POJ 2559. Largest Rectangle in a Histogram<\/a>\u3002<\/p>\n\u6211\u4eec\u53d1\u73b0\u4e4b\u524d\u662f\u8981\u5904\u7406\u51fa\uff0c\u4ee5 h[i] \u4e3a\u6700\u4f4e\u70b9\uff0c\u5de6\u53f3\u4e24\u8fb9\u5206\u522b\u53ef\u4ee5\u5ef6\u4f38\u591a\u8fdc\u3002
\n\u8fd9\u91cc\u6070\u597d\u662f\u6c42\uff0c\u4ee5 h[i] \u4e3a\u6700\u9ad8\u70b9\uff0c\u5de6\u53f3\u4e24\u8fb9\u5206\u522b\u53ef\u4ee5\u5ef6\u4f38\u591a\u8fdc\uff0c\u5047\u8bbe\u5c31\u662f Dl[i] \u548c Dr[i]\u3002
\n\u8fd9\u6837\u552f\u4e00\u4e0d\u540c\u7684\u662f\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u4e00\u4e2a\u7d2f\u8ba1\u4ee3\u4ef7\u6570\u7ec4 Sl[i] \u548c Sr[i]\uff0c\u5206\u522b\u8868\u793a\u4ee5 h[i] \u4e3a\u6700\u9ad8\u70b9\uff0c\u5f80\u5de6\u548c\u5f80\u53f3\u7d2f\u8ba1\u7684\u4ee3\u4ef7\u3002
\n\u56e0\u4e3a\u6700\u540e\u7b54\u6848\u5c31\u662f\uff1a
\n$$\\Sigma_{i=1}^n Dl[i] * Sr[i] + Dr[i] * Sl[i]$$<\/p>\n
\u6211\u4eec\u53ef\u4ee5\u5728\u7ef4\u62a4\u5355\u8c03\u6808\u7684\u8fc7\u7a0b\u4e2d\uff0c\u987a\u8def\u6c42 Sl \u51fa Sr\u3002\u4e0d\u653e\u8003\u5bdf\u4ece\u5de6\u5f80\u53f3\u626b\u63cf\u6c42 Dl \u7684\u8fc7\u7a0b\u3002
\n\u8bbe\u5f53\u524d\u626b\u63cf\u5230\u4f4d\u7f6e i\uff0c\u5c06\u8981\u88ab\u5f39\u51fa\u7684\u6808\u9876\u5143\u7d20\u4e3a sp\uff0c\u8fd9\u4e2a\u4f4d\u7f6e\u53f3\u8fb9\u4e00\u76f4\u5230 i \u8fd9\u4e2a\u533a\u95f4\u73b0\u5728\u90fd\u81f3\u5c11\u9700\u8981\u662f h[sp] \u7684\u9ad8\u5ea6\u624d\u7b26\u5408\u8981\u6c42\u3002
\n\u8bb0\u8fd9\u4e2a\u4ee3\u4ef7\u4e3a\u5c0f\u5199\u7684 sl\uff0c\u6211\u4eec\u9884\u5904\u7406\u90e8\u5206\u548c\u540e\u53ef\u4ee5 O(1) \u7684\u6c42\u51fa sl\u3002\u8bb0\u65b0\u7684\u6808\u9876\u5143\u7d20\u7684\u4f4d\u7f6e\u4e0e\u521a\u624d\u88ab\u6211\u4eec\u5f39\u51fa\u7684\u6808\u9876\u5143\u7d20\u7684\u4f4d\u7f6e\u4e4b\u95f4\u7684\u8ddd\u79bb\u4e3a sp – s.top()\uff0c
\nsl \u9700\u8981\u88ab\u7edf\u8ba1 sp – s.top() \u6b21\u3002\u6700\u540e\u52a0\u4e0a\u8fd9\u4e2a\u533a\u95f4\u672c\u8eab\u7684\u4ee3\u4ef7 Sl[sp]\u3002<\/p>\n
stack<int> s; s.push(0); REP_1(i, n) {\n Sl[i] = 0;\n while (h[i] > h[s.top()]) {\n int sp = s.top(); s.pop();\n Int sl = Int(h[sp]) * (i-sp-1) - (hh[i-1]-hh[sp]);\n Sl[i] += sl * (sp - s.top()) + Sl[sp];\n }\n Dl[i] = i - s.top();\n s.push(i);\n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"Problem B. Pancake Pyramid Brief Description \u7ed9\u5b9a\u957f\u5ea6\u4e3a n \u7684\u5e8f\u5217 h[i]\u3002 \u6bcf\u6b21\u4f60\u53ef\u4ee5\u9009\u62e9\u4e00\u6bb5\u8fde\u7eed\u5b50\u5e8f\u5217 [l, r]\uff0c\u4f60\u53ef\u4ee5\u7ed9\u5176\u4e2d\u67d0\u4e9b\u9879\u6267\u884c +1 \u64cd\u4f5c\uff0c\u4f7f\u5f97\u64cd\u4f5c\u540e\u5f62\u6210\u4e00\u4e2a\u91d1\u5b57\u5854\u5f62\u72b6\uff08\u5148\u9012\u589e\u518d\u9012\u51cf\uff09\u3002 \u95ee\u904d\u5386\u6240\u6709\u7684\u5b50\u5e8f\u5217\uff0c\u603b\u64cd\u4f5c\u6b21\u6570\u6700\u5c11\u662f\u591a\u5c11\u3002 Analysis \u76f8\u540c\u5143\u7d20\u53ef\u80fd\u4f1a\u5e26\u6765\u91cd\u590d\u8ba1\u6570\uff0c\u6211\u4eec\u7edf\u4e00\u5148\u8ba4\u4e3a\u76f8\u540c\u7684\u5143\u7d20\u51fa\u73b0\u65f6\uff0c\u5de6\u8fb9\u7684\u66f4\u5927\u3002 \u8003\u8651\u66b4\u529b\u505a\u6cd5\u3002\u6ce8\u610f\u5230\u6211\u4eec\u8fd9\u91cc \u53ea\u6709 +1 \u64cd\u4f5c\uff0c\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u8d2a\u5fc3\u3002 \u6bcf\u6b21\u679a\u4e3e\u533a\u95f4\uff0c\u8bbe: – M[l][r] \u8868\u793a [l, r] \u533a\u95f4\u6700\u5927\u7684\u6570\u7684\u4f4d\u7f6e\u3002 – L[l][r] \u8868\u793a\u628a [l, r] \u8fd9\u4e2a\u533a\u95f4\u5904\u7406\u6210\u9012\u589e\u5e8f\u5217\u7684\u6700\u5c0f\u4ee3\u4ef7\u3002 – R[l][r] \u8868\u793a\u628a [l, r] \u8fd9\u4e2a\u533a\u95f4\u5904\u7406\u6210\u9012\u51cf\u5e8f\u5217\u7684\u6700\u5c0f\u4ee3\u4ef7\u3002 \u90a3\u4e48\u6211\u4eec\u679a\u4e3e\u6240\u6709\u7684\u533a\u95f4\uff0c\u7edf\u8ba1\u6240\u6709 L[l][m] + R[m][r] \u5c31\u662f\u7b54\u6848\uff0c\u53ef\u4ee5\u9884\u5904\u7406\u8fd9\u4e9b\u6570\u7ec4\uff0c\u590d\u6742\u5ea6 O(n2)\uff0c\u53ef\u4ee5\u8fc7\u5c0f\u6570\u636e\u3002 \u8003\u8651\u5927\u6570\u636e\uff0c\u5176\u5b9e\u9898\u76ee\u91cc\u5df2\u7ecf\u75af\u72c2\u6697\u793a\u4f60\u4e86\u8981\u7528\u5355\u8c03\u6808\uff08stack\uff09\u3002\u3002\u3002 \u56de\u5fc6 POJ 2559. Largest Rectangle in a […]<\/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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[67],"tags":[],"class_list":["post-1510","post","type-post","status-publish","format-standard","hentry","category-google-code-jam"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-om","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1510","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=1510"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1510\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=1510"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=1510"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=1510"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}