{"id":729,"date":"2024-07-12T09:00:00","date_gmt":"2024-07-12T01:00:00","guid":{"rendered":"https:\/\/seanxd.com\/?p=729"},"modified":"2024-06-05T17:55:47","modified_gmt":"2024-06-05T09:55:47","slug":"zerojudge-j242","status":"publish","type":"post","link":"https:\/\/seanxd.com\/zh\/zerojudge-j242\/","title":{"rendered":"ZeroJudge J242: \u81ea\u7136\u6578\u7684\u5e73\u65b9\u6839"},"content":{"rendered":"\n\n\n

\u8f38\u5165\u6b63\u6574\u6578 N\uff0c\u5c07\u300csqrt(N)\u300d\u8f49\u63db\u6210\u300ca sqrt(b)\u300d\u4e4b\u683c\u5f0f\uff0c\u5176\u4e2d a \u8207 b \u90fd\u662f\u6b63\u6574\u6578\uff0ca2<\/sup>b = N\uff0c\u4e14 b \u7684\u56e0\u6578\u4e0d\u70ba\u4efb\u4f55\u5e73\u65b9\u6578\uff0c\u4ea6\u5373\uff0c\u5c0d\u4efb\u4f55\u81ea\u7136\u6578 x\uff0cx2<\/sup> \u4e0d\u80fd\u6574\u9664 b\u3002\u4f8b\u5982\uff1asqrt(12) = 2 sqrt(3)\uff0csqrt(15) = sqrt(15)\uff0csqrt(100) = 10\u3002<\/p>\n\n\n\n

\u7bc4\u4f8b\u6e2c\u8cc7<\/h2>\n\n\n\n
\u7bc4\u4f8b\u8f38\u5165<\/th>\u7bc4\u4f8b\u8f38\u51fa<\/th><\/tr><\/thead>
\u6bcf\u4e00\u7d44\u6e2c\u8a66\u8cc7\u6599\u50c5\u6709 1 \u500b\u6b63\u6574\u6578 N\u30021 < N < 231<\/sup>\u3002<\/td>\u8f38\u51fa\u70ba\u300ca sqrt(b)\u300d\uff0c\u4e26\u6ce8\u610f\uff1a
1\uff09 \u82e5 a = 1 \u5247\u4e0d\u5370\u51fa a\u3002
2\uff09 \u82e5 b = 1 \u5247\u4e0d\u5370\u51fa sqrt(b)\u3002
3\uff09 \u5728 a \u8207 sqrt \u4e4b\u9593\u7559\u4e00\u7a7a\u767d\uff0c\u5176\u9918\u5747\u7121\u7a7a\u767d\u3002<\/td><\/tr>
12<\/td>2 sqrt(3)<\/td><\/tr>
15<\/td>sqrt(15)<\/td><\/tr>
100<\/td>10<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u89e3\u984c\u601d\u8def<\/h2>\n\n\n\n

\u5148\u5224\u65b7 N \u662f\u5426\u70ba\u5b8c\u5168\u5e73\u65b9\u6578\uff0c\u5982\u679c pow(sqrt(N), 2) == N\uff0c\u4ee3\u8868 N \u70ba\u5b8c\u5168\u5e73\u65b9\u6578\uff0c\u76f4\u63a5\u8f38\u51fa sqrt(N) \u5373\u53ef\u3002<\/p>\n\n\n\n

\u5982\u679c N \u4e0d\u662f\u5b8c\u5168\u5e73\u65b9\u6578\uff0c\u9810\u8a2d\u5169\u500b\u8b8a\u6578 a = 1\u3001b = N\uff0c\u5169\u500b\u8b8a\u6578\u90fd\u9700\u8981 Long Long Int\u3002\u8dd1\u4e00\u500b While\u8ff4\u5708\uff0c\u4e26\u4e14\u8dd1\u4e00\u500b For\u8ff4\u5708\u4e26\u8dd1\u6bcf\u4e00\u500b\u5b8c\u5168\u5e73\u65b9\u6578\uff0c\u53ef\u4ee5\u5ba3\u544a\u4e00\u500b\u8b8a\u6578 plus \u70ba 3\uff0c\u4e26\u4e14\u5c07 For\u8ff4\u5708 \u5beb\u6210\uff1a\u300cfor (int i = 4; i<=N; i+=plus)\u300d\uff0c\u4e26\u4e14\u5728\u6bcf\u4e00\u6b21\u8ff4\u5708\u7d50\u675f\u4e4b\u5f8c\u5c07 plus += 2\u3002<\/p>\n\n\n\n

For\u8ff4\u5708 \u6bcf\u6b21\u90fd\u53ea\u6703\u8dd1\u5230\u5b8c\u5168\u5e73\u65b9\u6578\uff0c\u53ea\u8981\u5224\u65b7 i \u662f\u5426\u70ba b \u7684\u56e0\u6578\uff0c\u5982\u679c i \u70ba N \u7684\u56e0\u6578\uff0c\u5247\u5c07 b \/= i\u3001a *= sqrt(i)\uff0c\u5982\u679c\u672c\u6b21 While\u8ff4\u5708 \u6c92\u6709\u5224\u65b7\u5230\u56e0\u6578\uff0c\u5247\u5c07 While\u8ff4\u5708 Break \u6389\u3002<\/p>\n\n\n\n

\u5982\u679c a != 1\uff0c\u5c31\u8f38\u51fa a \u8ddf\u4e00\u500b\u7a7a\u683c\u5b57\u5143\u3002\u5728\u5224\u65b7\u5f0f\u5f8c\u9762\u8f38\u51fa sqrt(b)\u3002<\/p>\n\n\n\n

\u7bc4\u4f8b\u7a0b\u5f0f\u78bc\uff0dZeroJudge J242: \u81ea\u7136\u6578\u7684\u5e73\u65b9\u6839<\/a><\/h3>\n\n\n\n
#include <iostream>\n#include <math.h>\nusing namespace std;\n\nint main() {\n    cin.sync_with_stdio(0);\n    cin.tie(0);\n    long long int N;\n    cin >> N;\n    if (pow(int(sqrt(N)), 2) == N) cout << sqrt(N) << "\\n";\n    else {\n        long long int a = 1, b = N;\n        bool stop = false;\n        while (!stop) {\n            stop = true;\n            long long int plus = 3;\n            for (long long int i = 4; i<=N; i+=plus) {\n                if (b % i == 0) {\n                    b \/= i;\n                    a *= int(sqrt(i));\n                    stop = false;\n                }\n                plus += 2;\n            }\n        }\n        if (a != 1) cout << a << " ";\n        cout << "sqrt(" << b << ")\\n";\n    }\n}\n\n\/\/ZeroJudge J242\n\/\/Dr. SeanXD<\/code><\/pre><\/div>\n","protected":false},"excerpt":{"rendered":"
\u8f38\u5165\u6b63\u6574\u6578 N\uff0c\u5c07\u300csqrt(N)\u300d\u8f49\u63db\u6210\u300ca sqrt(b)\u300d\u4e4b\u683c\u5f0f\uff0c\u5176\u4e2d a \u8207 b \u90fd\u662f\u6b63\u6574\u6578\uff0ca2b  […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","footnotes":""},"categories":[29],"tags":[15,8,34,13,9],"class_list":["post-729","post","type-post","status-publish","format-standard","hentry","category-zerojudge-","tag-long-long-int","tag-8","tag-34","tag-13","tag-9"],"blocksy_meta":[],"_links":{"self":[{"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts\/729","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/comments?post=729"}],"version-history":[{"count":2,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts\/729\/revisions"}],"predecessor-version":[{"id":734,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts\/729\/revisions\/734"}],"wp:attachment":[{"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/media?parent=729"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/categories?post=729"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/tags?post=729"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}