{"id":27458,"date":"2024-10-27T14:11:49","date_gmt":"2024-10-27T14:11:49","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=27458"},"modified":"2024-11-26T07:18:07","modified_gmt":"2024-11-26T07:18:07","slug":"c-%ec%bd%94%eb%94%a9%ed%85%8c%ec%8a%a4%ed%8a%b8-%ea%b0%95%ec%a2%8c-%ea%b5%ac%ea%b0%84-%ea%b3%b1-%ea%b5%ac%ed%95%98%ea%b8%b0","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/27458\/","title":{"rendered":"C# \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uad6c\uac04 \uacf1 \uad6c\ud558\uae30"},"content":{"rendered":"

<\/p>\n

\ubb38\uc81c \uc124\uba85<\/h2>\n

\uc8fc\uc5b4\uc9c4 \uc815\uc218 \ubc30\uc5f4 nums<\/code>\uc640 \ucffc\ub9ac \ubc30\uc5f4 queries<\/code>\uac00 \uc788\uc2b5\ub2c8\ub2e4. \uac01 \ucffc\ub9ac\ub294 \ub450 \uc815\uc218 (l, r)<\/code>\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, \uc774\ub294 nums[l] * nums[l + 1] * ... * nums[r]<\/code>\uc758 \uac12\uc744 \uad6c\ud558\ub77c\ub294 \uc694\uccad\uc785\ub2c8\ub2e4. \ub2e8, nums<\/code> \ubc30\uc5f4\uc758 \ud06c\uae30\ub294 \ucd5c\ub300 10^5<\/code>, queries<\/code>\uc758 \uae38\uc774\ub294 \ucd5c\ub300 10^4<\/code>\uc785\ub2c8\ub2e4. \uc774\ub54c, \uacf1\uc148\uc758 \uacb0\uacfc\uac00 \ub9e4\uc6b0 \ucee4\uc9c8 \uc218 \uc788\uc73c\ubbc0\ub85c, \uacb0\uacfc\ub294 10^9 + 7<\/code>\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\n

\uc785\ub825 \ud615\uc2dd<\/h2>\n

\uccab \ubc88\uc9f8 \uc904\uc5d0 \ubc30\uc5f4\uc758 \ud06c\uae30 n<\/code>\uacfc \ucffc\ub9ac\uc758 \uc218 q<\/code>\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \ub450 \ubc88\uc9f8 \uc904\uc5d0 n<\/code>\uac1c\uc758 \uc815\uc218\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubc30\uc5f4 nums<\/code>\uac00 \uc8fc\uc5b4\uc9c0\uace0, q<\/code>\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 \uac01 \ucffc\ub9ac l<\/code>\uacfc r<\/code>\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4.<\/p>\n

\ucd9c\ub825 \ud615\uc2dd<\/h2>\n

\uac01 \ucffc\ub9ac\uc5d0 \ub300\ud574 \uacc4\uc0b0\ud55c \uacb0\uacfc\ub97c \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud569\ub2c8\ub2e4.<\/p>\n

\uc608\uc2dc<\/h2>\n
\n\uc785\ub825<\/strong>
\n 5 3
\n 2 3 4 5 6
\n 0 2
\n 1 3
\n 2 4
\n\ucd9c\ub825<\/strong>
\n 24
\n 60
\n 120\n<\/div>\n

\ubb38\uc81c \ud480\uc774<\/h2>\n

\uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574\uc11c\ub294 \uad6c\uac04 \uacf1\uc744 \ube60\ub974\uac8c \uacc4\uc0b0\ud560 \uc218 \uc788\ub294 \ubc29\ubc95\uc774 \ud544\uc694\ud569\ub2c8\ub2e4. \ub2e8\uc21c\ud788 \uac01 \ucffc\ub9ac\uc5d0 \ub300\ud574 \uad6c\uac04\uc744 \uc21c\ud68c\ud558\uba74\uc11c \uacf1\uc744 \uacc4\uc0b0\ud558\uba74 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4 O(q * n)<\/code>\uc5d0 \uc774\ub974\uac8c \ub418\uc5b4, \ucd5c\uc545\uc758 \uacbd\uc6b0 10^9<\/code>\uc758 \uc5f0\uc0b0\uc744 \uc218\ud589\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ub294 \uc2e4\uc6a9\uc801\uc774\uc9c0 \uc54a\uae30 \ub54c\ubb38\uc5d0, Prefix Product\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\ub97c \uc904\uc774\ub294 \uc804\ub7b5\uc744 \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n

Prefix Product \ubc29\ubc95<\/h3>\n

\uc6b0\uc120, nums<\/code> \ubc30\uc5f4\uc758 \uc6d0\uc18c\ub4e4\uc5d0 \ub300\ud55c \ub204\uc801 \uacf1\uc744 \uc800\uc7a5\ud558\uc5ec \ucffc\ub9ac\uc758 \uacb0\uacfc\ub97c \ube60\ub974\uac8c \uacc4\uc0b0\ud560 \uc218 \uc788\ub3c4\ub85d \ud569\ub2c8\ub2e4.<\/p>\n

C#\nint mod = 1000000007;\nint[] prefixProduct = new int[n + 1];\nprefixProduct[0] = 1;\n\nfor (int i = 1; i <= n; i++) {\n    prefixProduct[i] = (int)((1L * prefixProduct[i - 1] * nums[i - 1]) % mod);\n}\n<\/code><\/pre>\n
\uc5ec\uae30\uc11c prefixProduct[i]<\/code>\ub294 nums[0] * nums[1] * ... * nums[i - 1]<\/code>\uc758 \uac12\uc744 \uc800\uc7a5\ud569\ub2c8\ub2e4. \uc774 \uad6c\uc870\ub97c \ud1b5\ud574 \uc6b0\ub9ac\ub294 \uad6c\uac04 \uacf1\uc744 \uc27d\uace0 \ube60\ub974\uac8c \uacc4\uc0b0\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n
\uad6c\uac04 \uacf1 \uacc4\uc0b0\ud558\uae30<\/h3>\n
\uc774\uc81c \uac01 \ucffc\ub9ac (l, r)<\/code>\uc5d0 \ub300\ud574, \uad6c\uac04 \uacf1 nums[l] * nums[l + 1] * ... * nums[r]<\/code>\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uad6c\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4:<\/p>\n
C#\nint result = (int)((1L * prefixProduct[r + 1] * modInverse(prefixProduct[l]) % mod) % mod);\n<\/code><\/pre>\n
\uc5ec\uae30\uc11c modInverse<\/code> \ud568\uc218\ub294 \ubaa8\ub4c8\ub85c \uc5f0\uc0b0\uc5d0 \ub300\ud55c \uc5ed\uc6d0\uc744 \uad6c\ud558\ub294 \ud568\uc218\uc785\ub2c8\ub2e4. \uc5ed\uc6d0\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uad6c\ud604\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4:<\/p>\n
C#\nint modInverse(int a) {\n    return power(a, mod - 2);\n}\n\nint power(int x, int y) {\n    int res = 1;\n    while (y > 0) {\n        if ((y & 1) == 1) {\n            res = (int)((1L * res * x) % mod);\n        }\n        y >>= 1;\n        x = (int)((1L * x * x) % mod);\n    }\n    return res;\n}\n<\/code><\/pre>\n
\ucd5c\uc885 \ucf54\ub4dc<\/h3>\n
\uc704\uc758 \uc124\uba85\uc744 \ud1a0\ub300\ub85c \uc804\uccb4 \ucf54\ub4dc\ub97c \uc791\uc131\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n
C#\nusing System;\n\nclass Program {\n    static int mod = 1000000007;\n\n    static void Main() {\n        string[] firstLine = Console.ReadLine().Split();\n        int n = int.Parse(firstLine[0]);\n        int q = int.Parse(firstLine[1]);\n        int[] nums = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);\n        int[] prefixProduct = new int[n + 1];\n        prefixProduct[0] = 1;\n\n        for (int i = 1; i <= n; i++) {\n            prefixProduct[i] = (int)((1L * prefixProduct[i - 1] * nums[i - 1]) % mod);\n        }\n\n        for (int i = 0; i < q; i++) {\n            string[] query = Console.ReadLine().Split();\n            int l = int.Parse(query[0]);\n            int r = int.Parse(query[1]);\n            int result = (int)((1L * prefixProduct[r + 1] * modInverse(prefixProduct[l]) % mod) % mod);\n            Console.WriteLine(result);\n        }\n    }\n\n    static int modInverse(int a) {\n        return power(a, mod - 2);\n    }\n\n    static int power(int x, int y) {\n        int res = 1;\n        while (y > 0) {\n            if ((y & 1) == 1) {\n                res = (int)((1L * res * x) % mod);\n            }\n            y >>= 1;\n            x = (int)((1L * x * x) % mod);\n        }\n        return res;\n    }\n}\n<\/code><\/pre>\n
\uacb0\ub860<\/h2>\n
\uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 \ubc30\uc5f4\uc758 \uad6c\uac04 \uacf1\uc744 \ud6a8\uacfc\uc801\uc73c\ub85c \uacc4\uc0b0\ud558\uae30 \uc704\ud574 Prefix Product \ubc29\ubc95\uacfc \ubaa8\ub4c8\ub85c \uc5f0\uc0b0\uc758 \uc5ed\uc6d0\uc758 \uac1c\ub150\uc744 \ud65c\uc6a9\ud558\ub294 \ubc29\ubc95\uc744 \ud559\uc2b5\ud588\uc2b5\ub2c8\ub2e4. \uc774 \ubc29\ubc95\uc744 \uc751\uc6a9\ud558\uba74 \ub354\uc6b1 \ubcf5\uc7a1\ud55c \ucffc\ub9ac \ucc98\ub9ac\uc5d0\ub3c4 \uc720\uc6a9\ud558\uac8c \ud65c\uc6a9\ud560 \uc218 \uc788\uc744 \uac83\uc785\ub2c8\ub2e4. C# \uc5b8\uc5b4\uc758 \ud2b9\uc9d5\uc744 \uc0b4\ub824 \ud6a8\uc728\uc801\uc778 \ucf54\ub4dc\ub97c \uc791\uc131\ud558\uace0, \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c \ud574\uacb0 \ub2a5\ub825\uc744 \ud55c\uce35 \ub354 \ud5a5\uc0c1\uc2dc\ud0ac \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n
\ucd94\uac00\uc801\uc73c\ub85c, \uc774 \ubb38\uc81c\uc5d0\uc11c \uc0ac\uc6a9\ud55c Prefix Product \uae30\ubc95\uc740 \ub2e4\uc591\ud55c \ud615\ud0dc\uc758 \ucffc\ub9ac \ubb38\uc81c\uc5d0\uc11c \uc720\uc6a9\ud558\uac8c \uc801\uc6a9\ub420 \uc218 \uc788\uc73c\ubbc0\ub85c, \ub2e4\uc591\ud55c \ubb38\uc81c\uc5d0 \uc801\uc6a9\ud574\ubcf4\ub294 \uac83\ub3c4 \uc88b\uc2b5\ub2c8\ub2e4. \uac10\uc0ac\ud569\ub2c8\ub2e4!<\/p>\n
<\/body><\/p>\n","protected":false},"excerpt":{"rendered":"
\ubb38\uc81c \uc124\uba85 \uc8fc\uc5b4\uc9c4 \uc815\uc218 \ubc30\uc5f4 nums\uc640 \ucffc\ub9ac \ubc30\uc5f4 queries\uac00 \uc788\uc2b5\ub2c8\ub2e4. \uac01 \ucffc\ub9ac\ub294 \ub450 \uc815\uc218 (l, r)\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, \uc774\ub294 nums[l] * nums[l + 1] * … * nums[r]\uc758 \uac12\uc744 \uad6c\ud558\ub77c\ub294 \uc694\uccad\uc785\ub2c8\ub2e4. \ub2e8, nums \ubc30\uc5f4\uc758 \ud06c\uae30\ub294 \ucd5c\ub300 10^5, queries\uc758 \uae38\uc774\ub294 \ucd5c\ub300 10^4\uc785\ub2c8\ub2e4. \uc774\ub54c, \uacf1\uc148\uc758 \uacb0\uacfc\uac00 \ub9e4\uc6b0 \ucee4\uc9c8 \uc218 \uc788\uc73c\ubbc0\ub85c, \uacb0\uacfc\ub294 10^9 + 7\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud574\uc57c … \ub354 \ubcf4\uae30 “C# \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uad6c\uac04 \uacf1 \uad6c\ud558\uae30”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[24],"tags":[],"class_list":["post-27458","post","type-post","status-publish","format-standard","hentry","category-c--"],"yoast_head":"\nC# \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uad6c\uac04 \uacf1 \uad6c\ud558\uae30 - \ub77c\uc774\ube0c\uc2a4\ub9c8\ud2b8<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/atmokpo.com\/w\/27458\/\" \/>\n<meta property=\"og:locale\" content=\"ko_KR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"C# \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uad6c\uac04 \uacf1 \uad6c\ud558\uae30 - \ub77c\uc774\ube0c\uc2a4\ub9c8\ud2b8\" \/>\n<meta property=\"og:description\" content=\"\ubb38\uc81c \uc124\uba85 \uc8fc\uc5b4\uc9c4 \uc815\uc218 \ubc30\uc5f4 nums\uc640 \ucffc\ub9ac \ubc30\uc5f4 queries\uac00 \uc788\uc2b5\ub2c8\ub2e4. \uac01 \ucffc\ub9ac\ub294 \ub450 \uc815\uc218 (l, r)\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, \uc774\ub294 nums[l] * nums[l + 1] * ... * nums[r]\uc758 \uac12\uc744 \uad6c\ud558\ub77c\ub294 \uc694\uccad\uc785\ub2c8\ub2e4. \ub2e8, nums \ubc30\uc5f4\uc758 \ud06c\uae30\ub294 \ucd5c\ub300 10^5, queries\uc758 \uae38\uc774\ub294 \ucd5c\ub300 10^4\uc785\ub2c8\ub2e4. \uc774\ub54c, \uacf1\uc148\uc758 \uacb0\uacfc\uac00 \ub9e4\uc6b0 \ucee4\uc9c8 \uc218 \uc788\uc73c\ubbc0\ub85c, \uacb0\uacfc\ub294 10^9 + 7\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud574\uc57c … \ub354 \ubcf4\uae30 "C# \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uad6c\uac04 \uacf1 \uad6c\ud558\uae30"\" \/>\n<meta property=\"og:url\" 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