{"id":169,"date":"2018-10-20T00:24:17","date_gmt":"2018-10-19T16:24:17","guid":{"rendered":"http:\/\/SmokeyDays.top\/wordpress\/?p=169"},"modified":"2019-03-12T12:45:12","modified_gmt":"2019-03-12T04:45:12","slug":"lp3084-usaco13open-%e7%85%a7%e7%89%87-photo","status":"publish","type":"post","link":"http:\/\/SmokeyDays.top\/wordpress\/2018\/10\/20\/lp3084-usaco13open-%e7%85%a7%e7%89%87-photo\/","title":{"rendered":"lp3084 USACO13OPEN \u7167\u7247 Photo"},"content":{"rendered":"<p>\u4f20\u8bf4\u8fd9\u4e00\u9898\u53ef\u4ee5\u7528\u5dee\u5206\u7ea6\u675f\uff0c\u4e0d\u8fc7\u6211\u4e2a\u4eba\u7684\u7b2c\u4e00\u773c\u60f3\u6cd5\u662f\\(DP\\)\u3002<br \/>\n\u9996\u5148\u6211\u4eec\u4ee4\\(f_{i}\\)\u4e3a\uff0c\u7b2c\\(i\\)\u4e2a\u5976\u725b\u6709\u6591\u70b9\uff0c\\(DP\\)\u5230\u7b2c\\(i\\)\u4e2a\u5976\u725b\uff0c\u6b64\u65f6\u6700\u591a\u6709\u591a\u5c11\u53ea\u5976\u725b\u3002<br \/>\n\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\u4e24\u70b9\uff1a\u4e00\u4e2a\u533a\u95f4\u6700\u591a\u67091\u4e2a\u6709\u6591\u70b9\u7684\u5976\u725b\uff0c\u4e14\u4e00\u4e2a\u533a\u95f4\u6700\u5c11\u67091\u4e2a\u6709\u6591\u70b9\u7684\u5976\u725b\u3002<br \/>\n\u5bf9\u4e8e\u5f53\u524d\u7684\u70b9\uff0c\u6211\u4eec\u5f88\u5bb9\u6613\u53ef\u4ee5\u77e5\u9053\uff0c\u6240\u6709\u8986\u76d6\u5f53\u524d\u70b9\u7684\u533a\u95f4\uff0c\u5728\u5176\u4ed6\u7684\u5730\u65b9\u90fd\u4e0d\u80fd\u6709\u6709\u6591\u70b9\u7684\u5976\u725b\u3002<br \/>\n\u8fd9\u4e5f\u5c31\u7b49\u4ef7\u4e8e\uff0c\u8f6c\u79fb\u662f\u5fc5\u987b\u4ece\u5305\u542b\\(f_{i}\\)\u7684\u6240\u6709\u533a\u95f4\u4e2d\u7684\u5de6\u7aef\u70b9\u7684\u6700\u5c0f\u503c\u5f00\u59cb\u8f6c\u79fb\u7684\u3002<br \/>\n\u4e0e\u6b64\u540c\u65f6\uff0c\u6211\u4eec\u8fd8\u5fc5\u987b\u660e\u767d\uff0c\u56e0\u4e3a\u6bcf\u4e2a\u533a\u95f4\u6700\u5c11\u6709\u4e00\u4e2a\u6709\u6591\u70b9\u7684\u5976\u725b\uff0c\u56e0\u800c\u4e3a\u4e86\u4fdd\u8bc1\u6ee1\u8db3\u63d0\u8bae\uff0c\u8f6c\u79fb\u70b9\u5230\\(f_{i}\\)\u4e4b\u95f4\u7684\u6240\u6709\u533a\u95f4\u4e0d\u80fd\u6709\u7a7a\u7684\u3002<br \/>\n\u8fd9\u4e5f\u5c31\u7b49\u4ef7\u4e8e\uff0c\u6240\u6709\u4e0d\u5305\u542b\\(f_{i}\\)\uff08\u5f53\u7136\u663e\u7136\u533a\u95f4\u53f3\u7aef\u70b9\u8981\u5c0f\u4e8e\\(i\\)\uff09\u7684\u533a\u95f4\uff0c\u5b83\u4eec\u7684\u5de6\u7aef\u70b9\u4e2d\u7684\u6700\u5927\u503c\u5fc5\u987b\u8981\u5c0f\u4e8e\u8f6c\u79fb\u70b9\u3002\u8fd9\u6837\u624d\u80fd\u4e0a\u8ff0\u6027\u8d28\u3002<br \/>\n\u6b64\u65f6\u6211\u4eec\u53ea\u9700\u8981\u9884\u5904\u7406\u51fa\u5305\u542b\u70b9i\u4e14\u5de6\u7aef\u70b9\u6700\u5c0f\u7684\u533a\u95f4\uff0c\u4ee5\u53ca\u53f3\u7aef\u70b9\u5c0f\u4e8e\\(i\\)\u4e14\u5de6\u7aef\u70b9\u6700\u5927\u7684\u533a\u95f4\u3002\u6211\u4eec\u5206\u522b\u7528\\(e_{i}\\)\u548c\\(s_{i}\\)\u8868\u793a\u3002<br \/>\n\u5bf9\u4e8e\u8bfb\u5165\u7684\u6bcf\u4e00\u7ec4\\(a,b\\)\uff0c\u6211\u4eec\u505a\u5982\u4e0b\u5904\u7406\uff1a<br \/>\n\u4f7f\u7528\\(a\\)\u6765\u66f4\u65b0\\(s_{b+1}\\)\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u4ece\\(a\\)\u5f00\u59cb\u7684\u533a\u95f4\u5fc5\u7136\u4e0d\u5305\u542b\\(b+1\\)\uff0c\u56e0\u6b64\u53ef\u4ee5\u8fd9\u6837\u66f4\u65b0\u3002<br \/>\n\u4f7f\u7528\\(a-1\\)\u6765\u66f4\u65b0\\(e_{b}\\)\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u4ece\\(a\\)\u5f00\u59cb\u7684\u533a\u95f4\u5fc5\u7136\u5305\u542b\\(b\\)\u3002<br \/>\n\u6545\uff0c\u66f4\u65b0\u65b9\u6cd5\u4e3a\uff1a<br \/>\n$$ s_{b+1}=Max(s_{b+1},a),e_{b}=Min(e_{b},a-1); $$<br \/>\n\u7136\u540e\uff0c\u5bf9\u4e8e\u8fd9\u6837\u66f4\u65b0\u5f97\u5230\u7684\u7ed3\u679c\uff0c\u6211\u4eec\u8d2a\u5fc3\u5730\u5904\u7406\u3002<br \/>\n\u5bf9\u4e8e\\(s\\)\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u6240\u6709\u5bf9\u4e8e\u70b9\\(i-1\\)\u5408\u6cd5\u7684\u533a\u95f4\u2014\u2014\u4e5f\u5c31\u662f\u53f3\u7aef\u70b9\u5c0f\u4e8e\\(i-1\\)\u7684\u533a\u95f4\uff0c\u4e00\u5b9a\u4e0d\u5305\u542b\\(i\\)\u3002\u6240\u4ee5\u5f97\u5230\uff1a<br \/>\n$$ s_{i}=Max(s_{i},s_{i-1}); $$<br \/>\n\u5bf9\u4e8e\\(e\\)\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u6240\u6709\u5bf9\u4e8e\u70b9\\(i+1\\)\u6700\u4f18\u7684\u533a\u95f4\u2014\u2014\u4e5f\u5c31\u662f\u5305\u542b\\(i+1\\)\u4e14\u5de6\u7aef\u70b9\u6700\u5c0f\u7684\u533a\u95f4\uff0c\u4e00\u5b9a\u5305\u542b\\(i\\)\uff0c\u5426\u5219\u5b83\u5bf9\u4e8e\\(i\\)\u4e00\u5b9a\u4e0d\u4f1a\u66f4\u4f18\u3002\u6240\u4ee5\u5f97\u5230\uff1a<br \/>\n$$ e_{i}=Min(e_{i+1},e_{i}); $$<br \/>\n\u7531\u662f\u6211\u4eec\u5f97\u5230\u4e86DP\u9700\u8981\u7684\u4e24\u4e2a\u8f85\u52a9\u6570\u7ec4\uff0c\u4ece\u800c\u53ef\u4ee5\u5f00\u59cb\\(DP\\)\u3002<br \/>\n\u4f46\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0c\u8fd9\u6837\u5b50\u52a8\u6001\u786e\u5b9a\u6700\u5927\u503c\uff0c\u5982\u679c\u4f7f\u7528\u66b4\u529b\u679a\u4e3e\uff0c\u9700\u8981\u7684\u590d\u6742\u5ea6\u662f\\(O(n)\\)\u7684\uff0c\u5bf9\u4e8e\\(2E5\\)\u7684\u6570\u636e\uff0c\u901a\u8fc7\u4f1a\u5f88\u56f0\u96be\u3002<br \/>\n\u8fd9\u65f6\u5019\u8003\u8651\u4f18\u5316\uff0c\u4e0d\u8fc7\u5f88\u5bb9\u6613\u53ef\u4ee5\u53d1\u73b0\u662f\u5355\u8c03\u961f\u5217\u4f18\u5316\u3002<br \/>\n\u4e8e\u662f\u95ee\u9898\u5f97\u89e3\u3002<\/p>\n<p>\u4ea4\u4e0a\u53bbWA10\u3002<br \/>\n\u8fd9\u662f\u4ec0\u4e48\u539f\u56e0\u5462\uff1f<br \/>\n\u4ed4\u7ec6\u7814\u7a76\u4e00\u4e0b\uff0c\u53d1\u73b0\u8fd8\u662f\u7ec6\u8282\u7684\u95ee\u9898\u3002\u5bf9\u4e8e-1\u7684\u7279\u5224\u6ca1\u6709\u6e05\u695a\u3002<br \/>\n\u4fee\u6539\u4e4b\u540eAC\u3002<\/p>\n<pre class=\"pure-highlightjs\"><code class=\"cpp\">#include&lt;iostream&gt;\n#include&lt;cstdio&gt;\n#include&lt;queue&gt;\nusing namespace std;\n#define Max(_A,_B) ((_A)&gt;(_B)?(_A):(_B))\n#define Min(_A,_B) ((_A)&lt;(_B)?(_A):(_B))\n\nint n,m,f[200005],s[200005],e[200005];\nstruct data{\n\tint v;\n\tint id;\n};\ndeque&lt;data&gt; q;\ninline void psh(int i){\n\tdata x=(data){f[i],i};\n\twhile(!q.empty()&amp;&amp;q.back().v&lt;x.v){\n\t\tq.pop_back();\n\t}\n\tq.push_back(x);\n}\ninline int gt(const int &amp;i){\n\twhile(!q.empty()&amp;&amp;q.front().id&lt;s[i]){\n\t\tq.pop_front();\n\t}\n\treturn q.empty()?-1:q.front().v;\n}\nvoid init(){\n\tscanf(\"%d%d\",&amp;n,&amp;m);\n\tint a,b;\n\tfor(int i=1;i&lt;=n+1;++i){\n\t\te[i]=i-1; \n\t}\n\tfor(int i=1;i&lt;=m;++i){\n\t\tscanf(\"%d%d\",&amp;a,&amp;b);\n\t\ts[b+1]=Max(s[b+1],a),e[b]=Min(e[b],a-1);\n\t}\n\tfor(int i=2;i&lt;=n+1;++i){\n\t\ts[i]=Max(s[i],s[i-1]);\n\t}\n\tfor(int i=n;i&gt;=1;--i){\n\t\te[i]=Min(e[i+1],e[i]); \n\t}\n\tf[0]=0;\n\tpsh(0);\n\tint j=1,nw;\n\tfor(int i=1;i&lt;=n+1;++i){\n\t\twhile(j&lt;=e[i]&amp;&amp;j&lt;=n){\n\t\t\tpsh(j);\n\t\t\t++j;\n\t\t}\n\t\tnw=gt(i);\n\t\tf[i]=(nw==-1)?-1:nw+(int)(i&lt;=n);\n\t}\n\tprintf(\"%d\",f[n+1]);\n}\nint main(){\n\tinit();\n\treturn 0;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u4f20\u8bf4\u8fd9\u4e00\u9898\u53ef\u4ee5\u7528\u5dee\u5206\u7ea6\u675f\uff0c\u4e0d\u8fc7\u6211\u4e2a\u4eba\u7684\u7b2c\u4e00\u773c\u60f3\u6cd5\u662f\\(DP\\)\u3002 \u9996\u5148\u6211\u4eec\u4ee4\\(f_{i}\\)\u4e3a\uff0c\u7b2c\\(i\\) &hellip; <\/p>\n<p class=\"link-more\"><a href=\"http:\/\/SmokeyDays.top\/wordpress\/2018\/10\/20\/lp3084-usaco13open-%e7%85%a7%e7%89%87-photo\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u201clp3084 USACO13OPEN \u7167\u7247 Photo\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":[16,5],"tags":[],"_links":{"self":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/169"}],"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=169"}],"version-history":[{"count":2,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/169\/revisions"}],"predecessor-version":[{"id":706,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/169\/revisions\/706"}],"wp:attachment":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/media?parent=169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/categories?post=169"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/tags?post=169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}