{"id":26960,"date":"2024-10-27T11:54:01","date_gmt":"2024-10-27T11:54:01","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=26960"},"modified":"2024-11-26T07:25:16","modified_gmt":"2024-11-26T07:25:16","slug":"%ec%9e%90%eb%b0%94-%ec%bd%94%eb%94%a9%ed%85%8c%ec%8a%a4%ed%8a%b8-%ea%b0%95%ec%a2%8c-%ed%99%95%ec%9e%a5-%ec%9c%a0%ed%81%b4%eb%a6%ac%eb%93%9c-%ed%98%b8%ec%a0%9c%eb%b2%95","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/26960\/","title":{"rendered":"\uc790\ubc14 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95"},"content":{"rendered":"<article>\n<p>\ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95(Extended Euclidean Algorithm)\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uace0, \uc774\ub97c \ud65c\uc6a9\ud55c \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ub97c \ud574\uacb0\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95\uc740 \ub450 \uc815\uc218 <strong>a<\/strong>\uc640 <strong>b<\/strong>\uc758 \ucd5c\ub300\uacf5\uc57d\uc218(<strong>gcd<\/strong>)\ub97c \uad6c\ud558\uace0, \ub610\ud55c <strong>ax + by = gcd(a, b)<\/strong> \ud615\ud0dc\uc758 \uc815\uc218 \ud574\ub97c \uad6c\ud558\ub294 \ub370 \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \uc774 \uae30\ubc95\uc740 \ud604\ub300 \uc554\ud638\ud559\uc5d0\uc11c\ub3c4 \ub110\ub9ac \uc0ac\uc6a9\ub429\ub2c8\ub2e4.<\/p>\n<h2>\ubb38\uc81c \uc124\uba85<\/h2>\n<p>\ub2e4\uc74c \ubb38\uc81c\ub97c \ud574\uacb0\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<h3>\ubb38\uc81c<\/h3>\n<blockquote><p>\n        \ub450 \uc815\uc218 <strong>a<\/strong>\uc640 <strong>b<\/strong>\uac00 \uc8fc\uc5b4\uc9c8 \ub54c, <strong>ax + by = gcd(a, b)<\/strong>\uc758 \ud574\uc778 <strong>x<\/strong>, <strong>y<\/strong>\ub97c \ucc3e\uace0 \uc774 \uac12\uc744 \ucd9c\ub825\ud558\uc2dc\uc624.\n    <\/p><\/blockquote>\n<h2>\uc54c\uace0\ub9ac\uc998\uc758 \uc774\ud574<\/h2>\n<p>\ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95\uc740 \uae30\ubcf8 \uc720\ud074\ub9ac\ub4dc \uc54c\uace0\ub9ac\uc998\uc744 \ubc14\ud0d5\uc73c\ub85c \ud558\uc5ec, <strong>gcd(a, b)<\/strong>\ub97c \uad6c\ud558\uace0 \uc774\ub97c \uc774\uc6a9\ud558\uc5ec \uacc4\uc218 <strong>x<\/strong>, <strong>y<\/strong>\ub97c \uacc4\uc0b0\ud560 \uc218 \uc788\ub3c4\ub85d \ud569\ub2c8\ub2e4. \uae30\ubcf8\uc801\uc778 \uc720\ud074\ub9ac\ub4dc \uc54c\uace0\ub9ac\uc998\uc740 \ub450 \uc218\uc758 \ucd5c\ub300\uacf5\uc57d\uc218\ub97c \uad6c\ud558\ub294 \uc54c\uace0\ub9ac\uc998\uc73c\ub85c, \ub2e4\uc74c\uacfc \uac19\uc740 \uc7ac\uadc0\uc801 \uacfc\uc815\uc744 \ub530\ub985\ub2c8\ub2e4:<\/p>\n<pre>\n    gcd(a, 0) = a\n    gcd(0, b) = b\n    gcd(a, b) = gcd(b, a mod b)\n    <\/pre>\n<h2>\ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95<\/h2>\n<p>\ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95\uc5d0\uc11c\ub294 \ub354\uc6b1 \ub354 \ubc1c\uc804\ub41c \uc811\uadfc\uc744 \ud569\ub2c8\ub2e4. \uc55e\uc11c \uc5b8\uae09\ud55c \uac83\ucc98\ub7fc, \ub450 \uc815\uc218\uc758 \ucd5c\ub300\uacf5\uc57d\uc218\ub294 \ub2e8\uc21c\ud788 \uadf8 \uac12\uc744 \uad6c\ud558\ub294 \uac83\ubfd0\ub9cc \uc544\ub2c8\ub77c \ub450 \uc218\uc758 \uc815\uc218 \uacc4\uc218\uae4c\uc9c0 \ub3c4\ucd9c\ud569\ub2c8\ub2e4. \uae30\ubcf8 \uc544\uc774\ub514\uc5b4\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n<ol>\n<li>\uc720\ud074\ub9ac\ub4dc \uc54c\uace0\ub9ac\uc998\uc744 \uc0ac\uc6a9\ud558\uc5ec <strong>gcd(a, b)<\/strong>\ub97c \uc7ac\uadc0\uc801\uc73c\ub85c \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/li>\n<li>\uac01 \ub2e8\uacc4\uc5d0\uc11c\uc758 <strong>x<\/strong>\uc640 <strong>y<\/strong> \uac12\uc744 \ucd94\uc801\ud558\uba74\uc11c \ud544\uc694\ud55c \uacbd\uc6b0 \uc5c5\ub370\uc774\ud2b8\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n<h3>\uc7ac\uadc0\uc801 \uc811\uadfc<\/h3>\n<pre>\n    1. \uba3c\uc800, <strong>gcd(a, b)<\/strong>\ub97c \uad6c\ud55c \ud6c4\uc5d0,\n    2. <strong>x = y1 - (a \/ b) * x1<\/strong>\n    3. <strong>y = x1<\/strong>\ub85c \uc5c5\ub370\uc774\ud2b8\ud569\ub2c8\ub2e4.\n    <\/pre>\n<h2>\ubb38\uc81c \ud480\uc774 \uacfc\uc815<\/h2>\n<h3>\uc790\ubc14 \uad6c\ud604<\/h3>\n<p>\uc774\uc81c \uc790\ubc14\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc704\uc758 \uc54c\uace0\ub9ac\uc998\uc744 \uad6c\ud604\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc544\ub798\uc758 \ucf54\ub4dc\ub294 \ub450 \uc815\uc218 <strong>a<\/strong>\uc640 <strong>b<\/strong>\ub97c \uc785\ub825\uc73c\ub85c \ubc1b\uace0, <strong>gcd(a, b)<\/strong>\uc640 <strong>x<\/strong>, <strong>y<\/strong>\ub97c \ucd9c\ub825\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc785\ub2c8\ub2e4.<\/p>\n<pre>\n    <code>\n    public class ExtendedEuclidean {\n        static int[] extendedGcd(int a, int b) {\n            if (b == 0) {\n                return new int[] { a, 1, 0 };\n            }\n            int[] recResult = extendedGcd(b, a % b);\n            int gcd = recResult[0];\n            int x1 = recResult[1];\n            int y1 = recResult[2];\n            int x = y1;\n            int y = x1 - (a \/ b) * y1;\n            return new int[] { gcd, x, y };\n        }\n\n        public static void main(String[] args) {\n            int a = 30; \/\/ \uc785\ub825\uc73c\ub85c \uc0ac\uc6a9\ud560 \uccab \ubc88\uc9f8 \uc218\n            int b = 12; \/\/ \uc785\ub825\uc73c\ub85c \uc0ac\uc6a9\ud560 \ub450 \ubc88\uc9f8 \uc218\n            int[] result = extendedGcd(a, b);\n            System.out.println(\"GCD: \" + result[0]);\n            System.out.println(\"x: \" + result[1]);\n            System.out.println(\"y: \" + result[2]);\n        }\n    }\n    <\/code>\n    <\/pre>\n<h2>\ucf54\ub4dc \uc124\uba85<\/h2>\n<p>\uc704\uc758 \ucf54\ub4dc\uc5d0\uc11c <strong>extendedGcd<\/strong> \uba54\uc11c\ub4dc\ub294 \uc7ac\uadc0\uc801\uc73c\ub85c \ucd5c\ub300\uacf5\uc57d\uc218(limit)\uc640 \ud574\ub2f9 \uacc4\uc218 <strong>x<\/strong>, <strong>y<\/strong>\ub97c \ubc18\ud658\ud569\ub2c8\ub2e4. \uae30\ubcf8\uc801\uc73c\ub85c, \ub9cc\uc57d <strong>b<\/strong>\uac00 0\uc774\uba74 <strong>gcd(a, 0) = a<\/strong>\uc774\ubbc0\ub85c \uc774\ub97c \ubc18\ud658\ud569\ub2c8\ub2e4. \uadf8\ub807\uc9c0 \uc54a\uc73c\uba74, <strong>gcd(b, a % b)<\/strong> \ube44\uc728\uc744 \uc774\uc6a9\ud558\uc5ec \uc7ac\uadc0\uc801\uc73c\ub85c \uac12\uc744 \uad6c\ud569\ub2c8\ub2e4.<\/p>\n<h2>\ud14c\uc2a4\ud2b8\uc640 \uacb0\uacfc<\/h2>\n<p>\uc774\uc81c \uc704\uc758 \ucf54\ub4dc\ub97c \uc2e4\ud589\ud558\uc5ec \uc785\ub825\uac12\uc744 \uc870\uc815\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc6b0\ub9ac\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ub2e4\uc591\ud55c \uc785\ub825 \uc608\uc81c\ub97c \uace0\ub824\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4:<\/p>\n<h3>\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4<\/h3>\n<ul>\n<li><strong>a = 30, b = 12<\/strong><\/li>\n<li><strong>a = 56, b = 15<\/strong><\/li>\n<li><strong>a = 101, b = 10<\/strong><\/li>\n<\/ul>\n<p>\uac01 \uacbd\uc6b0\uc5d0 \ub300\ud55c \uacb0\uacfc\ub97c \ud655\uc778\ud574 \ubd05\uc2dc\ub2e4.<\/p>\n<h3>\uacb0\uacfc \uc608\uc2dc<\/h3>\n<blockquote>\n<p>\uc608\uc81c 1: a = 30, b = 12<\/p>\n<p>GCD: 6<\/p>\n<p>x: 1, y: -2<\/p>\n<\/blockquote>\n<blockquote>\n<p>\uc608\uc81c 2: a = 56, b = 15<\/p>\n<p>GCD: 1<\/p>\n<p>x: -4, y: 15<\/p>\n<\/blockquote>\n<blockquote>\n<p>\uc608\uc81c 3: a = 101, b = 10<\/p>\n<p>GCD: 1<\/p>\n<p>x: 1, y: -10<\/p>\n<\/blockquote>\n<h2>\uacb0\ub860<\/h2>\n<p>\uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95\uc758 \uae30\ubcf8\uc801 \uc774\ub860\uacfc \uc774\ub97c \ud65c\uc6a9\ud55c \ubb38\uc81c \ud574\uacb0 \uc811\uadfc \ubc29\ubc95\uc5d0 \ub300\ud574 \uc54c\uc544\ubcf4\uc558\uc2b5\ub2c8\ub2e4. \uc774\ub97c \ud1b5\ud574 \uc5ec\ub7ec\ubd84\ub4e4\uc740 \uc218\ud559\uc801 \uae30\ucd08\uc640 \ud568\uaed8 \uc790\ubc14 \ud504\ub85c\uadf8\ub798\ubc0d \uc2e4\ub825\uc744 \ud568\uaed8 \ud5a5\uc0c1\uc2dc\ud0ac \uc218 \uc788\uc5c8\uae30\ub97c \ubc14\ub78d\ub2c8\ub2e4. \ucd94\uac00\uc801\uc73c\ub85c, \ub2e4\uc591\ud55c \uc785\ub825\uac12\uc5d0 \ub300\ud574 \uad6c\ud604 \ubc0f \ud14c\uc2a4\ud2b8\ub97c \uc9c4\ud589\ud558\uba74\uc11c \uc54c\uace0\ub9ac\uc998\uc5d0 \ub300\ud55c \uc774\ud574\ub3c4\ub97c \ub192\uc5ec\ubcfc \uc218 \uc788\uae38 \ubc14\ub78d\ub2c8\ub2e4.<\/p>\n<h2>\ucd94\uac00 \ud559\uc2b5 \uc790\ub8cc<\/h2>\n<p>\ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95\uc5d0 \ub300\ud55c \ub354 \ub9ce\uc740 \uc815\ubcf4\ub294 \uc544\ub798\uc758 \ub9c1\ud06c\ub97c \ud1b5\ud574 \ucc38\uace0\ud558\uc2dc\uae30 \ubc14\ub78d\ub2c8\ub2e4.<\/p>\n<ul>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Extended_Euclidean_algorithm\" target=\"_blank\" rel=\"noopener\">\uc704\ud0a4\ubc31\uacfc &#8211; \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95<\/a><\/li>\n<li><a href=\"https:\/\/ocw.mit.edu\/courses\/electrical-engineering-and-computer-science\/6-006-introduction-to-algorithms-fall-2011\/\" target=\"_blank\" rel=\"noopener\">MIT OpenCourseWare &#8211; \uc54c\uace0\ub9ac\uc998 \uc785\ubb38<\/a><\/li>\n<\/ul>\n<\/article>\n","protected":false},"excerpt":{"rendered":"<p>\ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95(Extended Euclidean Algorithm)\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uace0, \uc774\ub97c \ud65c\uc6a9\ud55c \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ub97c \ud574\uacb0\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95\uc740 \ub450 \uc815\uc218 a\uc640 b\uc758 \ucd5c\ub300\uacf5\uc57d\uc218(gcd)\ub97c \uad6c\ud558\uace0, \ub610\ud55c ax + by = gcd(a, b) \ud615\ud0dc\uc758 \uc815\uc218 \ud574\ub97c \uad6c\ud558\ub294 \ub370 \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \uc774 \uae30\ubc95\uc740 \ud604\ub300 \uc554\ud638\ud559\uc5d0\uc11c\ub3c4 \ub110\ub9ac \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \ubb38\uc81c \uc124\uba85 \ub2e4\uc74c \ubb38\uc81c\ub97c \ud574\uacb0\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \ubb38\uc81c \ub450 \uc815\uc218 a\uc640 b\uac00 &hellip; <a href=\"https:\/\/atmokpo.com\/w\/26960\/\" class=\"more-link\">\ub354 \ubcf4\uae30<span class=\"screen-reader-text\"> &#8220;\uc790\ubc14 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95&#8221;<\/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":[22],"tags":[],"class_list":["post-26960","post","type-post","status-publish","format-standard","hentry","category-22"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\uc790\ubc14 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95 - \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\/26960\/\" \/>\n<meta property=\"og:locale\" content=\"ko_KR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\uc790\ubc14 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95 - \ub77c\uc774\ube0c\uc2a4\ub9c8\ud2b8\" \/>\n<meta property=\"og:description\" content=\"\ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95(Extended Euclidean Algorithm)\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uace0, \uc774\ub97c \ud65c\uc6a9\ud55c \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ub97c \ud574\uacb0\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95\uc740 \ub450 \uc815\uc218 a\uc640 b\uc758 \ucd5c\ub300\uacf5\uc57d\uc218(gcd)\ub97c \uad6c\ud558\uace0, \ub610\ud55c ax + by = gcd(a, b) \ud615\ud0dc\uc758 \uc815\uc218 \ud574\ub97c \uad6c\ud558\ub294 \ub370 \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \uc774 \uae30\ubc95\uc740 \ud604\ub300 \uc554\ud638\ud559\uc5d0\uc11c\ub3c4 \ub110\ub9ac \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \ubb38\uc81c \uc124\uba85 \ub2e4\uc74c \ubb38\uc81c\ub97c \ud574\uacb0\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \ubb38\uc81c \ub450 \uc815\uc218 a\uc640 b\uac00 &hellip; \ub354 \ubcf4\uae30 &quot;\uc790\ubc14 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \ud655\uc7a5 \uc720\ud074\ub9ac\ub4dc \ud638\uc81c\ubc95&quot;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/atmokpo.com\/w\/26960\/\" \/>\n<meta property=\"og:site_name\" content=\"\ub77c\uc774\ube0c\uc2a4\ub9c8\ud2b8\" \/>\n<meta property=\"article:published_time\" content=\"2024-10-27T11:54:01+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-11-26T07:25:16+00:00\" \/>\n<meta name=\"author\" content=\"root\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" 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