{"id":906,"date":"2019-08-15T00:40:29","date_gmt":"2019-08-14T16:40:29","guid":{"rendered":"http:\/\/SmokeyDays.top\/wordpress\/?p=906"},"modified":"2019-08-15T00:40:29","modified_gmt":"2019-08-14T16:40:29","slug":"lp2501-haoi2006-%e6%95%b0%e5%ad%97%e5%ba%8f%e5%88%97","status":"publish","type":"post","link":"http:\/\/SmokeyDays.top\/wordpress\/2019\/08\/15\/lp2501-haoi2006-%e6%95%b0%e5%ad%97%e5%ba%8f%e5%88%97\/","title":{"rendered":"lp2501 HAOI2006 \u6570\u5b57\u5e8f\u5217"},"content":{"rendered":"\n<p>\u6211\u4eec\u5206\u522b\u8003\u8651\u4e00\u4e8c\u95ee\u3002<br>\n\u5bf9\u4e8e\u7b2c\u4e00\u95ee\uff0c\u6211\u4eec\u601d\u8003\u4e00\u4e2a\u5b50\u5e8f\u5217\u662f\u5408\u6cd5\u7684\u300c\u4e0d\u7528\u4fee\u6539\u300d\u7684\u5b50\u5e8f\u5217\u7684\u5145\u8981\u6761\u4ef6\u3002<br>\n\u5bb9\u6613\u60f3\u5230\u7684\uff0c\u8fd9\u4e2a\u6761\u4ef6\u662f\uff1a<br>\n$$ \\forall i,j\\in S, i=j-i$$<br>\n\u81ea\u7136\u8bed\u8a00\u5316\u5730\u8bf4\uff0c\u5c31\u662f\uff0c\u5bf9\u4e8e\u8fd9\u4e2a\u4e0d\u7528\u4fee\u6539\u7684\u5b50\u5e8f\u5217\u4e2d\u7684\u4efb\u610f\u4e24\u4e2a\u5143\u7d20\uff0c\u5b83\u4eec\u7684\u503c\u7684\u5dee\u8ddd\u81f3\u5c11\u8981\u5927\u4e8e\u5b83\u4eec\u95f4\u7684\u5143\u7d20\u4e2a\u6570\uff0c\u8fd9\u6837\u624d\u80fd\u653e\u5f97\u4e0b\u5b83\u4eec\u4e2d\u95f4\u7684\u5143\u7d20\u3002<br>\n\u79fb\u9879\uff0c\u6211\u4eec\u5f97\u5230\uff1a<br>\n$$a_j-j&gt;=a_i-i$$<br>\n\u6240\u4ee5\uff0c\u6211\u4eec\u4ee4\\(b_i=a_i-i\\)\uff0c\u90a3\u4e48\u7b2c\u4e00\u95ee\u4e2d\u4e0d\u7528\u4fee\u6539\u7684\u4e2a\u6570\u5c31\u662f\\(b\\)\u7684\u6700\u957f\u4e0d\u4e0b\u964d\u5b50\u5e8f\u5217\u957f\u5ea6\u3002<br>\n\u5bf9\u4e8e\u7b2c\u4e8c\u95ee\uff0c\u9996\u5148\uff0c\u5b83\u53ef\u4ee5\u88ab\u8f6c\u5316\u4e3a\u300c\u6700\u5c0f\u4fee\u6539\u4ee3\u4ef7\u6c42\\(b\\)\u5355\u8c03\u4e0d\u51cf\u300d\u3002<br>\n\u6211\u4eec\u6709\u4e00\u4e2a\u7ed3\u8bba\uff1a\u76f8\u90bb\u4e24\u5173\u952e\u70b9\\(i,j\\)\u95f4\u4e00\u5b9a\u53ef\u4ee5\u627e\u5230\u4e00\u6761\u5206\u754c\u7ebf\uff0c\u4f7f\u5f97\u7ebf\u5de6\u7aef\u7684\u6240\u6709\u70b9\u53d8\u5316\u6210\\(b_i\\)\uff0c\u53f3\u7aef\u6240\u6709\u70b9\u53d8\u5316\u6210\\(b_j\\)\u4f1a\u6700\u4f18\u3002<br>\n\u8fd9\u662f\u5982\u4f55\u8bc1\u660e\u7684\u5462\uff1f<br>\n\u9996\u5148\uff0c\u6211\u4eec\u77e5\u9053\uff0c\\(i,j\\)\u4e4b\u95f4\u7684\u4efb\u610f\u4e00\u4e2a\u70b9\uff0c\u5b83\u7684\u503c\u5fc5\u7136\u8981\u5c0f\u4e8e\\(b_i\\)\u6216\u8005\u5927\u4e8e\\(b_j\\)\uff0c\u5426\u5219\u9009\u53d6\u8fd9\u4e2a\u70b9\u53ea\u4f1a\u8ba9\u7b54\u6848\u66f4\u4f18\u3002<br>\n\u7136\u540e\uff0c\u6211\u4eec\u5c1d\u8bd5\u8fdb\u884c\u53cd\u8bc1\u3002\u5982\u679c\u6709\u4e00\u4e2a\u70b9\u4fee\u6539\u4ee5\u540e\u4f4d\u4e8e\u4e2d\u95f4\uff0c\u5e76\u4e14\u5b83\u53ef\u4ee5\u88ab\u4fee\u6539\u5230\u67d0\u4e00\u8fb9\uff0c\u90a3\u4e48\u663e\u7136\u4fee\u6539\u5230\u67d0\u4e00\u8fb9\u4e4b\u540e\u7b54\u6848\u4f1a\u66f4\u5c0f\u3002<br>\n\u5982\u679c\u5c06\u5206\u754c\u7ebf\u5b9a\u5728\u67d0\u5904\uff0c\u4f1a\u4f7f\u5f97\u67d0\u4e9b\u70b9\u4e0e\u5b83\u4eec\u7684\u6700\u4f18\u5904\u4e8e\u7684\u8fb9\u4e0d\u76f8\u540c\uff0c\u90a3\u4e48\u8003\u8651\u8fd9\u4e9b\u70b9\u4e0e\u5206\u754c\u70b9\u4e4b\u95f4\u7684\u5176\u4ed6\u70b9\u7684\u6570\u91cf\u3002<br>\n\u5982\u679c\u5176\u4ed6\u70b9\u7684\u6570\u91cf\u5c0f\u4e8e\u8fd9\u4e9b\u70b9\uff0c\u90a3\u4e48\u4e0d\u59a8\u628a\u8fd9\u4e9b\u70b9\u4fee\u6539\u540e\u7684\u4f4d\u7f6e\u6362\u5230\u53e6\u4e00\u8fb9\uff0c\u8fd9\u6837\u7b54\u6848\u5c31\u53d8\u5c0f\u4e86\u70b9\u6570\u5dee*\u4e0a\u4e0b\u4e24\u8fb9\u8ddd\u79bb\u3002<br>\n\u5426\u5219\uff0c\u4e0d\u5982\u4e0d\u4fee\u6539\u3002<br>\n\u6240\u4ee5\u6211\u4eec\u8bc1\u660e\u4e86\u8fd9\u4e2a\u7ed3\u8bba\u3002<br>\n\u7136\u540e\u662f\u5173\u4e8e\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u3002\u53ef\u4ee5\u8bc1\u660e\uff0c\u5728\u5e8f\u5217\u968f\u673a\u7684\u60c5\u51b5\u4e0b\uff0c\u6700\u957f\u4e0d\u4e0b\u964d\u5b50\u5e8f\u5217\u7684\u671f\u671b\u957f\u5ea6\u662flogn\u7ea7\u522b\u7684\u3002\uff08\u6211\u4e0d\u4f1a\u8bc1\uff0c\u4e5f\u627e\u4e0d\u5230\u6587\u7ae0\u3002\u6c42\u5927\u4f6c\u6559\u6559\u6211\uff09<\/p>\n\n\n\n<p>\u6ce8\u610f\uff1a\u8981\u63d0\u524d\u628a\\(b_0\\)\u8bbe\u6210\\(-INF\\)\uff0c\u5e76\u5728\u672b\u5c3e\u63d2\u5165\u4e00\u4e2a\\(INF\\)\u7684\u70b9\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#include&lt;iostream>\n#include&lt;cstdio>\n#include&lt;cstring>\n#include&lt;algorithm>\n#include&lt;queue>\n#include&lt;vector>\nusing namespace std;\n\ntypedef long long ll;\nconst int N=35005;\nconst int INF=0x3f3f3f3f;\ninline ll Abs(ll X){\n\treturn X>=0?X:-X;\n}\ninline ll Min(ll A,ll B){\n\treturn A&lt;B?A:B;\n}\nint n,a[N],b[N],nm[N];\nll f[N],sm1[N],sm2[N];\nstruct ee{\n\tint v;\n\tint nxt;\n}e[N];\nint h[N],et=0;\ninline void add(int U,int V){\n\te[++et]=(ee){V,h[U]};\n\th[U]=et;\n}\nvoid init(){\n\tscanf(\"%d\",&amp;n);\n\tfor(int i=1;i&lt;=n;++i){\n\t\tscanf(\"%d\",&amp;a[i]);\n\t\tb[i]=a[i]-i;\n\t}\n\tint cnt=0,nw;\n\tb[0]=-INF;f[0]=-INF;\n\tb[++n]=INF;\n\tfor(int i=1;i&lt;=n;++i){\n\t\tif(b[i]>=f[cnt]){\n\t\t\tf[++cnt]=b[i];\n\t\t\tnm[i]=cnt;\n\t\t}else{\n\t\t\tnw=upper_bound(f+1,f+cnt,b[i])-f;\n\t\t\tf[nw]=b[i];\n\t\t\tnm[i]=nw;\n\t\t}\n\t}\n\tprintf(\"%d\\n\",n-cnt);\n\tfor(int i=n;i>=0;--i){\n\t\tadd(nm[i],i);\n\t\tf[i]=INF;\n\t}\n\tf[0]=0;\n\tint v;\n\tfor(int i=1;i&lt;=n;++i){\n\t\tfor(int j=h[nm[i]-1];j;j=e[j].nxt){\n\t\t\tv=e[j].v;\n\t\t\tif(v>i||b[v]>b[i]){\n\t\t\t\tcontinue;\n\t\t\t}\n\t\t\tsm1[v]=0;\n\t\t\tfor(int k=v+1;k&lt;=i;++k){\n\t\t\t\tsm1[k]=sm1[k-1]+Abs(b[k]-b[v]);\n\t\t\t}\n\t\t\tsm2[i-1]=0;\n\t\t\tfor(int k=i-2;k>=v;--k){\n\t\t\t\tsm2[k]=sm2[k+1]+Abs(b[k+1]-b[i]);\n\t\t\t}\n\t\t\tfor(int k=v;k&lt;i;++k){\n\t\t\t\tf[i]=Min(f[i],f[v]+sm1[k]+sm2[k]);\n\t\t\t}\n\t\t}\n\t}\n\tprintf(\"%lld\\n\",f[n]);\n}\nint main(){\n\tinit();\n\treturn 0;\n}\n\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u6211\u4eec\u5206\u522b\u8003\u8651\u4e00\u4e8c\u95ee\u3002 \u5bf9\u4e8e\u7b2c\u4e00\u95ee\uff0c\u6211\u4eec\u601d\u8003\u4e00\u4e2a\u5b50\u5e8f\u5217\u662f\u5408\u6cd5\u7684\u300c\u4e0d\u7528\u4fee\u6539\u300d\u7684\u5b50\u5e8f\u5217\u7684\u5145\u8981\u6761\u4ef6\u3002 \u5bb9\u6613\u60f3\u5230\u7684\uff0c\u8fd9\u4e2a &hellip; <\/p>\n<p class=\"link-more\"><a href=\"http:\/\/SmokeyDays.top\/wordpress\/2019\/08\/15\/lp2501-haoi2006-%e6%95%b0%e5%ad%97%e5%ba%8f%e5%88%97\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u201clp2501 HAOI2006 \u6570\u5b57\u5e8f\u5217\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[34,8,9,6,5],"tags":[],"_links":{"self":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/906"}],"collection":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/comments?post=906"}],"version-history":[{"count":1,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/906\/revisions"}],"predecessor-version":[{"id":907,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/906\/revisions\/907"}],"wp:attachment":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/media?parent=906"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/categories?post=906"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/tags?post=906"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}