DIV 1 950. ProductQuery:
\n\u4e00\u4e2a\u5f85\u5b9a\u7684\u957f\u5ea6\u4e3a n \u7684\u6a21 10 \u6570\u7ec4\uff0c\u4e00\u7ec4\u8be2\u95ee (l, r, o)\uff0c\u8868\u793a\u4ece\u7b2c l \u4f4d\u8fde\u4e58\u5230\u7b2c r \u4f4d\u7684\u7ed3\u679c\u662f o .. .
\n\u8981\u6c42\u7ed9\u5b9a m \u7ec4\u8be2\u95ee\u4e4b\u540e\u8fd8\u539f\u6b64\u6570\u7ec4\u7684\u53ef\u80fd\u7ec4\u6570\u3002
\n(n \u2264 100, m \u2264 50 )
\n<\/p>\n
\u8be2\u95ee\u4e4b\u95f4\u5b58\u5728\u4e92\u76f8\u5d4c\u5957\u7684\u5173\u7cfb\uff0c\u5f00\u7ebf\u6bb5\u6811\u53c8\u65e0\u4ece\u4e0b\u624b\uff0c\u8003\u8651\u80a2\u89e3\u95ee\u9898\u3002<\/p>\n
\r\n\uff08\u663e\u7136\u4ece\u6570\u8bba\u89d2\u5ea6\u5f00\u59cb yy\u3002\u3002\uff09\r\n\u5bf9\u4e8e\u6a21 p \u6570\u7ec4\uff0c\u8be2\u95ee (l, r, o):\r\no = 0, \u5219 [l, r] \u533a\u95f4\u81f3\u5c11\u5b58\u5728\u4e00\u4e2a 0 \r\no = x, \u5219 [l, r] \u533a\u95f4\u4e0d\u80fd\u51fa\u73b0 0\uff0c\u6700\u540e\u4e00\u4f4d\u603b\u80fd\u627e\u5230\u4e00\u4e2a\u9006\u5143\u3002\r\n<\/pre>\n\uff08\u5bf9 10 \u5206\u89e3\u540e\u5f88\u81ea\u7136\u4f1a\u5f62\u6210 \u6a212 \u548c \u6a215 \u4e24\u4e2a\u5b50\u95ee\u9898\u3002\u3002\uff09
\n\u8003\u8651\u4e00\u822c\u7684\u6a21 p \u7248\u672c\u7684\u5b50\u95ee\u9898\uff0c\u89c2\u5bdf\u540e\u53d1\u73b0\uff0c\u5bf9\u5355\u4e2a\u6570\u53ea\u5b58\u5728\u4e09\u79cd\u72b6\u6001 \uff1a<\/p>\n\r\n0\r\n[1, p) \u4efb\u4f55\u4e00\u4e2a\u6570\r\n[1, p) \u4e2d\u7684\u67d0\u4e00\u4e2a\u6570\uff08\u88ab\u5404\u79cd\u7b49\u5f0f\u56fa\u5b9a\u4f4f\u4e86\u3002\uff09\r\n<\/pre>\n\u5bf9\u4e8e 0 \u7684\u60c5\u51b5\u53ef\u4ee5\u7acb\u523b\u5224\u65ad\u51fa\u6765\uff0c\u5bf9\u540e\u4e24\u79cd\u60c5\u51b5\uff0c\u53ef\u4ee5\u56fa\u5b9a\u4efb\u610f\u4e00\u4e2a\u6570\u4f4d\u540e\u5224\u65ad\u662f\u5426\u5b58\u5728\u77db\u76fe\u3002
\n\uff08\u56e0\u4e3a\u5bf9\u4e8e\u72b6\u6001 3\uff0c\u5982\u679c\u786e\u5b9e\u662f\u67d0\u4e00\u4e2a\u6570\u3002\u3002\u53ef\u4ee5\u901a\u8fc7\u9ed8\u8ba4\u4e00\u4e2a\u6570\u4f4d\u540e\u628a\u8fd9\u4e2a\u6570\u663e\u793a\u7684\u901a\u8fc7\u7b49\u5f0f\u8868\u793a\u51fa\u6765\u3002\u3002\uff09<\/p>\n\u3002\u3002\u3002\u8fd9\u6837\u8bbe\u8ba1 dp[i] \u8868\u793a\u7b2c i \u4e2a\u4f4d\u7f6e\u5982\u679c\u662f 0 \u7684\u65f6\u5019\u5b58\u5728\u7684\u6240\u6709\u65b9\u6848\u6570\uff0c\uff08\u5728\u6570\u7ec4\u672b\u5c3e\u518d\u6dfb\u52a0\u4e00\u4e2a\u9ed8\u8ba4\u4e3a 0 \u7684\u865a\u5777\u5783\u4ee5\u8bb0\u5f55\u6240\u6709\u65b9\u6848\u3002\uff09\u3002\u3002\u679a\u4e3e\u7684\u65f6\u5019\u627e\u524d\u9762\u5176\u4ed6\u53ef\u80fd\u662f 0 \u7684\u4f4d\u7f6e\uff0c\u7136\u540e\u7d2f\u8ba1 Count(l, r) \u8868\u793a l, r \u533a\u95f4\u6240\u6709\u7684\u6570\u90fd\u662f\u72b6\u6001 2 \u548c\u72b6\u6001 3 \u6240\u53ef\u80fd\u7684\u65b9\u6848\u6570\u3002\u3002<\/p>\n
\uff08\u3002\u3002\u8fd9\u6837\u5c31\u4e0d\u5b58\u5728\u8be2\u95ee\u4e4b\u95f4\u7684\u5d4c\u5957\u5f71\u54cd\u3002\u3002Count \u51fd\u6570\u8fd4\u56de\u7684\u7ed3\u679c\u4f1a\u662f p-1 \u7684\u67d0\u4e2a\u6574\u6b21\u5e42 \u6216\u8005 \u4e0d\u5408\u6cd5\u8fd4\u56de 0\u3002\u3002\uff09<\/p>\n
\u603b\u7684\u590d\u6742\u5ea6\u5927\u6982\u662f O(n2m) \u5427..<\/p>\n
\r\nconst int N = 50;\r\n\r\nDB dp[N][N][N][N];\r\n\r\nclass RandomColoring {\r\npublic:\r\n\tdouble getProbability(int N, int maxR, int maxG, int maxB, int startR, int startG, int startB, int d1, int d2) {\r\n\r\n\t\tRST(dp), dp[0][startR][startG][startB] = 1;\r\n\r\n\t\t#define u dp[i][r][g][b]\r\n\t\t#define v dp[i+1][r+dr][g+dg][b+db]\r\n\r\n\t\tREP(i, N) REP(r, maxR) REP(g, maxG) REP(b, maxB) if (u){\r\n\r\n\t\t int S = 0;\r\n\r\n\t\t FOR(dr, max(-r, -d2), min(maxR-r, d2+1)) FOR(dg, max(-g, -d2), min(maxG-g, d2+1)) FOR(db, max(-b, -d2), min(maxB-b, d2+1)){\r\n\t\t if (abs(dr) < d1 && abs(dg) < d1 && abs(db) < d1) continue;\r\n ++S;\r\n\t\t }\r\n\r\n\t\t FOR(dr, max(-r, -d2), min(maxR-r, d2+1)) FOR(dg, max(-g, -d2), min(maxG-g, d2+1)) FOR(db, max(-b, -d2), min(maxB-b, d2+1)){\r\n\t\t if (abs(dr) < d1 && abs(dg) < d1 && abs(db) < d1) continue;\r\n v += u \/ S;\r\n\t\t }\r\n\t\t}\r\n\r\n DB res = 0; int i = N - 1; REP(r, maxR) REP(g, maxG) REP(b, maxB) if (u){\r\n if (abs(r - startR) > d2 || abs(g - startG) > d2 || abs(b - startB) > d2 ||\r\n abs(r - startR) < d1 && abs(g - startG) < d1 && abs(b - startB) < d1)\r\n res += u;\r\n }\r\n\r\n\t\treturn res;\r\n\t}\r\n};\r\n<\/pre>\n\r\nconst int N = 50;\r\n\r\nDB dp[N][N][N][N], s[N+1][N+1][N+1];\r\nint w[N][N][N], maxR, maxG, maxB;\r\n\r\nDB sum(int x0, int y0, int z0, int x1, int y1, int z1){\r\n checkMin(++x1, maxR), checkMin(++y1, maxG), checkMin(++z1, maxB), checkMax(x0, 0), checkMax(y0, 0), checkMax(z0, 0);\r\n return s[x1][y1][z1] - s[x0][y1][z1] - s[x1][y0][z1] - s[x1][y1][z0] + s[x0][y0][z1] + s[x0][y1][z0] + s[x1][y0][z0] - s[x0][y0][z0];\r\n}\r\n\r\nclass RandomColoring {\r\npublic:\r\n\tdouble getProbability(int N, int maxR, int maxG, int maxB, int startR, int startG, int startB, int d1, int d2) {\r\n\r\n ::maxR = maxR, ::maxG = maxG, ::maxB = maxB;\r\n\t\tRST(dp, w, s), dp[0][startR][startG][startB] = 1;\r\n\r\n\t\tREP_1(r, maxR) REP_1(g, maxG) REP_1(b, maxB) s[r][g][b] = r * g * b;\r\n\t\tREP(r, maxR) REP(g, maxG) REP(b, maxB) w[r][g][b] = sum(r-d2, g-d2, b-d2, r+d2, g+d2, b+d2) - (d1 ? sum(r-d1+1, g-d1+1, b-d1+1, r+d1-1, g+d1-1, b+d1-1) : 0);\r\n\r\n\t\t#define u dp[i][r-1][g-1][b-1]\r\n\t\t#define w w[r-1][g-1][b-1]\r\n\t\t#define v dp[i+1][r][g][b]\r\n\r\n --N; REP(i, N){\r\n\r\n\t\t REP_1(r, maxR) REP_1(g, maxG) REP_1(b, maxB) {\r\n\t\t if (u && w) u \/= w;\r\n s[r][g][b] = u + s[r-1][g][b] + s[r][g-1][b] + s[r][g][b-1] - s[r-1][g-1][b] - s[r-1][g][b-1] - s[r][g-1][b-1] + s[r-1][g-1][b-1];\r\n }\r\n\r\n REP(r, maxR) REP(g, maxG) REP(b, maxB){\r\n v = sum(r-d2, g-d2, b-d2, r+d2, g+d2, b+d2) - (d1 ? sum(r-d1+1, g-d1+1, b-d1+1, r+d1-1, g+d1-1, b+d1-1) : 0);\r\n }\r\n\t\t}\r\n\r\n\t\t#undef u\r\n #define u dp[i][r][g][b]\r\n\r\n DB res = 0; int i = N; REP(r, maxR) REP(g, maxG) REP(b, maxB) if (u){\r\n if (abs(r - startR) > d2 || abs(g - startG) > d2 || abs(b - startB) > d2 ||\r\n abs(r - startR) < d1 && abs(g - startG) < d1 && abs(b - startB) < d1)\r\n res += u;\r\n }\r\n\r\n\t\treturn res;\r\n\t}\r\n};\r\n<\/pre>\n\r\nconst int Null = -1;\r\nconst int N = 109;\r\n\r\nVI L, R, O; VII adj[N];\r\nint A[N], n, m, mod;\r\n\r\n\r\nint _I(int x){\r\n FOR(i, 1, mod) if (i * x % mod == 1) return i;\r\n}\r\n\r\n#define v adj[u][i].first\r\n#define r adj[u][i].second\r\n\r\nbool dfs(int u, int val) {\r\n if (A[u] == Null) A[u] = val; else return A[u] == val;\r\n REP(i, SZ(adj[u])) if (!dfs(v, (u <= v ? r : _I(r)) * val % mod)) return false;\r\n return true;\r\n}\r\n\r\n#undef v\r\n#undef r\r\n\r\nint count(int l, int r) {\r\n\r\n if (r - l <= 0) return 1;\r\n\r\n REP(i, m){\r\n int a = L[i], b = R[i], o = O[i] % mod;\r\n if (!o && l <= a && b < r) return 0;\r\n }\r\n\r\n FOR_1(i, 0, n+1) CLR(adj[i]);\r\n\r\n REP(i, m){\r\n int a = L[i], b = R[i] + 1, o = O[i] % mod;\r\n if (a >= l && b <= r){\r\n adj[a].PB(MP(b, o));\r\n adj[b].PB(MP(a, o));\r\n }\r\n }\r\n\r\n int cnt = -1; FLC(A, Null);\r\n\r\n for (int i = l; i <= r; ++i) {\r\n if (A[i] == Null) {\r\n if (!dfs(i, 1)) return 0;\r\n ++cnt;\r\n }\r\n }\r\n\r\n return pow(mod-1, cnt);\r\n}\r\n\r\nint dp[N]; bool Z[N]; \/\/ could be zero ?\r\n\r\nLL calc(int mod) {\r\n\r\n FLC(Z, true), ::mod = mod; REP_1(i, n) REP(j, m){\r\n int l = L[j], r = R[j], o = O[j] % mod;\r\n if (o && l <= i && i <= r){Z[i] = false; break;}\r\n }\r\n\r\n RST(dp), dp[0] = 1;\r\n\r\n REP_1(i, n + 1) if (Z[i]){\r\n REP(l, i) if (Z[l]) INC(dp[i], pdt(dp[l], count(l + 1, i))); \/\/[l+1, i)\r\n }\r\n\r\n return dp[n+1];\r\n}\r\n\r\n\r\nclass ProductQuery {\r\npublic:\r\n int theInput(int N, vector<int> Qfrom, vector<int> Qto, vector<int> output) {\r\n n = N, m = SZ(Qfrom), L = Qfrom, R = Qto, O = output; REP(i, m) ++L[i], ++R[i];\r\n return pdt(calc(2), calc(5));\r\n }\r\n};\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"Brief description: DIV 1 950. ProductQuery: \u4e00\u4e2a\u5f85\u5b9a\u7684\u957f\u5ea6\u4e3a n \u7684\u6a21 10 \u6570\u7ec4\uff0c\u4e00\u7ec4\u8be2\u95ee (l, r, o)\uff0c\u8868\u793a\u4ece\u7b2c l \u4f4d\u8fde\u4e58\u5230\u7b2c r \u4f4d\u7684\u7ed3\u679c\u662f o .. . \u8981\u6c42\u7ed9\u5b9a m \u7ec4\u8be2\u95ee\u4e4b\u540e\u8fd8\u539f\u6b64\u6570\u7ec4\u7684\u53ef\u80fd\u7ec4\u6570\u3002 (n \u2264 100, m \u2264 50 )<\/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":[17],"tags":[38],"class_list":["post-178","post","type-post","status-publish","format-standard","hentry","category-topcoder","tag-38"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-2S","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/178","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=178"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/178\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=178"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=178"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}