{"id":851,"date":"2019-01-30T14:00:25","date_gmt":"2019-01-30T06:00:25","guid":{"rendered":"https:\/\/0.mnihyc.com\/blog\/?p=851"},"modified":"2020-02-09T03:06:57","modified_gmt":"2020-02-08T19:06:57","slug":"yzoj-p3754-gab%e6%95%b0%e5%88%97","status":"publish","type":"post","link":"https:\/\/0.mnihyc.com\/blog\/archives\/851","title":{"rendered":"YZOJ P3754 Gab\u6570\u5217"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P3754 Gab\u6570\u5217<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a2000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a131072KB<\/p>\n<p style=\"text-align: center;\">\u96be\u5ea6\uff1a <span style=\"color: #ffcc00;\">\\(4.5\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7ed9\u5b9a\u6570\u5217 \\(a_1,a_2,\\cdots,a_n\\)\uff0c\u5b9a\u4e49\u6570\u5217 \\(b_1,b_2,\\cdots,b_m\\) \u4e3a Gab\u6570\u5217 \u5f53\u4e14\u4ec5\u5f53\u5b83\u6ee1\u8db3\uff1a<\/p>\n<p style=\"padding-left: 30px;\">1\uff0c\\(\\forall 1\\le i\\le m\\) \u6ee1\u8db3 \\(b_i\\in\\mathbf{N^*}\\) \u4e14 \\(1\\le b_i\\le n\\)<\/p>\n<p style=\"padding-left: 30px;\">2\uff0c\\(\\sum_\\limits{i=1}^{m}b_i\\le k\\)<\/p>\n<p>\u6c42 \\(\\sum_\\limits{i=1}^{m}a_{b_i}\\) \u7684\u6700\u5927\u503c\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c\u4e09\u4e2a\u6574\u6570 \\(n\\)\uff0c\\(m\\) \u548c \\(k\\) \u3002<\/p>\n<p>\u7b2c\u4e8c\u884c \\(n\\) \u4e2a\u6574\u6570 \\(a_i\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u8f93\u51fa\u4ec5\u4e00\u884c\uff0c\u4e3a\u6700\u5927\u503c\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">5 6 16\r\n4 2 2 4 7<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">30<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8bf4\u660e<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u5e94\u7684 Gab\u6570\u5217 \u53ef\u4ee5\u4e3a \\(\\{1,5,5,1,1,1\\}\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u8303\u56f4<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e \\(15\\%\\) \u7684\u6570\u636e\uff0c\\(n,m\\le 8\\)\uff0c\\(k\\le 50\\)\uff1b<\/p>\n<p>\u5bf9\u4e8e \\(40\\%\\) \u7684\u6570\u636e\uff0c\\(n,m,k\\le 200\\)\uff1b<\/p>\n<p>\u5bf9\u4e8e\u53e6\u5916 \\(5\\%\\) \u7684\u6570\u636e\uff0c\u6ee1\u8db3 \\(m=k\\)\uff1b<\/p>\n<p>\u5bf9\u4e8e\u53e6\u5916 \\(5\\%\\) \u7684\u6570\u636e\uff0c\u5bf9\u4e8e \\(1\\le i\\le j\\le n\\)\uff0c\\(a_i\\ge a_j\\)\uff1b<\/p>\n<p>\u5bf9\u4e8e \\(100\\%\\) \u7684\u6570\u636e\uff0c\\(n\\le 3000\\)\uff0c\\(k\\le 8000\\)\uff0c\\(m\\le 1000\\)\uff0c\\(1\\le a_i\\le 10^9\\)\uff0c\\(m\\le k\\)\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><!--more--><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>\u60f3\u900f\u4e86\u8fd9\u4e2a\u5c31\u662f\u4e2a\u80cc\u5305\u3002<\/p>\n<p>\u8bb0 \\(f_{i,j}\\) \u4e3a\u5df2\u9009 \\(i\\) \u4e2a\uff0c\u5bb9\u91cf\u4e3a \\(j\\) \u7684\u80cc\u5305\u7684\u6700\u5927\u4ef7\u503c\uff0c\u5219 \\(f_{i,j}=max\\{f_{i-1,j-k}+a_k\\}\\) \u3002<\/p>\n<p>\u90a3\u4e48\u8fd9\u6837\u662f \\(O(NMK)\\) \u4f1a TLE \uff0c\u600e\u4e48\u4f18\u5316\uff1f\uff1f\uff1f<\/p>\n<p>\u6ce8\u610f\u5230\u5176\u5b9e \\(k\\) \u4e0d\u5fc5\u679a\u4e3e \\(1\\) ~ \\(j\\) \uff0c\u53ea\u9700 \\(1\\) ~ \\(\\frac{j}{i}\\) \u5373\u53ef\u3002<\/p>\n<p>\u7384\u5b66\u7406\u89e3\u4e00\u4e0b\uff0c\u8fd9\u91cc\u662fdalao\u4eec\u7684\u89e3\u91ca<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-852\" src=\"https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/QQ\u622a\u56fe20190130135419.png\" alt=\"\" width=\"768\" height=\"152\" srcset=\"https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/QQ\u622a\u56fe20190130135419.png 768w, https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/QQ\u622a\u56fe20190130135419-300x59.png 300w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-853\" src=\"https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/QQ\u622a\u56fe20190130135507.png\" alt=\"\" width=\"336\" height=\"100\" srcset=\"https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/QQ\u622a\u56fe20190130135507.png 336w, https:\/\/0.mnihyc.com\/blog\/wp-content\/uploads\/2019\/01\/QQ\u622a\u56fe20190130135507-300x89.png 300w\" sizes=\"auto, (max-width: 336px) 100vw, 336px\" \/><\/p>\n<p>&nbsp;<\/p>\n<pre class=\"minimize:true lang:default decode:true \">#include &lt;cstdio&gt;\r\n#include &lt;cstdlib&gt;\r\n#include &lt;cstring&gt;\r\n#include &lt;climits&gt;\r\n\r\n#define _max(_a,_b) ((_a)&gt;(_b)?(_a):(_b))\r\n\r\ntypedef long long LLONG;\r\n\r\nint a[3050];\r\nLLONG f[1050][8050];\r\n\r\nint main()\r\n{\r\n\tregister int N,M,K;scanf(\"%d%d%d\",&amp;N,&amp;M,&amp;K);\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tscanf(\"%d\",&amp;a[i]);\r\n\tfor(register int i=0;i&lt;=M;i++)\r\n\t\tfor(register int j=0;j&lt;=K;j++)\r\n\t\t\tf[i][j]=LLONG_MIN;\r\n\tf[0][0]=0;\r\n\tfor(register int i=1;i&lt;=M;i++)\r\n\t\tfor(register int j=1;j&lt;=K;j++)\r\n\t\t\tfor(register int k=1;k&lt;=N &amp;&amp; j-k&gt;=0 &amp;&amp; k*i&lt;=j;k++)\r\n\t\t\t\tf[i][j]=_max(f[i][j],f[i-1][j-k]+a[k]);\r\n\tLLONG ans=0;\r\n\tfor(register int i=1;i&lt;=K;i++)\r\n\t\tans=_max(ans,f[M][i]);\r\n\tprintf(\"%lld\\n\",ans);\r\n\treturn 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/timgsa.baidu.com\/timg?image&amp;quality=80&amp;size=b9999_10000&amp;sec=1548837940980&amp;di=c5b11668f343ae53fe90f4e306d84087&amp;imgtype=0&amp;src=http%3A%2F%2Fmmbiz.qpic.cn%2Fmmbiz_jpg%2FVGNszaZ66LNYY6uibBmLQCpM2scZwediauxAOiaZKHpa7C8yV0ia5abBMYFH7qO12rJY22UBvHufQwicGibvgN3DqMPw%2F640%3Fwx_fmt%3Djpeg\"><span style=\"color: #0000ff;\">\u71c3\u9e45<\/span><\/a>\u6211\u6bd4\u8f83\u83dc\uff0cdalao\u4eec\u9ad8\u7aef\u7684\u65b9\u6cd5\u6211\u8fd8\u662f\u60f3\u5f97\u4e00\u77e5\u534a\u89e3\uff0c\u4e8e\u662f\u8fd9\u662f\u6211\u81ea\u5df1\u7684\u7406\u89e3\u3002<\/p>\n<p>\u5176\u5b9e\u53ef\u4ee5\u8003\u8651\u4f7f\u7528\u8bb0\u641c\u7684\u65b9\u6cd5\u6765\u5b9e\u73b0\u8fd9\u4e2a\u80cc\u5305\u3002<\/p>\n<p>\u641c\u7d22\u7684\u65f6\u5019\u8ba1\u4e24\u4e2a\u72b6\u6001\uff0c\u8868\u793a\u5f53\u524d\u641c\u7d22\u5230 \\(b\\) \u6570\u7ec4\u4e2d\u7684\u7b2c\u51e0\u4e2a\u6570\uff08\\(step\\)\uff09\u548c\u8fd8\u5269\u4e0b\u591a\u5c11\u5bb9\u91cf\u53ef\u4ee5\u4f7f\u7528\uff08\\(left\\)\uff09\u3002\u521d\u59cb\u5c31\u662f \\(DFS(1,K)\\) \uff0c\u8f6c\u79fb\u5c31\u662f \\(max\\{DFS(step+1, left-i)+a_i\\}, i=1 \\) ~ \\(N\\) \u3002<\/p>\n<p>\u641c\u7d22\u7684\u65f6\u5019\u6ee1\u8db3 \\(left \\geq 0\\) \u3002\u7ed3\u675f\u72b6\u6001\u5c31\u662f \\(step&gt;M\\) \u3002 \u7136\u540e\u518d\u8bb0\u5fc6\u5316\u4e00\u4e0b\uff0c\u590d\u6742\u5ea6\u5c31\u662f \\(O(NMK)\\) \u548c\u88f8\u7684\u80cc\u5305\u76f8\u540c\u3002<\/p>\n<p>\u8003\u8651\u5bf9\u8fd9\u4e2a\u641c\u7d22\u8fdb\u884c\u4f18\u5316\uff0c\u6700\u5e38\u89c1\u7684\u5c31\u662f\u8c03\u6574\u641c\u7d22\u5e8f\u3002\u5148\u641c\u5927\u7684\u80af\u5b9a\u6bd4\u5148\u641c\u5c0f\u7684\u66f4\u5feb\uff0c\u53c8\u56e0\u4e3a\u987a\u5e8f\u5bf9\u7b54\u6848\u6ca1\u6709\u5f71\u54cd\uff0c\u6240\u4ee5\u4ece\u5927\u5230\u5c0f\u641c\u7d22 \\(b\\) \u6570\u7ec4\u4e2d\u7684\u5143\u7d20\uff0c\u4e5f\u5c31\u662f\u6ee1\u8db3 \\(\\forall 1 \\leq i \\leq j \\leq N\\) \u90fd\u6709 \\(b_i \\geq b_j\\) \u3002 \u5177\u4f53\u5b9e\u73b0\u5c31\u662f\u518d\u8ba1\u4e00\u4e2a\u53d8\u91cf \\(prev\\) \u8868\u793a \\(b_{step-1}\\) \u9009\u7684\u6570\uff0c\u90a3\u4e48 \\(b_{step}\\) \u9009\u7684\u6570\u4e00\u5b9a\u4e0d\u80fd\u6bd4\u5b83\u5927\u3002<\/p>\n<p>\u8981\u6ce8\u610f\u7684\u662f\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u662f\u5b8c\u5168\u80cc\u5305\u95ee\u9898\uff0c\u5982\u679c\u4e0d\u6309\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f\u679a\u4e3e \\(b_{step}\\) \u9009\u7684\u6570\u7684\u8bdd\u5c31\u4f1a\u9020\u6210\u6709\u91cd\u590d\u7684\u72b6\u6001\u3002\u6240\u4ee5\u679a\u4e3e\u7684\u65f6\u5019\u4e0d\u80fd\u4ece \\(prev\\) ~ \\(1\\) \uff0c\u4e00\u5b9a\u8981\u4ece \\(1\\) ~ \\(prev\\) \uff01<\/p>\n<p>\u8fd9\u6837\u65f6\u95f4\u590d\u6742\u5ea6\uff08\u6211\u4e0d\u4f1a\u8bc1\uff09\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7\u672c\u9898\u3002<\/p>\n<p>\u4ee3\u7801\uff08\u8dd1\u5f97\u5de8\u6162\uff09\uff1a<\/p>\n<pre class=\"lang:default decode:true \">#include &lt;cstdio&gt;\r\n#include &lt;climits&gt;\r\n#define _max(_a,_b) ((_a)&gt;(_b)?(_a):(_b))\r\ntypedef long long LLONG;\r\nint N,M,K;\r\nint a[3050];\r\nLLONG saved[1050][8050];\r\nLLONG DFS(int step,int left,int prev)\r\n{\r\n    if(left&lt;0)return LLONG_MIN;\r\n    if(step&gt;M)return (left&gt;=0 ? 0 : LLONG_MIN);\r\n    if(saved[step][left])return saved[step][left];\r\n    LLONG ans=LLONG_MIN;\r\n    for(register int i=1;i&lt;=prev;i++)\r\n        ans=_max(ans,DFS(step+1,left-i,i)+a[i]);\r\n    return saved[step][left]=(ans&lt;0?LLONG_MIN:ans);\r\n}\r\nint main()\r\n{\r\n    scanf(\"%d%d%d\",&amp;N,&amp;M,&amp;K);\r\n    for(register int i=1;i&lt;=N;i++)scanf(\"%d\",&amp;a[i]);\r\n    printf(\"%lld\\n\",DFS(1,K,N));\r\n    return 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YZOJ P3754 Gab\u6570\u5217 \u65f6\u95f4\u9650\u5236\uff1a2000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a131072KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf &hellip; <a href=\"https:\/\/0.mnihyc.com\/blog\/archives\/851\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P3754 Gab\u6570\u5217<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[52,40,60],"tags":[],"class_list":["post-851","post","type-post","status-publish","format-standard","hentry","category-mediuma","category-bagdp","category-memsearch"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ 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