u5b83\u7684\u6700\u5c0f\u8d28\u56e0\u5b50\u7b5b\u6389\u4e00\u6b21\uff0c\u4ece\u800c\u5b9e\u73b0\u771f\u6b63\u7684\u7ebf\u6027\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\u3002<\/p>\n\n\n\n

\u57fa\u672c\u539f\u7406<\/h3>\n\n\n\n

\u6bcf\u4e2a\u5408\u6570\u53ea\u4f1a\u88ab\u5b83\u7684\u6700\u5c0f\u8d28\u56e0\u5b50\u7b5b\u6389\u3002<\/p>\n\n\n\n

\u5b9e\u73b0\u8981\u70b9\uff1a<\/p>\n\n\n\n

    \n
  1. \u7ef4\u62a4\u4e00\u4e2a\u7d20\u6570\u5217\u8868 primes<\/code><\/li>\n\n\n\n
  2. \u904d\u5386\u6bcf\u4e2a\u6570 i<\/code>\uff08\u4ece2\u5230n\uff09<\/li>\n\n\n\n
  3. \u7528\u5f53\u524d\u7d20\u6570\u5217\u8868\u4e2d\u7684\u7d20\u6570 p<\/code> \u4e0e i<\/code> \u76f8\u4e58\uff0c\u6807\u8bb0\u5408\u6570<\/li>\n\n\n\n
  4. \u5f53 i % p == 0<\/code> \u65f6\u505c\u6b62\uff08\u4fdd\u8bc1\u6700\u5c0f\u8d28\u56e0\u5b50\u539f\u5219\uff09<\/li>\n<\/ol>\n\n\n\n

    \u57fa\u7840\u5b9e\u73b0<\/h3>\n\n\n\n
    const int N = 105;\nbool isPrime[N] = {0, 0};\nfor (int i = 2; i < N; i++) isPrime[i] = true;\nint primes[N], t = 0; \/\/ \u8d28\u6570\u8868\n    \nfor (int i = 2; i <= n; i++) {\n    if (isPrime[i]) {\n        primes[t++] = i;  \/\/ i\u662f\u7d20\u6570\uff0c\u52a0\u5165\u5217\u8868\n    }\n    \/\/ \u7528\u5f53\u524d\u7d20\u6570\u53bb\u6807\u8bb0\u5408\u6570\n    for (int p = 0; p < t && i * p <= n; p++) {\n        isPrime[i * primes[p]] = false;  \/\/ \u6807\u8bb0\u5408\u6570\n        \/\/ \u5173\u952e\uff1a\u5982\u679cp\u662fi\u7684\u6700\u5c0f\u8d28\u56e0\u5b50\uff0c\u505c\u6b62\n        if (i % primes[p] == 0) break;\n    }\n}<\/code><\/pre>\n\n\n\n
    \u6807\u51c6\u5b9e\u73b0<\/h3>\n\n\n\n
    vector<int> eulersieve(int n) {\n    vector<bool> isPrime(n + 1, true);\n    vector<int> primes;\n    isPrime[0] = isPrime[1] = false;\n    for (int i = 2; i <= n; i++) {\n        if (isPrime[i]) {\n            primes.push_back(i);  \/\/ i\u662f\u7d20\u6570\uff0c\u52a0\u5165\u5217\u8868\n        }\n        \/\/ \u7528\u5f53\u524d\u7d20\u6570\u53bb\u6807\u8bb0\u5408\u6570\n        for (int p : primes) {\n            if (i * p > n) break;  \/\/ \u8d85\u51fa\u8303\u56f4\n            isPrime[i * p] = false;  \/\/ \u6807\u8bb0\u5408\u6570\n            \/\/ \u5173\u952e\uff1a\u5982\u679cp\u662fi\u7684\u6700\u5c0f\u8d28\u56e0\u5b50\uff0c\u505c\u6b62\n            if (i % p == 0) break;\n        }\n    }\n    return primes;\n}\nvector<int> primes = eulersieve(n);<\/code><\/pre>\n\n\n\n
    \u65f6\u95f4\u590d\u6742\u5ea6\u4e0e\u7a7a\u95f4\u590d\u6742\u5ea6<\/h3>\n\n\n\n
      \n
    • \u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(n)<\/li>\n\n\n\n
    • \u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(n)<\/li>\n<\/ul>\n\n\n\n
      \u5e94\u7528\u573a\u666f<\/h3>\n\n\n\n
      1. \u5feb\u901f\u5206\u89e3\u8d28\u56e0\u6570<\/h4>\n\n\n\n
      2. \u7ebf\u6027\u7b5b\u6b27\u62c9\u51fd\u6570 \u03c6(n)<\/h4>\n\n\n\n
      3. \u7ebf\u6027\u7b5b\u83ab\u6bd4\u4e4c\u65af\u51fd\u6570 \u03bc(n)<\/h4>\n\n\n\n
      4. \u7ebf\u6027\u7b5b\u7ea6\u6570\u4e2a\u6570 d(n)<\/h4>\n\n\n\n
      \u57c3\u6c0f\u7b5b vs \u6b27\u62c9\u7b5b<\/h3>\n\n\n\n
      \u7279\u6027<\/th>\u57c3\u6c0f\u7b5b<\/th>\u6b27\u62c9\u7b5b<\/th><\/tr><\/thead>
      \u65f6\u95f4\u590d\u6742\u5ea6<\/td>O(n log log n)<\/td>O(n)<\/td><\/tr>
      \u5e38\u6570\u56e0\u5b50<\/td>\u5c0f<\/td>\u8f83\u5927<\/td><\/tr>
      \u7a7a\u95f4\u590d\u6742\u5ea6<\/td>O(n)<\/td>O(n)<\/td><\/tr>
      \u5b9e\u73b0\u590d\u6742\u5ea6<\/td>\u7b80\u5355<\/td>\u4e2d\u7b49<\/td><\/tr>
      \u5b9e\u9645\u901f\u5ea6\uff08n\u22641e7\uff09<\/td>\u5feb<\/td>\u7565\u5feb<\/td><\/tr>
      \u5b9e\u9645\u901f\u5ea6\uff08n\u22641e8\uff09<\/td>\u8f83\u6162<\/td>\u5feb<\/td><\/tr>
      \u53ef\u6269\u5c55\u6027<\/td>\u5bb9\u6613\u5e76\u884c\u5316<\/td>\u96be\u4ee5\u5e76\u884c\u5316<\/td><\/tr>
      \u989d\u5916\u4fe1\u606f<\/td>\u4ec5\u7d20\u6570\u5224\u65ad<\/td>\u53ef\u83b7\u5f97\u6700\u5c0f\u8d28\u56e0\u5b50\u7b49<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
      \u9009\u62e9\u5efa\u8bae<\/h3>\n\n\n\n
        \n
      1. n \u2264 10^7<\/strong>\uff1a\u4e24\u8005\u5dee\u522b\u4e0d\u5927\uff0c\u9009\u57c3\u6c0f\u7b5b\uff08\u4ee3\u7801\u7b80\u5355\uff09<\/li>\n\n\n\n
      2. n > 10^7<\/strong>\uff1a\u9009\u6b27\u62c9\u7b5b\uff08\u771f\u6b63\u7684\u7ebf\u6027\uff09<\/li>\n\n\n\n
      3. \u9700\u8981\u6700\u5c0f\u8d28\u56e0\u5b50<\/strong>\uff1a\u5fc5\u987b\u7528\u6b27\u62c9\u7b5b<\/li>\n\n\n\n
      4. \u9700\u8981\u7b5b\u79ef\u6027\u51fd\u6570<\/strong>\uff08\u6b27\u62c9\u51fd\u6570\u3001\u83ab\u6bd4\u4e4c\u65af\u51fd\u6570\u7b49\uff09\uff1a\u5fc5\u987b\u7528\u6b27\u62c9\u7b5b<\/li>\n\n\n\n
      5. \u5185\u5b58\u53d7\u9650<\/strong>\uff1a\u57c3\u6c0f\u7b5b\u53ef\u7528 bitset \u4f18\u5316<\/li>\n<\/ol>\n\n\n\n
        <\/p>\n","protected":false},"excerpt":{"rendered":"
        \u6b27\u62c9\u7b5b\u662f\u57c3\u6c0f\u7b5b\u7684\u4f18\u5316\u7248\u672c\uff0c\u6838\u5fc3\u601d\u60f3\u662f\u6bcf\u4e2a\u5408\u6570\u53ea\u88ab\u5b83\u7684\u6700\u5c0f\u8d28\u56e0\u5b50\u7b5b\u6389\u4e00\u6b21\uff0c\u4ece\u800c\u5b9e\u73b0\u771f\u6b63\u7684\u7ebf\u6027\u65f6\u95f4\u590d\u6742\u5ea6 O(n) […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[61],"tags":[],"class_list":["post-787","post","type-post","status-publish","format-standard","hentry","category-zl"],"_links":{"self":[{"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/posts\/787","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/comments?post=787"}],"version-history":[{"count":8,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/posts\/787\/revisions"}],"predecessor-version":[{"id":888,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/posts\/787\/revisions\/888"}],"wp:attachment":[{"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/media?parent=787"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/categories?post=787"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/tags?post=787"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}