{"id":620,"date":"2020-06-10T22:33:26","date_gmt":"2020-06-10T14:33:26","guid":{"rendered":"http:\/\/www.guanhaobo.cn\/?p=620"},"modified":"2020-06-10T22:33:26","modified_gmt":"2020-06-10T14:33:26","slug":"bjtuoj-1924-jerry99%e7%9a%84%e6%95%b0%e5%88%97","status":"publish","type":"post","link":"https:\/\/www.guanhaobo.cn\/?p=620","title":{"rendered":"BJTUOJ 1924 \u2014 jerry99\u7684\u6570\u5217"},"content":{"rendered":"

\u9898\u76ee<\/h3>\n

jerry99\u7684\u6570\u5b66\u80fd\u529b\u5f88\u5f3a\uff0c\u7ecf\u5e38\u4f1a\u7814\u7a76\u4e00\u4e9b\u590d\u6742\u7684\u6570\u5b66\u95ee\u9898\u3002<\/p>\n

\u5df2\u77e5\u6570\u5217 a1,a2,…,an\uff0c\u5176\u4e2d ai \u662f\u6700\u63a5\u8fd1 \u221ai \u7684\u6574\u6570\u3002<\/p>\n

jerry99\u60f3\u77e5\u9053 a1\u00d7a2\u00d7…\u00d7an \u7684\u7ed3\u679c\uff0c\u4f46\u662f\u4ed6\u7684\u4f5c\u4e1a\u592a\u591a\u4e86\uff0c\u4f60\u80fd\u5e2e\u5e2e\u4ed6\u5417\uff1f<\/p>\n

\u7531\u4e8e\u7ed3\u679c\u53ef\u80fd\u5f88\u5927\uff0c\u8bf7\u5c06\u7ed3\u679c\u5bf9 10^9+7 \u53d6\u6a21\u3002<\/p>\n

\u9898\u76ee\u94fe\u63a5<\/h3>\n

\u6570\u5b66\u516c\u5f0f\u4e71\u7801\u4e86\uff0c\u5efa\u8bae\u5927\u5bb6\u770b\u539f\u9898\u3002
\nhttps:\/\/citel.bjtu.edu.cn\/acm\/problem\/1924<\/a><\/p>\n

\u8f93\u5165\u6570\u636e<\/h3>\n

\u7b2c\u4e00\u884c\u4e3a\u4e00\u4e2a\u6574\u6570 T (1\u2264T\u2264100) \uff0c\u8868\u793a\u4e00\u5171\u6709 T \u7ec4\u6570\u636e\u3002
\n\u5bf9\u4e8e\u6bcf\u7ec4\u6570\u636e\uff1a
\n\u8f93\u5165\u4e00\u884c\uff0c\u5305\u542b\u4e00\u4e2a\u6574\u6570 n (1\u2264n\u2264109)\u3002<\/p>\n

\u8f93\u51fa\u6570\u636e<\/h3>\n

\u5bf9\u4e8e\u6bcf\u7ec4\u6570\u636e\uff0c\u8f93\u51fa\u4e00\u884c\u4e00\u4e2a\u6574\u6570\uff0c\u8868\u793a \u03a0(n i=1)ai(mod10^9+7)\u3002<\/p>\n

\u6837\u4f8b\u8f93\u5165<\/h3>\n
6\n1\n2\n3\n4\n5\n998244353\n<\/code><\/pre>\n
\u6837\u4f8b\u8f93\u51fa<\/h3>\n
1\n1\n2\n4\n8\n361817674\n<\/code><\/pre>\n
\u6837\u4f8b\u8bf4\u660e<\/h3>\n
\u5bf9\u4e8e\u524d 5 \u7ec4\u6570\u636e\uff1a
\na1=1
\na2=1
\na3=2
\na4=2
\na5=2
\n\u6545\u53ef\u6c42\u5f97\u76f8\u5e94\u7ed3\u679c\u3002<\/p>\n
\u95ee\u9898\u5206\u6790<\/h3>\n
\u89c2\u5bdf\u9898\u76ee\u7ed9\u51fa\u7684\u6837\u4f8b\u8bf4\u660e\uff0c\u5c31\u4f1a\u60f3\u5230\u8fd9\u9053\u9898\u76ee\u6709\u53ef\u80fd\u662f\u5b58\u5728\u6570\u5b66\u89c4\u5f8b\u7684\u3002\u4e8e\u662f\u6211\u4eec\u7a0d\u5fae\u591a\u8ba1\u7b97\u51e0\u4e2a ai \u7684\u503c\uff0c\u5982\u4e0b\uff1a<\/p>\n
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4\n<\/code><\/pre>\n
2\u4e2a1\uff0c4\u4e2a2\uff0c6\u4e2a3\uff0c8\u4e2a4
\n\u5230\u8fd9\u91cc\u5c31\u53ef\u4ee5\u786e\u5b9a\u5b58\u5728\u6570\u5b66\u89c4\u5f8b\uff0c\u5373\u4f1a\u6309\u987a\u5e8f\u51fa\u73b0 2x \u4e2a x
\n\u5bf9\u4e8e\u6574\u6570 n\uff0c\u6211\u4eec\u4ece x=1 \u5f00\u59cb\u679a\u4e3e\u6c42\u548c\uff0c\u76f4\u5230\u548c sum \u6700\u7ec8\u7b49\u4e8e n\u3002\u5f53\u7136\uff0c\u6700\u540e\u4e00\u4e2a 2x + sum<\/code> \u4e0d\u4e00\u5b9a\u6b63\u597d\u7b49\u4e8e n\uff0c\u9700\u8981\u5224\u65ad\u4e00\u4e0b\u3002
\n\u6c42 x \u7684 2x \u6b21\u5e42\uff0c\u9700\u8981\u7528\u5feb\u901f\u5e42\u6765\u7f29\u77ed\u65f6\u95f4\u3002
\n\u6838\u5fc3\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n
sum = 0;\nx = 1;\nans = 1;\nwhile (sum < n)\n{\n    if (sum + 2 * x < n)\n    {\n        sum += 2 * x;\n        ans = (ans * quickpow(x, 2 * x)) % mod;\n        x++;\n    }\n    else\n    {\n        ans = (ans * quickpow(x, n - sum)) % mod;\n        sum = n;\n    }\n}\ncout << ans << endl;\n<\/code><\/pre>\n
AC\u4ee3\u7801<\/h3>\n
#include <bits\/stdc++.h>\nusing namespace std;\nconst int mod = 1e9 + 7;\n\nlong long quickpow(long long a, long long b)\n{\n    long long ans = 1, base = a;\n    while (b != 0)\n    {\n        if (b & 1 != 0) \/\/b\u7684\u4e8c\u8fdb\u5236\u6700\u53f3\u4e00\u4f4d\u4e3a1\n        {\n            ans = (ans * base) % mod;\n        }\n        base = (base * base) % mod;\n        b >>= 1;\n    }\n    return ans % mod;\n}\nint main()\n{\n    int t, n, i, x = 1, sum = 0;\n    long long ans;\n    cin >> t;\n    while (t--)\n    {\n        cin >> n;\n        sum = 0;\n        x = 1;\n        ans = 1;\n        while (sum < n)\n        {\n            if (sum + 2 * x < n)\n            {\n                sum += 2 * x;\n                ans = (ans * quickpow(x, 2 * x)) % mod;\n                x++;\n            }\n            else\n            {\n                ans = (ans * quickpow(x, n - sum)) % mod;\n                sum = n;\n            }\n        }\n        cout << ans << endl;\n    }\n    return 0;\n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u9898\u76ee jerry99\u7684\u6570\u5b66\u80fd\u529b\u5f88\u5f3a\uff0c\u7ecf\u5e38\u4f1a\u7814\u7a76\u4e00\u4e9b\u590d\u6742\u7684\u6570\u5b66\u95ee\u9898\u3002 \u5df2\u77e5\u6570\u5217 a1,a2,…,an […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[7,49],"class_list":["post-620","post","type-post","status-publish","format-standard","hentry","category-algo","tag-bjtuoj","tag-49"],"_links":{"self":[{"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/posts\/620","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=620"}],"version-history":[{"count":0,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/posts\/620\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=620"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=620"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}