$y = f_j + x^2 $<\/li>\n<\/ul>\n\u8fd9\u91cc $x$ \u548c $k$ \u5747\u5355\u8c03\uff08\u56e0\u4e3a $s_i$ \u5355\u8c03\uff09\uff0c\u5355\u8c03\u961f\u5217\u5373\u53ef\u3002<\/p>\n
\r\n\/\/}\/* .................................................................................................................................. *\/\r\n\r\nconst int N = int(5e4) + 9;\r\n\r\nLL f[N], s[N]; int q[N], cz, op;\r\nint n, L;\r\n\r\n#define k (-2*(s[i]-L))\r\n#define x(i) (s[i])\r\n#define y(i) (f[i]+sqr(x(i)))\r\n#define eval(i) (k*x(i)+y(i))\r\n\r\nLL det(LL x1, LL y1, LL x2, LL y2){\r\n return x1*y2 - x2*y1;\r\n}\r\n\r\nint dett(int p0, int p1, int p2){\r\n LL t = det(x(p1)-x(p0), y(p1)-y(p0), x(p2)-x(p0), y(p2)-y(p0));\r\n return t < 0 ? -1 : t > 0;\r\n}\r\n\r\nint main(){\r\n\r\n#ifndef ONLINE_JUDGE\r\n freopen("in.txt", "r", stdin);\r\n freopen("out.txt", "w", stdout);\r\n#endif\r\n\r\n RD(n, L); REP_1(i, n) s[i] = s[i-1] + RD();\r\n REP_1(i, n) s[i] += i; ++L;\r\n\r\n cz = 0, op = 0; q[cz] = 0; REP_1(i, n){\r\n while (cz < op && eval(q[cz]) >= eval(q[cz+1])) ++cz;\r\n f[i] = eval(q[cz]) + sqr(s[i]-L);\r\n while (cz < op && dett(q[op-1], q[op], i) <= 0) --op;\r\n q[++op] = i;\r\n }\r\n\r\n OT(f[n]);\r\n}\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"[mathjax] Brief description: \u7565\u3002\uff09 Analysis: \u9996\u5148\u5199\u597d\u66b4\u529b\u3002 \u89c2\u5bdf\uff0c\u5fae\u8c03\uff0c\u5206\u79bb\u5e38\u6570\u3002 REP_1(i, n) s[i] += i; ++L; \u5199\u6210\u659c\u7387\u4f18\u5316\u7684\u6807\u51c6\u5f62\u5f0f\uff0cb = kx + y \u8fd9\u91cc\u6709\uff1a $k = -2(s_i-L)$ $x = s_j $ $y = f_j + x^2 $ \u8fd9\u91cc $x$ \u548c $k$ \u5747\u5355\u8c03\uff08\u56e0\u4e3a $s_i$ \u5355\u8c03\uff09\uff0c\u5355\u8c03\u961f\u5217\u5373\u53ef\u3002 \/\/}\/* …………………………………………………………………………………………………………………. *\/ const int N = int(5e4) + 9; LL f[N], s[N]; int q[N], cz, […]<\/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":[22],"tags":[118],"class_list":["post-989","post","type-post","status-publish","format-standard","hentry","category-bzoj","tag-118"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-fX","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/989","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=989"}],"version-history":[{"count":2,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/989\/revisions"}],"predecessor-version":[{"id":2355,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/989\/revisions\/2355"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=989"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=989"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=989"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
![\" f_i = \min_{0 <= j < i}{ f_j + (i-j+s_i-s_{j-1}-L)^2 | j < i} \"](\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-b65df11f16719832f3dcfcb18b53ef08_l3.png\" "\\"Rendered")
<\/p>\n![\" \begin{aligned} f_i &= \min_{0 \leq j < i}{ f_j + ((s_i-L)-s_j)^2 } \ &= \min_{0 \leq j < i}{ -2(s_i-L)s_j + (f_j+s_j^2) } + (s_i-L)^2 \end{aligned} \"](\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-f372edbae04de60e4207f3e0234fa92d_l3.png\" "\\"Rendered")
<\/p>\n