{"id":3428,"date":"2025-06-12T16:04:57","date_gmt":"2025-06-12T08:04:57","guid":{"rendered":"https:\/\/www.shuizilong.com\/house\/?p=3428"},"modified":"2025-06-13T08:02:30","modified_gmt":"2025-06-13T00:02:30","slug":"atcoder-beginner-contest-409","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/atcoder-beginner-contest-409\/","title":{"rendered":"AtCoder Beginner Contest 409"},"content":{"rendered":"<p>\u5148\u628a\u6240\u6709\u6570\u90fd\u51cf\u4e00\uff0cn \u8868\u793a\u8fdb\u884c\u4e86 n \u4e2a\u56de\u5408\u3002<\/p>\n<p>\u8bbe E[i] \u4e3a\u6700\u540e i \u51fa\u73b0\u7684\u671f\u671b\u6b21\u6570\u3002\u90a3\u4e48\u663e\u7136 E[n] \u6700\u5bb9\u6613\u6c42\uff0c\u5c31\u662f\u6bcf\u6b21\u90fd p\uff0cE[0] \u4e5f\u5bb9\u6613\u6c42\uff0c\u6bcf\u4e2a\u56de\u5408\u7684 delta \u53ea\u4e0e\u5f53\u524d\u6709\u591a\u5c11\u4e2a 0 \u6709\u5173\uff0c\u770b\u8d77\u6765\u53ef\u4ee5\u9012\u63a8\u3002<br \/>\nE[n-1] \u5219\u9700\u8981\u8ba8\u8bba\u4e00\u4e0b\uff0cE[n-2] \u5c31\u66f4\u8981\u8ba8\u8bba\u4e86\u3002<\/p>\n<p>\u4ed4\u7ec6\u89c2\u5bdf\uff0c\u6211\u4eec\u53d1\u73b0\u4e0d\u5f97\u4e0d\u679a\u4e3e\u7b2c\u4e00\u6b21\u51fa\u73b0 i \u7684\u65f6\u523b\uff0c\u8bbe A[i][j] \u7b49\u4e8e i \u7b2c\u4e00\u6b21\u51fa\u73b0\u5728 j \u65f6\u523b\u7684\u6982\u7387\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n<p>E[i] = A[i][j] B[n-j] | j = 0..n<\/p>\n<p>\u8fd9\u91cc B[i] \u8868\u793a\u5f53\u524d\u6700\u9ad8\u4f4d\u540e\u7eed\u518d\u8fdb\u884c i \u4e2a\u56de\u5408\u671f\u671b\u51fa\u73b0\u591a\u5c11\u6b21\uff0c\u548c\u6c42 E[0] \u7c7b\u4f3c\uff0c\u8fd9\u4e2a\u503c\u53ea\u4e0e\u540e\u7eed\u8fdb\u884c\u7684\u56de\u5408\u6570\u6709\u5173\uff01<\/p>\n<p>\u8fdb\u4e00\u6b65\uff0c\u8003\u5bdf A[i][j]\uff0c\u6700\u540e\u7b2c j \u65f6\u523b\u5fc5\u7136\u662f p \u4e8b\u4ef6\uff0c\u524d\u9762\u4e8c\u9879\u5206\u5e03\u5373\u53ef\uff1a<\/p>\n<p>A[i][j] = C(j-1, i-1) p^i (1-p)^(j-i)<\/p>\n<p>\u8003\u5bdf B[i] \u6709\uff1a<\/p>\n<p>B[0] = 1<br \/>\nB[i] = B[i-1] + B[i-1] \/ n-i<\/p>\n<p>\u4e8e\u662f\u53ef\u4ee5\u5f97\u5230\u66b4\u529b O(n2) dp\u3002<\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\n#include &amp;lt;lastweapon\/io&amp;gt;\n#include &amp;lt;lastweapon\/number&amp;gt;\nusing namespace lastweapon;\n\nconst int N = 1009;\nInt Fact&#x5B;N], iFact&#x5B;N];\nInt E&#x5B;N], A&#x5B;N], B&#x5B;N];\nint n, p, q;\n\nInt Binom(int n, int m) {\n    if (m &amp;lt; 0 || m &amp;gt; n) return 0;\n    return Fact&#x5B;n] * iFact&#x5B;m] * iFact&#x5B;n-m];\n}\n\nint main(){\n    MOD = 998244353; RD(n, p); p = Int(p) \/ 100; q = Int(1) - p;\n    Fact&#x5B;0] = 1; REP_1(i, n) Fact&#x5B;i] = Fact&#x5B;i-1] * i;\n    iFact&#x5B;n] = _I(Fact&#x5B;n]); DWN_1(i, n, 1) iFact&#x5B;i-1] = iFact&#x5B;i] * i;\n    B&#x5B;0] = 1; FOR(i, 1, n) B&#x5B;i] = B&#x5B;i-1] * (q+n-i) \/ (n-i);\n\n&lt;pre&gt;&lt;code&gt;E&#x5B;0] = B&#x5B;n-1]; FOR(i, 1, n) {\n    FOR(j, i, n) E&#x5B;i] += Binom(j-1, i-1) * pow(p, i) * pow(q, j-i) * B&#x5B;n-1-j];\n}\n\nREP(i, n) printf(&amp;amp;quot;%d\\n&amp;amp;quot;, E&#x5B;i]);\n&lt;\/code&gt;&lt;\/pre&gt;\n\n}\n\n<\/pre>\n<p>\u518d\u5377\u79ef\u5373\u53ef\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5148\u628a\u6240\u6709\u6570\u90fd\u51cf\u4e00\uff0cn \u8868\u793a\u8fdb\u884c\u4e86 n \u4e2a\u56de\u5408\u3002 \u8bbe E[i] \u4e3a\u6700\u540e i \u51fa\u73b0\u7684\u671f\u671b\u6b21\u6570\u3002\u90a3\u4e48\u663e\u7136 E[n] \u6700\u5bb9\u6613\u6c42\uff0c\u5c31\u662f\u6bcf\u6b21\u90fd p\uff0cE[0] \u4e5f\u5bb9\u6613\u6c42\uff0c\u6bcf\u4e2a\u56de\u5408\u7684 delta \u53ea\u4e0e\u5f53\u524d\u6709\u591a\u5c11\u4e2a 0 \u6709\u5173\uff0c\u770b\u8d77\u6765\u53ef\u4ee5\u9012\u63a8\u3002 E[n-1] \u5219\u9700\u8981\u8ba8\u8bba\u4e00\u4e0b\uff0cE[n-2] \u5c31\u66f4\u8981\u8ba8\u8bba\u4e86\u3002 \u4ed4\u7ec6\u89c2\u5bdf\uff0c\u6211\u4eec\u53d1\u73b0\u4e0d\u5f97\u4e0d\u679a\u4e3e\u7b2c\u4e00\u6b21\u51fa\u73b0 i \u7684\u65f6\u523b\uff0c\u8bbe A[i][j] \u7b49\u4e8e i \u7b2c\u4e00\u6b21\u51fa\u73b0\u5728 j \u65f6\u523b\u7684\u6982\u7387\uff0c\u6211\u4eec\u6709\uff1a E[i] = A[i][j] B[n-j] | j = 0..n \u8fd9\u91cc B[i] \u8868\u793a\u5f53\u524d\u6700\u9ad8\u4f4d\u540e\u7eed\u518d\u8fdb\u884c i \u4e2a\u56de\u5408\u671f\u671b\u51fa\u73b0\u591a\u5c11\u6b21\uff0c\u548c\u6c42 E[0] \u7c7b\u4f3c\uff0c\u8fd9\u4e2a\u503c\u53ea\u4e0e\u540e\u7eed\u8fdb\u884c\u7684\u56de\u5408\u6570\u6709\u5173\uff01 \u8fdb\u4e00\u6b65\uff0c\u8003\u5bdf A[i][j]\uff0c\u6700\u540e\u7b2c j \u65f6\u523b\u5fc5\u7136\u662f p \u4e8b\u4ef6\uff0c\u524d\u9762\u4e8c\u9879\u5206\u5e03\u5373\u53ef\uff1a A[i][j] = C(j-1, i-1) p^i [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[1],"tags":[],"class_list":["post-3428","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-Ti","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/3428","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=3428"}],"version-history":[{"count":7,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/3428\/revisions"}],"predecessor-version":[{"id":3435,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/3428\/revisions\/3435"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=3428"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=3428"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=3428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}