{"id":1770,"date":"2021-09-19T19:04:28","date_gmt":"2021-09-19T11:04:28","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=1770"},"modified":"2021-09-20T20:57:33","modified_gmt":"2021-09-20T12:57:33","slug":"tree-dp-2","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/tree-dp-2\/","title":{"rendered":"\u6811\u5f62\u80cc\u5305"},"content":{"rendered":"<ul>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P2014\">Luogu P2014 [CTSC1997]\u9009\u8bfe<\/a><\/li>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/U53204\">Luogu U53204 \u3010\u6570\u636e\u52a0\u5f3a\u7248\u3011\u9009\u8bfe<\/a><\/li>\n<li><a href=\"https:\/\/ouuan.github.io\/post\/%E6%A0%91%E4%B8%8A%E8%83%8C%E5%8C%85%E7%9A%84%E4%B8%8A%E4%B8%8B%E7%95%8C%E4%BC%98%E5%8C%96\/\">ouuan\u7684\u535a\u5ba2 \u6811\u4e0a\u80cc\u5305\u7684\u4e0a\u4e0b\u754c\u4f18\u5316<\/a><\/li>\n<\/ul>\n<h2>\u66b4\u529b\u679a\u4e3e O(n3)<\/h2>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\nconst int M = int(3e2) + 9;\r\nconst int N = int(3e2) + 9;\r\nint dp&#x5B;N]&#x5B;M], cost&#x5B;N], value&#x5B;N]; VI adj&#x5B;N];\r\nint n, m;\r\n\r\nvoid dfs(int u = 0) {\r\n    FLC(dp&#x5B;u], 0x80);\r\n    DWN_1(i, m, cost&#x5B;u]) dp&#x5B;u]&#x5B;i] = value&#x5B;u];\r\n\r\n    for (auto v: adj&#x5B;u]) {\r\n        dfs(v);\r\n        DWN_1(i, m, cost&#x5B;u]) {\r\n            FOR_1(j, cost&#x5B;u], i) {\r\n                checkMax(dp&#x5B;u]&#x5B;i], dp&#x5B;u]&#x5B;j] + dp&#x5B;v]&#x5B;i-j]);\r\n            }\r\n        }\r\n    }\r\n}\r\n\r\nint main() {\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    RD(n, m);\r\n    REP_1(i, n) {\r\n        int p; RD(p, value&#x5B;i]); cost&#x5B;i] = 1;\r\n        adj&#x5B;p].push_back(i);\r\n    }\r\n    dfs();\r\n    cout &lt;&lt; dp&#x5B;0]&#x5B;m] &lt;&lt; endl;\r\n}\r\n<\/pre>\n<h2>\u72b6\u6001\u7ee7\u627f O(n2)<\/h2>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\nconst int N = int(1e5) + 9;\r\nconst int M = int(1e5) + 9;\r\nint cost&#x5B;N], value&#x5B;N]; VI adj&#x5B;N];\r\nint n, m;\r\n\r\nvoid dfs(int u, int m, VI&amp; dpu) {\r\n    m -= cost&#x5B;u];\r\n    for (auto v: adj&#x5B;u]) {\r\n        VI dpv = dpu; dfs(v, m, dpv);\r\n        FOR_1(i, 0, m) checkMax(dpu&#x5B;i], dpv&#x5B;i]);\r\n    }\r\n    m += cost&#x5B;u];\r\n    DWN_1(i, m, cost&#x5B;u]) dpu&#x5B;i] = dpu&#x5B;i-cost&#x5B;u]] + value&#x5B;u];\r\n    REP(i, cost&#x5B;u]) dpu&#x5B;i] = -INF;\r\n}\r\n\r\nint main() {\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    RD(n, m);\r\n    REP_1(i, n) {\r\n        int p; RD(p, value&#x5B;i]); cost&#x5B;i] = 1;\r\n        adj&#x5B;p].push_back(i);\r\n    }\r\n    VI dp0; dp0.resize(m+1);\r\n    dfs(0, m, dp0);\r\n    cout &lt;&lt; dp0&#x5B;m] &lt;&lt; endl;\r\n}\r\n<\/pre>\n<p>P1273 \u6709\u7ebf\u7535\u89c6\u7f51<br \/>\n<a href=\"https:\/\/www.luogu.com.cn\/problem\/P1273\">https:\/\/www.luogu.com.cn\/problem\/P1273<\/a><\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\n\r\nconst int N = (3e3) + 9;\r\nVII adj&#x5B;N]; int sz&#x5B;N];\r\nint dp&#x5B;N]&#x5B;N], bonus&#x5B;N];\r\nint n, m, z;\r\n\r\nbool isLeaf(int u) {\r\n    return u &gt; n-m;\r\n}\r\n\r\nvoid dfs0(int u) {\r\n    sz&#x5B;u] = isLeaf(u);\r\n    for (auto e: adj&#x5B;u]) {\r\n        int v = e.fi;\r\n        dfs0(v);\r\n        sz&#x5B;u] += sz&#x5B;v];\r\n    }\r\n}\r\n\r\nvoid dfs(int u) {\r\n    FLC(dp&#x5B;u], 0x80);\r\n    dp&#x5B;u]&#x5B;0] = 0;\r\n\r\n    if (isLeaf(u)) {\r\n        dp&#x5B;u]&#x5B;1] = bonus&#x5B;u];\r\n        return;\r\n    }\r\n\r\n    for (auto e: adj&#x5B;u]) {\r\n        int v = e.fi, w = e.se;\r\n        dfs(v);\r\n        DWN_1(i, sz&#x5B;u], 1) {\r\n            REP_1(j, sz&#x5B;v]) {\r\n                checkMax(dp&#x5B;u]&#x5B;i], dp&#x5B;u]&#x5B;i-j] + dp&#x5B;v]&#x5B;j] - w);\r\n            }\r\n        }\r\n    }\r\n}\r\n\r\nint main(){\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    RD(n, m); REP_1(u, n-m) {\r\n        Rush {\r\n            int v, c; RD(v, c);\r\n            adj&#x5B;u].PB({v,c});\r\n        }\r\n    }\r\n\r\n    FOR_1(u, n-m+1, n) RD(bonus&#x5B;u]);\r\n\r\n    dfs0(1); dfs(1);\r\n    DWN_1(i, m, 0) {\r\n        if (dp&#x5B;1]&#x5B;i] &gt;= 0) {\r\n            cout &lt;&lt; i &lt;&lt; endl;\r\n            return 0;\r\n        }\r\n    }\r\n}\r\n<\/pre>\n<h2>\u9053\u8def\u91cd\u5efa<\/h2>\n<p><a href=\"https:\/\/www.luogu.com.cn\/problem\/P1272\">https:\/\/www.luogu.com.cn\/problem\/P1272<\/a><br \/>\n<a href=\"https:\/\/www.luogu.com.cn\/problem\/U53878\">https:\/\/www.luogu.com.cn\/problem\/U53878<\/a><\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\n\r\nconst int N = (1e5) + 9;\r\nVI adj&#x5B;N]; int sz&#x5B;N];\r\nint n, m, z;\r\n\r\nVI dp&#x5B;N];\r\n\/\/ dp&#x5B;u]&#x5B;i]\uff0c\u4fdd\u7559 u \u8282\u70b9\u540c\u65f6\u5b50\u6811\u518d\u4fdd\u7559 i \u4e2a\u8282\u70b9\u7684\u5b50\u6811\uff0c\u6700\u5c11\u5220\u591a\u5c11\u8fb9\r\n\r\nvoid dfs(int u, int p){\r\n\r\n    sz&#x5B;u] = 1; dp&#x5B;u].PB(0);\r\n\r\n    for (auto v: adj&#x5B;u]) if (v != p) {\r\n        dfs(v, u);\r\n\r\n        REP(i, SZ(dp&#x5B;u])) dp&#x5B;u]&#x5B;i] += 1;\r\n        DO(min(sz&#x5B;v], m+1-sz&#x5B;u])) dp&#x5B;u].PB(INF);\r\n        sz&#x5B;u] += sz&#x5B;v];\r\n\r\n        DWN(i, SZ(dp&#x5B;u]), 1) {\r\n            REP(j, min(SZ(dp&#x5B;v]), i)) {\r\n                checkMin(dp&#x5B;u]&#x5B;i], dp&#x5B;u]&#x5B;i-1-j] + dp&#x5B;v]&#x5B;j] - 1);\r\n            }\r\n        }\r\n    }\r\n\r\n    if (sz&#x5B;u] &gt; m) checkMin(z, dp&#x5B;u]&#x5B;m] + bool(p));\r\n}\r\n\r\nsigned main(){\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    RD(n, m); --m; DO(n-1){\r\n        int a, b; RD(a, b);\r\n        adj&#x5B;a].PB(b);\r\n        adj&#x5B;b].PB(a);\r\n    }\r\n    z = INF; dfs(1, 0);\r\n    cout &lt;&lt; z &lt;&lt; endl;\r\n}\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Luogu P2014 [CTSC1997]\u9009\u8bfe Luogu U53204 \u3010\u6570\u636e\u52a0\u5f3a\u7248\u3011\u9009\u8bfe ouuan\u7684\u535a\u5ba2 \u6811\u4e0a\u80cc\u5305\u7684\u4e0a\u4e0b\u754c\u4f18\u5316 \u66b4\u529b\u679a\u4e3e O(n3) const int M = int(3e2) + 9; const int N = int(3e2) + 9; int dp&#x5B;N]&#x5B;M], cost&#x5B;N], value&#x5B;N]; VI adj&#x5B;N]; int n, m; void dfs(int u = 0) { FLC(dp&#x5B;u], 0x80); DWN_1(i, m, cost&#x5B;u]) dp&#x5B;u]&#x5B;i] = value&#x5B;u]; for (auto v: adj&#x5B;u]) { dfs(v); DWN_1(i, m, [&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-1770","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-sy","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1770","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=1770"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1770\/revisions"}],"predecessor-version":[{"id":1771,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1770\/revisions\/1771"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=1770"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=1770"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=1770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}