{"id":4350,"date":"2018-12-24T14:52:21","date_gmt":"2018-12-24T11:52:21","guid":{"rendered":"http:\/\/java.mazurok.com\/?p=4350"},"modified":"2018-12-25T21:04:09","modified_gmt":"2018-12-25T18:04:09","slug":"e-olymp-1482-%d1%83%d0%bc%d0%bd%d0%be%d0%b6%d0%b5%d0%bd%d0%b8%d0%b5-%d0%bc%d0%b0%d1%82%d1%80%d0%b8%d1%86","status":"publish","type":"post","link":"https:\/\/java.mazurok.com\/?p=4350","title":{"rendered":"e-olymp 1482. \u0423\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446"},"content":{"rendered":"

\u0417\u0430\u0434\u0430\u0447\u0430<\/h1>\n

\u041f\u0443\u0441\u0442\u044c \u0434\u0430\u043d\u044b \u0434\u0432\u0435 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b $A$ \u0438 $B$ \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 $m \\times n$ \u0438 $n \\times q$ \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e:
\n$$A = \\begin{bmatrix} a_{11} & a_{12} & \\ldots & a_{1n} \\\\ a_{21} & a_{22} & \\ldots & a_{2n} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ a_{m1} & a_{m2} & \\ldots & a_{mn} \\end{bmatrix} \\; , \\; B = \\begin{bmatrix} b_{11} & b_{12} & \\ldots & b_{1q} \\\\ b_{21} & b_{22} & \\ldots & b_{2q} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ b_{n1} & b_{n2} & \\ldots & b_{nq} \\end{bmatrix} .$$
\n\u0422\u043e\u0433\u0434\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 $C$ \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c\u044e $m \\times q$ \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0438\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c:
\n$$C = \\begin{bmatrix} c_{11} & c_{12} & \\ldots & c_{1q} \\\\ c_{21} & c_{22} & \\ldots & c_{2q} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ c_{m1} & c_{m2} & \\ldots & c_{mq} \\end{bmatrix} ,$$
\n\u0433\u0434\u0435:
\n$$c_{i,j} = \\sum_{r=1}^{n} a_{i,r}b_{r,j} \\; \\left(i = 1, 2, \\ldots m; j = 1, 2, \\ldots q\\right).$$
\n\u041e\u043f\u0435\u0440\u0430\u0446\u0438\u044f \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u043c\u0430\u0442\u0440\u0438\u0446 \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u043c\u0430 \u0442\u043e\u043b\u044c\u043a\u043e \u0432 \u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435, \u0435\u0441\u043b\u0438 \u0447\u0438\u0441\u043b\u043e \u0441\u0442\u043e\u043b\u0431\u0446\u043e\u0432 \u0432 \u043f\u0435\u0440\u0432\u043e\u043c \u0441\u043e\u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u0435 \u0440\u0430\u0432\u043d\u043e \u0447\u0438\u0441\u043b\u0443 \u0441\u0442\u0440\u043e\u043a \u0432\u043e \u0432\u0442\u043e\u0440\u043e\u043c; \u0432 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e \u0444\u043e\u0440\u043c\u0430 \u043c\u0430\u0442\u0440\u0438\u0446 \u0441\u043e\u0433\u043b\u0430\u0441\u043e\u0432\u0430\u043d\u0430.<\/p>\n

\u0417\u0430\u0434\u0430\u043d\u043e \u0434\u0432\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b $A$ \u0438 $B$. \u041d\u0430\u0439\u0442\u0438 \u0438\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435.<\/p>\n

\u0412\u0445\u043e\u0434\u043d\u044b\u0435 \u0434\u0430\u043d\u043d\u044b\u0435<\/h2>\n

\u0412 \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0440\u043e\u043a\u0435 \u0437\u0430\u0434\u0430\u043d\u043e $2$ \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u043b\u0430 $n_a$ \u0438 $m_a$ \u2013 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b $A$. \u0412 \u043f\u043e\u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 $n_a$ \u0441\u0442\u0440\u043e\u043a\u0430\u0445 \u0437\u0430\u0434\u0430\u043d\u043e \u043f\u043e $m_a$ \u0447\u0438\u0441\u0435\u043b \u2013 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b $a_{ij}$ \u043c\u0430\u0442\u0440\u0438\u0446\u044b $A$. \u0412 $\\left(n_a + 2\\right)$-\u0439 \u0441\u0442\u0440\u043e\u043a\u0435 \u0437\u0430\u0434\u0430\u043d\u043e $2$ \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u043b\u0430 $n_b$ \u0438 $m_b$ \u2013 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b $B$. \u0412 \u043f\u043e\u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 $n_b$ \u0441\u0442\u0440\u043e\u043a\u0430\u0445 \u0437\u0430\u0434\u0430\u043d\u043e \u043f\u043e $m_b$ \u0447\u0438\u0441\u0435\u043b \u2013 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b $b_{ij}$ \u043c\u0430\u0442\u0440\u0438\u0446\u044b $B$. \u0420\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446 \u043d\u0435 \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u0435\u0442 $100 \\times 100$, \u0432\u0441\u0435 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u043c\u0430\u0442\u0440\u0438\u0446 \u0446\u0435\u043b\u044b\u0435 \u0447\u0438\u0441\u043b\u0430, \u043d\u0435 \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u044e\u0449\u0438\u0435 \u043f\u043e \u043c\u043e\u0434\u0443\u043b\u044e $100$.<\/p>\n

\u0412\u044b\u0445\u043e\u0434\u043d\u044b\u0435 \u0434\u0430\u043d\u043d\u044b\u0435<\/h2>\n

\u0412 \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0440\u043e\u043a\u0435 \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c \u0438\u0442\u043e\u0433\u043e\u0432\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b $C$: $n_c$ \u0438 $m_c$. \u0412 \u043f\u043e\u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 $n_c$ \u0441\u0442\u0440\u043e\u043a\u0430\u0445 \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0447\u0435\u0440\u0435\u0437 \u043f\u0440\u043e\u0431\u0435\u043b \u043f\u043e $m_c$ \u0447\u0438\u0441\u0435\u043b \u2013 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0435 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b $c_{ij}$ \u043c\u0430\u0442\u0440\u0438\u0446\u044b $C$. \u0415\u0441\u043b\u0438 \u0443\u043c\u043d\u043e\u0436\u0430\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u043d\u0435\u043b\u044c\u0437\u044f \u2014 \u0432 \u043f\u0435\u0440\u0432\u043e\u0439 \u0438 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u0441\u0442\u0440\u043e\u043a\u0435 \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0447\u0438\u0441\u043b\u043e $-1$.<\/p>\n

\u0422\u0435\u0441\u0442\u044b<\/h2>\n\n\n\n\n\n\n\n\n
\u0412\u0445\u043e\u0434\u043d\u044b\u0435 \u0434\u0430\u043d\u043d\u044b\u0435<\/td>\n\u0412\u044b\u0445\u043e\u0434\u043d\u044b\u0435 \u0434\u0430\u043d\u043d\u044b\u0435<\/td>\n<\/tr>\n
2 3
\n1 3 4
\n5 -2 3
\n3 3
\n1 3 2
\n2 1 3
\n0 -1 1<\/td>\n		2 3
\n7 2 15
\n1 10 7<\/td>\n<\/tr>\n
3 3
\n1 5 3
\n2 6 1
\n7 -1 -3
\n3 2
\n3 6
\n-1 1
\n3 1<\/td>\n		3 2
\n7 14
\n3 19
\n13 38<\/td>\n<\/tr>\n
4 4
\n4 8 -18 16
\n3 7 14 -42
\n2 1 1 7
\n4 9 5 -2
\n4 4
\n1 0 0 0
\n0 1 0 0
\n0 0 1 0<\/td>\n		4 4
\n4 8 -18 16
\n3 7 14 -42
\n2 1 1 7
\n4 9 5 -2<\/td>\n<\/tr>\n
3 3
\n5 7 -1
\n8 9 3
\n0 -6 17
\n2 3
\n7 -15 1
\n8 8 2<\/td>\n		-1<\/td>\n<\/tr>\n
2 3
\n57 -49 31
\n89 11 -37
\n3 1
\n19
\n-19
\n0<\/td>\n		2 1
\n2014
\n1482<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u041a\u043e\u0434 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u044b<\/h2>\n
import java.util.Scanner;\r\npublic class Main {\r\n\tpublic static void main(String[] args) {\r\n\t\tScanner scanner = new Scanner(System.in);\r\n\t\tint na = scanner.nextInt();\r\n\t\tint ma = scanner.nextInt();\r\n\t\tint[][] a = new int[na][ma];\r\n\t\tfor (int i = 0; i < na; i++) {\r\n\t\t\tfor (int j = 0; j < ma; j++) {\r\n            \t\t\ta[i][j] = scanner.nextInt();\r\n\t\t\t}\r\n\t\t}\r\n\t\tint nb = scanner.nextInt();\r\n\t\tint mb = scanner.nextInt();\r\n\t\tif (ma != nb) {\r\n\t\t\tSystem.out.print(-1);\r\n\t\t\treturn;\r\n\t\t}\r\n\t\tint[][] b = new int[nb][mb];\r\n\t\tfor (int i = 0; i < nb; i++) {\r\n\t\t\tfor (int j = 0; j < mb; j++) {\r\n\t\t\t\tb[i][j] = scanner.nextInt();\r\n\t\t\t}\r\n\t\t}\r\n\t\tint[][] c = new int[na][mb];\r\n\t\tfor (int i = 0; i < na; i++) {\r\n\t\t\tfor (int j = 0; j < mb; j++) {\r\n\t\t\t\tfor (int r = 0; r < ma; r++) {\r\n\t\t\t\t\tc[i][j] += a[i][r] * b[r][j];\r\n\t\t\t\t}\r\n\t\t\t}\r\n\t\t}\r\n\t\tSystem.out.print(na + " " + mb + "\\n");\r\n\t\tfor (int i = 0; i < na; i++) {\r\n\t\t\tfor (int j = 0; j < mb; j++) {\r\n\t\t\t\tSystem.out.print(c[i][j]);\r\n\t\t\t\tif (j + 1 != mb) System.out.print(" ");\r\n\t\t\t}\r\n\t\t\tSystem.out.print("\\n");\r\n\t\t}\r\n\t}\r\n}<\/pre>\n
\u0420\u0435\u0448\u0435\u043d\u0438\u0435<\/h2>\n
\u0414\u043b\u044f \u043d\u0430\u0447\u0430\u043b\u0430, \u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u043c \u0434\u0430\u043d\u043d\u044b\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b $A$ \u0438\u0437 \u0432\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u043f\u043e\u0442\u043e\u043a\u0430 \u0438 \u0437\u0430\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u043c \u0438\u0445 \u0432 \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u044b\u0439 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043c\u0430\u0441\u0441\u0438\u0432. \u0414\u0430\u043b\u0435\u0435, \u043f\u043e\u043b\u0443\u0447\u0438\u0432 \u0434\u0430\u043d\u043d\u044b\u0435 \u043e \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 \u0432\u0442\u043e\u0440\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u043c\u0430 \u043b\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f, \u0438 \u0435\u0441\u043b\u0438 \u043d\u0435\u0442, \u0442\u043e \u043f\u0440\u0435\u0440\u0432\u0430\u0442\u044c \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u044b. \u0415\u0441\u043b\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u0434\u0430\u043d\u043d\u044b\u0445 \u043c\u0430\u0442\u0440\u0438\u0446 \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u043c\u0430, \u0442\u043e \u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u043c \u0438 \u0437\u0430\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u043c \u0434\u0430\u043d\u043d\u044b\u0435 \u0432\u0442\u043e\u0440\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u044b, \u043f\u043e\u0441\u043b\u0435 \u0447\u0435\u0433\u043e, \u043f\u043e \u043f\u0440\u0438\u0432\u0435\u0434\u0451\u043d\u043d\u043e\u0439 \u0432\u044b\u0448\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446 $C = A \\times B.$ \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b\u0432\u043e\u0434\u0438\u043c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u0443\u044e \u043c\u0430\u0442\u0440\u0438\u0446\u0443 $C$.<\/p>\n
\u0421\u0441\u044b\u043b\u043a\u0438<\/h2>\n
\u0423\u0441\u043b\u043e\u0432\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 e-olymp<\/a>
\n\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u043d\u0430 ideone<\/a>
\n\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u043d\u0430 e-olymp<\/a>
\n\u0423\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446 \u043d\u0430 Wikipedia<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
\u0417\u0430\u0434\u0430\u0447\u0430 \u041f\u0443\u0441\u0442\u044c \u0434\u0430\u043d\u044b \u0434\u0432\u0435 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b $A$ \u0438 $B$ \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 $m \\times n$ \u0438 $n \\times q$ \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e: $$A = \\begin{bmatrix} a_{11} & a_{12} & \\ldots & a_{1n} \\\\ a_{21} & a_{22} & \\ldots & a_{2n} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ a_{m1} & a_{m2} & \\ldots & a_{mn} \\end{bmatrix} \\; , … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":117,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25,26],"tags":[362,136,138,146,267],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/posts\/4350"}],"collection":[{"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/users\/117"}],"replies":[{"embeddable":true,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4350"}],"version-history":[{"count":5,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/posts\/4350\/revisions"}],"predecessor-version":[{"id":4358,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=\/wp\/v2\/posts\/4350\/revisions\/4358"}],"wp:attachment":[{"href":"https:\/\/java.mazurok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4350"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4350"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/java.mazurok.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4350"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}