{"id":2972,"date":"2023-06-03T23:20:58","date_gmt":"2023-06-03T15:20:58","guid":{"rendered":"https:\/\/www.shuizilong.com\/house\/?p=2972"},"modified":"2023-06-04T03:56:12","modified_gmt":"2023-06-03T19:56:12","slug":"izho-2017-problem-f-hard-route","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/izho-2017-problem-f-hard-route\/","title":{"rendered":"IZhO 2017. Problem F. Hard route"},"content":{"rendered":"<ul>\n<li><a href=\"https:\/\/oj.uz\/problem\/view\/IZhO17_road\">https:\/\/oj.uz\/problem\/view\/IZhO17_road<\/a><\/li>\n<\/ul>\n<p>\u5982\u679c\u4e0d\u8003\u8651\u65b9\u6848\u6570\u7684\u8bdd\u662f\u975e\u5e38\u597d\u5199\u7684\uff0c\u7c7b\u4f3c\u4e0a\u4e00\u9898\uff0c\u6211\u4eec\u53ea\u9700\u8981\u7ef4\u62a4\u5411\u4e0b\u7684 top3 \u548c\u5411\u4e0a\u7684 top1 \u5373\u53ef\u3002<br \/>\n\u7136\u540e\u7528\u5747\u503c\u4e0d\u7b49\u5f0f\u53ef\u4ee5\u5f97\u5230\u6700\u4f18\u89e3\u4e00\u5b9a\u662f a*(b+c) | a >= b >= c\u3002<\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\n#include &lt;lastweapon\/io&gt;\r\nusing namespace lastweapon;\r\n\r\nconst int N = int(1e5) + 9;\r\n\r\nint dn&#x5B;N]&#x5B;3], up&#x5B;N];\r\nVI adj&#x5B;N]; int n;\r\n\r\nvoid upd(int d&#x5B;], int v) {\r\n    if (v &gt; d&#x5B;0]) d&#x5B;2] = d&#x5B;1], d&#x5B;1] = d&#x5B;0], d&#x5B;0] = v;\r\n    else if (v &gt; d&#x5B;1]) d&#x5B;2] = d&#x5B;1], d&#x5B;1] = v;\r\n    else if (v &gt; d&#x5B;2]) d&#x5B;2] = v;\r\n}\r\n\r\nvoid dfs1(int u = 1, int p = 0) {\r\n    for (auto v: adj&#x5B;u]) if (v != p) {\r\n        dfs1(v, u);\r\n        upd(dn&#x5B;u], dn&#x5B;v]&#x5B;0] + 1);\r\n    }\r\n}\r\n\r\nvoid dfs2(int u = 1, int p = 0) {\r\n    for (auto v: adj&#x5B;u]) if (v != p) {\r\n        checkMax(up&#x5B;v], max(up&#x5B;u], dn&#x5B;u]&#x5B;0] != dn&#x5B;v]&#x5B;0] + 1 ? dn&#x5B;u]&#x5B;0] : dn&#x5B;u]&#x5B;1]) + 1);\r\n        dfs2(v, u);\r\n    }\r\n}\r\n\r\nLL f(int x) {\r\n    if (dn&#x5B;x]&#x5B;1] == 0) return 0;\r\n    if (up&#x5B;x] &gt; dn&#x5B;x]&#x5B;0]) return (LL)up&#x5B;x] * (dn&#x5B;x]&#x5B;0] + dn&#x5B;x]&#x5B;1]);\r\n    if (up&#x5B;x] &gt; dn&#x5B;x]&#x5B;2]) return (LL)dn&#x5B;x]&#x5B;0] * (up&#x5B;x] + dn&#x5B;x]&#x5B;1]);\r\n    if (dn&#x5B;x]&#x5B;2] == 0) return 0;\r\n    return (LL)dn&#x5B;x]&#x5B;0] * (dn&#x5B;x]&#x5B;1] + dn&#x5B;x]&#x5B;2]);\r\n}\r\n\r\nint main() {\r\n\r\n#ifndef ONLINE_JUDGE\r\n    freopen(&quot;in.txt&quot;, &quot;r&quot;, stdin);\r\n    \/\/freopen(&quot;\/Users\/minakokojima\/Documents\/GitHub\/ACM-Training\/Workspace\/out.txt&quot;, &quot;w&quot;, stdout);\r\n#endif\r\n\r\n    DO(RD(n)-1) {\r\n        int x, y; RD(x, y);\r\n        adj&#x5B;x].PB(y);\r\n        adj&#x5B;y].PB(x);\r\n    }\r\n\r\n    dfs1(); dfs2();\r\n\r\n    LL z = 0; REP_1(i, n) checkMax(z, f(i));\r\n    cout &lt;&lt; z &lt;&lt; endl;\r\n}\r\n\r\n<\/pre>\n<p>\u8003\u8651\u65b9\u6848\u6570\u7684\u8bdd\uff0c\u5b9e\u73b0\u8d77\u6765\u4f1a\u9ebb\u70e6\u5f88\u591a\u3002<br \/>\n\u4e3b\u8981\u4e0a\u9762\u7684 a\\b\\c \u91cc\uff0ca \u662f\u4e0d\u53c2\u4e0e\u8ba1\u6570\u7684\uff0c\u53ea\u80fd\u5404\u79cd\u8ba8\u8bba\u3002<\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\n#include &lt;lastweapon\/io&gt;\r\nusing namespace lastweapon;\r\n\r\nconst int N = int(5e5) + 9;\r\n\r\nstruct rec : public pair&lt;LL, LL&gt; {\r\n    rec(LL a = 0, LL b = 0){\r\n        fi = a, se = b;\r\n    }\r\n    rec&amp; operator +=(const rec&amp;r){\r\n        if (fi == r.fi) se += r.se;\r\n        else checkMax(*this, r);\r\n        rTs;\r\n    }\r\n};\r\n\r\nrec d&#x5B;N], z = {0, 1};\r\nVI adj&#x5B;N]; int n;\r\n\r\nvoid upd(rec d&#x5B;], rec v) {\r\n    if (v &gt; d&#x5B;0]) d&#x5B;2] = d&#x5B;1], d&#x5B;1] = d&#x5B;0], d&#x5B;0] = v;\r\n    else if (v &gt; d&#x5B;1]) d&#x5B;2] = d&#x5B;1], d&#x5B;1] = v;\r\n    else if (v &gt; d&#x5B;2]) d&#x5B;2] = v;\r\n}\r\n\r\nvoid dfs1(int u = 1, int p = 0) {\r\n    d&#x5B;u] = {0, 1};\r\n    for (auto v: adj&#x5B;u]) if (v != p) {\r\n        dfs1(v, u);\r\n        d&#x5B;u] += d&#x5B;v];\r\n    }\r\n    d&#x5B;u].fi += 1;\r\n}\r\n\r\nvoid dfs2(int u = 1, int p = 0, rec up = {0, 1}) {\r\n\r\n    rec f&#x5B;3] = {up};\r\n    for (auto v: adj&#x5B;u]) if (v != p) upd(f, d&#x5B;v]);\r\n\r\n    if (f&#x5B;2].fi) {\r\n        LL best = f&#x5B;0].fi * (f&#x5B;1].fi + f&#x5B;2].fi);\r\n        if (best &gt;= z.fi) {\r\n            LL ways, ways2 = up.fi == f&#x5B;2].fi ? up.se : 0;\r\n            for (auto v: adj&#x5B;u]) if (v != p) if (d&#x5B;v].fi == f&#x5B;2].fi) ways2 += d&#x5B;v].se;\r\n\r\n            if (f&#x5B;1].fi == f&#x5B;2].fi) {\r\n                ways = sqr(ways2);\r\n                if (up.fi == f&#x5B;2].fi) ways -= sqr(up.se);\r\n                for (auto v: adj&#x5B;u]) if (v != p) if (d&#x5B;v].fi == f&#x5B;2].fi) ways -= sqr(d&#x5B;v].se);\r\n                ways \/= 2;\r\n            } else {\r\n                ways = ((f&#x5B;0].fi == f&#x5B;1].fi ? f&#x5B;0].se : 0) + f&#x5B;1].se) * ways2;\r\n            }\r\n            z += rec(best, ways);\r\n        }\r\n    }\r\n\r\n    LL ways0 = 0, ways1 = 0;\r\n    if (up.fi == f&#x5B;0].fi) ways0 += up.se;\r\n    else if (up.fi == f&#x5B;1].fi) ways1 += up.se;\r\n    for (auto v: adj&#x5B;u]) if (v != p) {\r\n        if (d&#x5B;v].fi == f&#x5B;0].fi) ways0 += d&#x5B;v].se;\r\n        else if (d&#x5B;v].fi == f&#x5B;1].fi) ways1 += d&#x5B;v].se;\r\n    }\r\n\r\n    for (auto v: adj&#x5B;u]) if (v != p) {\r\n        LL a = f&#x5B;0].fi+1, b = ways0;\r\n        if (d&#x5B;v].fi == f&#x5B;0].fi) {\r\n            if (d&#x5B;v].se == ways0) a = f&#x5B;1].fi+1, b = ways1;\r\n            else b = ways0 - d&#x5B;v].se;\r\n        }\r\n        dfs2(v, u, {a, b});\r\n    }\r\n}\r\n\r\nint main() {\r\n\r\n#ifndef ONLINE_JUDGE\r\n    freopen(&quot;in.txt&quot;, &quot;r&quot;, stdin);\r\n    \/\/freopen(&quot;\/Users\/minakokojima\/Documents\/GitHub\/ACM-Training\/Workspace\/out.txt&quot;, &quot;w&quot;, stdout);\r\n#endif\r\n\r\n    DO(RD(n)-1) {\r\n        int x, y; RD(x, y);\r\n        adj&#x5B;x].PB(y);\r\n        adj&#x5B;y].PB(x);\r\n    }\r\n\r\n    dfs1(); dfs2();\r\n    cout &lt;&lt; z.fi &lt;&lt; &quot; &quot; &lt;&lt; z.se &lt;&lt; endl;\r\n}\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>https:\/\/oj.uz\/problem\/view\/IZhO17_road \u5982\u679c\u4e0d\u8003\u8651\u65b9\u6848\u6570\u7684\u8bdd\u662f\u975e\u5e38\u597d\u5199\u7684\uff0c\u7c7b\u4f3c\u4e0a\u4e00\u9898\uff0c\u6211\u4eec\u53ea\u9700\u8981\u7ef4\u62a4\u5411\u4e0b\u7684 top3 \u548c\u5411\u4e0a\u7684 top1 \u5373\u53ef\u3002 \u7136\u540e\u7528\u5747\u503c\u4e0d\u7b49\u5f0f\u53ef\u4ee5\u5f97\u5230\u6700\u4f18\u89e3\u4e00\u5b9a\u662f a*(b+c) | a >= b >= c\u3002 #include &lt;lastweapon\/io&gt; using namespace lastweapon; const int N = int(1e5) + 9; int dn&#x5B;N]&#x5B;3], up&#x5B;N]; VI adj&#x5B;N]; int n; void upd(int d&#x5B;], int v) { if (v &gt; d&#x5B;0]) d&#x5B;2] = d&#x5B;1], d&#x5B;1] = d&#x5B;0], d&#x5B;0] = v; else if (v [&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-2972","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-LW","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2972","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=2972"}],"version-history":[{"count":2,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2972\/revisions"}],"predecessor-version":[{"id":2974,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2972\/revisions\/2974"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=2972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=2972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=2972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}