{"id":556,"date":"2020-06-01T20:53:56","date_gmt":"2020-06-01T12:53:56","guid":{"rendered":"http:\/\/www.guanhaobo.cn\/?p=556"},"modified":"2020-06-01T20:53:56","modified_gmt":"2020-06-01T12:53:56","slug":"bjtuoj-1923-%e6%86%a8%e4%b8%ad%e6%86%a8%e7%9a%84%e5%b9%bd%e5%85%b0%e6%8b%bf%e9%93%81","status":"publish","type":"post","link":"https:\/\/www.guanhaobo.cn\/?p=556","title":{"rendered":"BJTUOJ 1923 \u2014 \u61a8\u4e2d\u61a8\u7684\u5e7d\u5170\u62ff\u94c1"},"content":{"rendered":"

\u9898\u76ee<\/h3>\n

\u94c1\u61a8\u61a8\u9a91\u58eb\u56e2\u56e2\u957f\u61a8\u4e2d\u61a8\u6709\u7740\u7279\u6b8a\u7684\u80fd\u529b\u6765\u6fc0\u53d1\u9a91\u58eb\u7684\u6597\u5fd7\u2014\u2014\u4ed6\u4f1a\u6ce1\u597d\u559d\u7684\u5e7d\u5170\u62ff\u94c1\uff0c\u4e00\u676f\u5e7d\u5170\u62ff\u94c1\u80fd\u6fc0\u53d1\u4e00\u4f4d\u9a91\u58eb\u7684\u6597\u5fd7\u3002<\/p>\n

\u5236\u4f5c\u4e00\u676f\u62ff\u94c1\u9700\u8981 n \u79cd\u539f\u6750\u6599\uff0c\u6bcf\u79cd\u539f\u6750\u6599\u5404\u9700\u8981 a1,a2,\u2026,an \u4efd\uff0c\u61a8\u4e2d\u61a8\u73b0\u6709\u6bcf\u79cd\u539f\u6750\u6599\u5404 b1,b2,\u2026,bn \u4efd\u3002<\/p>\n

\u53e6\u5916\uff0c\u4ed6\u8fd8\u6709\u53e6\u5916 m \u4efd\u4e07\u80fd\u6750\u6599\uff0c\u6bcf\u4e00\u4efd\u4e07\u80fd\u6750\u6599\u90fd\u80fd\u4f5c\u4e3a\u4efb\u610f\u4e00\u79cd\u539f\u6750\u6599\u7684\u4e00\u4efd\u7528\u4e8e\u5236\u4f5c\u5976\u8336\u3002<\/p>\n

\u73b0\u5728\u7ed9\u4f60\u539f\u6750\u6599\u548c\u795e\u79d8\u6750\u6599\u7684\u4efd\u6570\uff0c\u6c42\u61a8\u4e2d\u61a8\u6700\u591a\u80fd\u5236\u4f5c\u51e0\u676f\u5e7d\u5170\u62ff\u94c1\u3002<\/p>\n

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

https:\/\/citel.bjtu.edu.cn\/acm\/problem\/1923<\/a><\/p>\n

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

\u7b2c\u4e00\u884c\u4e3a\u4e24\u4e2a\u6574\u6570 n,m (1\u2264n\u226410^5,0\u2264m\u226410^7)\uff0c\u5206\u522b\u8868\u793a\u539f\u6750\u6599\u7684\u79cd\u7c7b\u548c\u4e07\u80fd\u6750\u6599\u7684\u4efd\u6570\u3002
\n\u7b2c\u4e8c\u884c\u4e3a n \u4e2a\u6574\u6570 a1,a2,\u2026,an (1\u2264ai\u226410^4)\uff0cai \u4ee3\u8868\u5236\u4f5c\u4e00\u676f\u5976\u8336\u9700\u8981\u7b2c i \u79cd\u6750\u6599\u7684\u4efd\u6570\u3002
\n\u7b2c\u4e09\u884c\u4e3a n \u4e2a\u6574\u6570 b1,b2,\u2026,bn (1\u2264bi\u226410^8)\uff0cbi \u4ee3\u8868\u61a8\u4e2d\u61a8\u62e5\u6709\u7684\u7b2c i \u79cd\u6750\u6599\u7684\u4efd\u6570\u3002<\/p>\n

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

\u4e00\u4e2a\u6574\u6570\uff0c\u8868\u793a\u61a8\u4e2d\u61a8\u6700\u591a\u80fd\u5236\u4f5c\u5976\u8336\u7684\u676f\u6570\u3002<\/p>\n

\u6837\u4f8b\u8f93\u5165<\/h3>\n
5 7\n1 2 1 2 3\n5 5 5 5 5\n<\/code><\/pre>\n
\u6837\u4f8b\u8f93\u51fa<\/h3>\n
3<\/code><\/p>\n
\u6837\u4f8b\u8bf4\u660e<\/h3>\n
\u628a 1 \u4efd\u4e07\u80fd\u6750\u6599\u5f53\u4f5c\u7b2c 2 \u79cd\u539f\u6750\u6599\uff0c
\n\u628a 1 \u4efd\u4e07\u80fd\u6750\u6599\u5f53\u4f5c\u7b2c 4 \u79cd\u539f\u6750\u6599\uff0c
\n\u628a 4 \u4efd\u4e07\u80fd\u6750\u6599\u5f53\u4f5c\u7b2c 5 \u79cd\u539f\u6750\u6599\uff0c
\n\u5171\u6d88\u8017\u4e07\u80fd\u6750\u6599 6 \u4efd\uff0c\u80fd\u5236\u4f5c 3 \u676f\u5976\u8336\u3002
\n\u53ef\u4ee5\u8bc1\u660e\uff0c\u5269\u4f59\u7684\u6750\u6599\u4e0d\u80fd\u5236\u4f5c\u66f4\u591a\u5976\u8336\u3002<\/p>\n
\u95ee\u9898\u5206\u6790<\/h3>\n
\u601d\u8def\u4e00<\/h4>\n
\u6700\u591a\u80fd\u5236\u4f5c\u51e0\u676f\u62ff\u94c1\uff0c\u662f\u7531\uff08b[i] \/ a[i]\uff09\u6700\u5c0f\u7684\u90a3\u4e2a\u539f\u6750\u6599\u6240\u51b3\u5b9a\u7684\u3002\u6211\u4eec\u53ea\u9700\u8981\u6bcf\u6b21\u90fd\u628a\u4e07\u80fd\u6750\u6599\u53d8\u6210\u6bd4\u4f8b\u6700\u5c0f\u7684\u90a3\u79cd\u6750\u6599\u5373\u53ef\u3002
\n\u4f46\u662f\u4e00\u6b21\u5e94\u8be5\u6295\u5165\u591a\u5c11\u539f\u6750\u6599\u5462\uff1f\u4e00\u6b21\u53ea\u6295\u653e\u4e00\u4efd\u663e\u7136\u5f88\u6162\u3002\u6bd4\u8f83\u5feb\u7684\u65b9\u6cd5\u662f\u4f7f\u5f97\u6bd4\u4f8b\u6700\u5c0f\u7684\u6750\u6599\u6070\u597d\u8d85\u8fc7\u7b2c\u4e8c\u5c0f\u7684\u6750\u6599\u3002
\n\u5177\u4f53\u7b56\u7565\u5982\u4e0b\uff1a
\n1. \u627e\u51fa\u6bd4\u4f8b\uff08b[i] \/ a[i]\uff09\u6700\u5c0f\u7684\u6750\u6599 A \u548c\u7b2c\u4e8c\u5c0f\u7684\u6750\u6599 B
\n2. \u5206\u914d\u82e5\u5e72\u4e07\u80fd\u6750\u6599\u7ed9 A, \u4f7f\u5f97 A \u7684\u6bd4\u4f8b\uff08b[i] \/ a[i]\uff09\u6070\u597d\u5927\u4e8e B \u7684\u6bd4\u4f8b<\/p>\n
\u5faa\u73af\u6267\u884c\u4ee5\u4e0a\u7b56\u7565\uff0c\u76f4\u5230\u4e07\u80fd\u6750\u6599\u5168\u90e8\u7528\u5b8c\uff0c\u6b64\u65f6\u6bd4\u4f8b\uff08b[i] \/ a[i]\uff09\u7684\u6700\u5c0f\u503c\u5c31\u662f\u95ee\u9898\u7684\u7b54\u6848\u3002<\/p>\n
\u601d\u8def\u4e8c\uff08\u63a8\u8350\uff09<\/h4>\n
\u5bf9\u7b54\u6848\u8fdb\u884c\u4e8c\u5206\u67e5\u627e\u3002
\n\u7531\u6570\u636e\u8303\u56f4\u6613\u5f97\uff0c\u7b54\u6848\u57280<\/code>\u52302*10^8<\/code>\u4e4b\u95f4\u3002
\n\u5bf9\u8fb9\u754c\u53d6\u5747\u503c\u8bbe\u4e3amid<\/code>\uff0c\u9a8c\u8bc1\u662f\u5426\u53ef\u4ee5\u5236\u4f5c\u51famid<\/code>\u676f\u62ff\u94c1\uff0c\u5982\u679c\u662f\uff0c\u8bf4\u660e\u7b54\u6848\u5927\u4e8e\u7b49\u4e8emid<\/code>\uff1b\u53cd\u4e4b\u8bf4\u660e\u7b54\u6848\u5c0f\u4e8emid<\/code>\u3002\u6839\u636e\u9a8c\u8bc1\u7ed3\u679c\u66f4\u65b0\u8fb9\u754c\uff0c\u76f4\u5230\u5de6\u8fb9\u754c\u5927\u4e8e\u53f3\u8fb9\u754c\uff0c\u9000\u51fa\u5faa\u73af\uff0c\u6b64\u65f6\u6700\u540e\u4e00\u4e2a\u9a8c\u8bc1\u6210\u529f\u7684\u503c\u5c31\u662f\u95ee\u9898\u7684\u7b54\u6848\u3002
\n\u6838\u5fc3\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n
while (ghbleft <= ghbright)\n{\n    mid = ghbleft + (ghbright - ghbleft) \/ 2;\n    if (ok())\n    {\n        ans = mid;\n        ghbleft = mid + 1;\n    }\n    else\n        ghbright = mid - 1;\n}\ncout << ans << endl;\n<\/code><\/pre>\n
AC\u4ee3\u7801<\/h3>\n
\u601d\u8def\u4e00\uff081219 ms\uff09<\/h4>\n
\u8fd9\u4e2a\u65b9\u6cd5\u5b9e\u9645\u5df2\u7ecf\u8d85\u65f6\u4e86\uff0c\u4e0d\u8fc7\u6bd4\u8d5b\u7684\u65f6\u5019\u653e\u5bbd\u4e86\u65f6\u95f4\uff0c\u6240\u4ee5\u4e5f\u662f\u53ef\u4ee5AC\u7684\u3002<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint a[100005];\nstruct node\n{\n    int i;\n    int x;\n    double num; \/\/\u5236\u4f5c\u7684\u6570\u91cf\n    bool operator<(const node &s1) const\n    {\n        return num > s1.num;\n    }\n} p;\npriority_queue<node, vector<node> \/**\/> q;\nint main()\n{\n    int n, m, i;\n    cin >> n >> m;\n    for (i = 0; i < n; i++)\n        cin >> a[i];\n    for (i = 0; i < n; i++)\n    {\n        p.i = i;\n        cin >> p.x;\n        p.num = p.x * 1.0 \/ a[i];\n        q.push(p);\n    }\n    while (m > 0)\n    {\n        node fp = q.top();\n        q.pop();\n        int temp = q.top().num - fp.num;\n        temp = min(m, temp + 1);\n        fp.x += temp;\n        m -= temp;\n        fp.num = fp.x * 1.0 \/ a[fp.i];\n        q.push(fp);\n    }\n    node fp = q.top();\n    printf(\"%d\\n\", (int)fp.num);\n    return 0;\n}\n<\/code><\/pre>\n
\u601d\u8def\u4e8c\uff0813 ms\uff09<\/h4>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint a[100005], b[100005];\nint ghbleft = 0, ghbright = 2e8, mid, ans, n, m;\nbool ok()\n{\n    int t = m;\n    for (int i = 0; i < n; i++)\n    {\n        int num = a[i] * mid;\n        if (b[i] < num)\n            t -= num - b[i];\n        if (t < 0)\n            return false;\n    }\n    return true;\n}\nint main()\n{\n    int i;\n    cin >> n >> m;\n    for (i = 0; i < n; i++)\n        cin >> a[i];\n    for (i = 0; i < n; i++)\n        cin >> b[i];\n    while (ghbleft <= ghbright)\n    {\n        mid = ghbleft + (ghbright - ghbleft) \/ 2;\n        if (ok())\n        {\n            ans = mid;\n            ghbleft = mid + 1;\n        }\n        else\n            ghbright = mid - 1;\n    }\n    cout << ans << endl;\n    return 0;\n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u9898\u76ee \u94c1\u61a8\u61a8\u9a91\u58eb\u56e2\u56e2\u957f\u61a8\u4e2d\u61a8\u6709\u7740\u7279\u6b8a\u7684\u80fd\u529b\u6765\u6fc0\u53d1\u9a91\u58eb\u7684\u6597\u5fd7\u2014\u2014\u4ed6\u4f1a\u6ce1\u597d\u559d\u7684\u5e7d\u5170\u62ff\u94c1\uff0c\u4e00\u676f\u5e7d\u5170\u62ff\u94c1\u80fd\u6fc0\u53d1\u4e00\u4f4d\u9a91\u58eb […]<\/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":[7,32],"class_list":["post-556","post","type-post","status-publish","format-standard","hentry","category-algo","tag-bjtuoj","tag-32"],"_links":{"self":[{"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/posts\/556","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=556"}],"version-history":[{"count":0,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=\/wp\/v2\/posts\/556\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.guanhaobo.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}