{"id":27863,"date":"2024-10-27T15:20:02","date_gmt":"2024-10-27T15:20:02","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=27863"},"modified":"2024-11-26T07:14:21","modified_gmt":"2024-11-26T07:14:21","slug":"%ec%9e%90%eb%b0%94%ec%8a%a4%ed%81%ac%eb%a6%bd%ed%8a%b8-%ec%bd%94%eb%94%a9%ed%85%8c%ec%8a%a4%ed%8a%b8-%ea%b0%95%ec%a2%8c-%ec%98%a4%ec%9d%bc%eb%9f%ac-%ed%94%bc-%ed%95%a8%ec%88%98-%ea%b5%ac%ed%98%84","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/27863\/","title":{"rendered":"\uc790\ubc14\uc2a4\ud06c\ub9bd\ud2b8 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uc624\uc77c\ub7ec \ud53c \ud568\uc218 \uad6c\ud604\ud558\uae30"},"content":{"rendered":"<p>\uc548\ub155\ud558\uc138\uc694, \uc5ec\ub7ec\ubd84! \uc624\ub298\uc740 \uc790\ubc14\uc2a4\ud06c\ub9bd\ud2b8\ub85c \uc624\uc77c\ub7ec \ud53c \ud568\uc218(\ud835\udf19(n))\ub97c \uad6c\ud604\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc124\uba85\ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4. \uc624\uc77c\ub7ec \ud53c \ud568\uc218\ub294 \uc8fc\uc5b4\uc9c4 \uc815\uc218 n\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc815\uc218 \uc911 n\uacfc \uc11c\ub85c \uc18c\uc778 \uc815\uc218\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub294 \uc218\ub860 \uad00\ub828 \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\uc5d0\uc11c \ub9e4\uc6b0 \uc790\uc8fc \ub4f1\uc7a5\ud558\uba70, \ub2e4\uc591\ud55c \ucf54\ub529 \ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc720\uc6a9\ud558\uac8c \ud65c\uc6a9\ub420 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<h2>\uc624\uc77c\ub7ec \ud53c \ud568\uc218\ub780?<\/h2>\n<p>\uc624\uc77c\ub7ec \ud53c \ud568\uc218 \ud835\udf19(n)\uc740 n\uacfc \uc11c\ub85c \uc18c\uc778 1\ubd80\ud130 n\uae4c\uc9c0\uc758 \uc591\uc758 \uc815\uc218\uc758 \uac1c\uc218\ub97c \ubc18\ud658\ud569\ub2c8\ub2e4. \ub2e4\uc2dc \ub9d0\ud558\uba74, \ub450 \uc218 a\uc640 b\uac00 \uc11c\ub85c \uc18c\ub77c\ub294 \uac83\uc740 \ub450 \uc218\uc758 \ucd5c\ub300\uacf5\uc57d\uc218(GCD)\uac00 1\uc77c \ub54c\ub97c \uc758\ubbf8\ud569\ub2c8\ub2e4.<\/p>\n<p>\uc608\ub97c \ub4e4\uc5b4:<\/p>\n<ul>\n<li>\ud835\udf19(1) = 1 (1\uacfc \uc11c\ub85c \uc18c\uc778 \uc218\ub294 1 \ud558\ub098\ubfd0)<\/li>\n<li>\ud835\udf19(2) = 1 (2\ubcf4\ub2e4 \uc791\uace0 2\uc640 \uc11c\ub85c \uc18c\uc778 \uc218\ub294 1)<\/li>\n<li>\ud835\udf19(3) = 2 (3\ubcf4\ub2e4 \uc791\uace0 3\uacfc \uc11c\ub85c \uc18c\uc778 \uc218\ub294 1, 2)<\/li>\n<li>\ud835\udf19(4) = 2 (4\ubcf4\ub2e4 \uc791\uace0 4\uc640 \uc11c\ub85c \uc18c\uc778 \uc218\ub294 1, 3)<\/li>\n<li>\ud835\udf19(5) = 4 (5\ubcf4\ub2e4 \uc791\uace0 5\uc640 \uc11c\ub85c \uc18c\uc778 \uc218\ub294 1, 2, 3, 4)<\/li>\n<\/ul>\n<h2>\ubb38\uc81c \uc815\uc758<\/h2>\n<p>\uc774\uc81c \ucf54\ub529 \ud14c\uc2a4\ud2b8 \ubb38\uc81c\ub97c \uc815\uc758\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<pre>\n<b>\ubb38\uc81c<\/b>: \uc8fc\uc5b4\uc9c4 \uc815\uc218 n\uc5d0 \ub300\ud574 \uc624\uc77c\ub7ec \ud53c \ud568\uc218\ub97c \uacc4\uc0b0\ud558\ub294 \ud568\uc218\ub97c \uc791\uc131\ud558\ub77c.\n<b>\uc785\ub825<\/b>: \uc815\uc218 n (1 \u2264 n \u2264 10<sup>6<\/sup>)\n<b>\ucd9c\ub825<\/b>: \uc624\uc77c\ub7ec \ud53c \ud568\uc218 \ud835\udf19(n)\uc758 \uac12\n<\/pre>\n<h2>\ubb38\uc81c \ud574\uacb0 \uc811\uadfc\ubc95<\/h2>\n<p>\uc624\uc77c\ub7ec \ud53c \ud568\uc218\ub97c \uacc4\uc0b0\ud558\ub294 \ubc29\ubc95\uc5d0\ub294 \uc5ec\ub7ec \uac00\uc9c0\uac00 \uc788\uc2b5\ub2c8\ub2e4. \uac00\uc7a5 \ud6a8\uc728\uc801\uc778 \ubc29\ubc95\uc740 \uc5d0\ub77c\ud1a0\uc2a4\ud14c\ub124\uc2a4\uc758 \uccb4\ub97c \ubcc0\ud615\ud558\uc5ec \ud835\udf19(n) \uac12\uc744 \ud55c \ubc88\uc5d0 \uad6c\ud558\ub294 \uac83\uc785\ub2c8\ub2e4. \uc774 \ubc29\ubc95\uc758 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\ub294 O(n log log n)\uc785\ub2c8\ub2e4. <\/p>\n<h3>\uc624\uc77c\ub7ec \ud53c \ud568\uc218\uc758 \uc131\uc9c8<\/h3>\n<p>\ud835\udf19(n)\uc744 \uacc4\uc0b0\ud558\uae30 \uc704\ud574 \ud544\uc694\ud55c \uc911\uc694\ud55c \uc131\uc9c8\uc740 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n<ul>\n<li>\ud835\udf19(p) = p &#8211; 1, \uc5ec\uae30\uc11c p\ub294 \uc18c\uc218<\/li>\n<li>\ud835\udf19(p<sub>1<\/sub> * p<sub>2<\/sub> * &#8230; * p<sub>k<\/sub>) = p<sub>1<\/sub> * p<sub>2<\/sub> * &#8230; * p<sub>k<\/sub> * (1 &#8211; 1\/p<sub>1<\/sub>) * (1 &#8211; 1\/p<sub>2<\/sub>) * &#8230; * (1 &#8211; 1\/p<sub>k<\/sub>)<\/li>\n<li>\ud835\udf19(n) = n * (1 &#8211; 1\/p<sub>1<\/sub>) * (1 &#8211; 1\/p<sub>2<\/sub>) * &#8230; * (1 &#8211; 1\/p<sub>k<\/sub>), \uc5ec\uae30\uc11c p<sub>i<\/sub>\ub294 n\uc758 \uc18c\uc778\uc218\ub4e4\uc785\ub2c8\ub2e4.<\/li>\n<\/ul>\n<h2>\uc790\ubc14\uc2a4\ud06c\ub9bd\ud2b8 \ucf54\ub4dc \uad6c\ud604<\/h2>\n<p>\uc704\uc758 \uc131\uc9c8\uc744 \ubc14\ud0d5\uc73c\ub85c \uc624\uc77c\ub7ec \ud53c \ud568\uc218\ub97c \uad6c\ud604\ud558\ub294 \ucf54\ub4dc\ub97c \uc791\uc131\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<pre>\n<code class=\"language-javascript\">\nfunction eulerPhi(n) {\n    \/\/ \ubc30\uc5f4 \uc120\uc5b8 \ubc0f \ucd08\uae30\ud654\n    const phi = Array.from({ length: n + 1 }, (_, i) =&gt; i);\n    \n    \/\/ \uc5d0\ub77c\ud1a0\uc2a4\ud14c\ub124\uc2a4\uc758 \uccb4\ub97c \uc0ac\uc6a9\ud55c \uc18c\uc218 \ucc3e\uae30\n    for (let p = 2; p &lt;= n; p++) {\n        if (phi[p] === p) { \/\/ p\uac00 \uc18c\uc218\uc778 \uacbd\uc6b0\n            for (let k = p; k &lt;= n; k += p) {\n                \/\/ \ud835\udf19(k) \uac12 \uc5c5\ub370\uc774\ud2b8\n                phi[k] = Math.floor(phi[k] * (1 - 1 \/ p));\n            }\n        }\n    }\n    \n    \/\/ n\uc5d0 \ub300\ud55c phi(n) \ubc18\ud658\n    return phi[n];\n}\n\n\/\/ \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\nconsole.log(eulerPhi(1));  \/\/ 1\nconsole.log(eulerPhi(2));  \/\/ 1\nconsole.log(eulerPhi(3));  \/\/ 2\nconsole.log(eulerPhi(4));  \/\/ 2\nconsole.log(eulerPhi(5));  \/\/ 4\n<\/code>\n<\/pre>\n<h3>\ucf54\ub4dc \uc124\uba85<\/h3>\n<p>\ucf54\ub4dc\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc791\ub3d9\ud569\ub2c8\ub2e4:<\/p>\n<ol>\n<li>\uc6b0\uc120 n + 1 \ud06c\uae30\uc758 \ubc30\uc5f4 phi\ub97c \uc0dd\uc131\ud558\uace0, \uac01 \uc694\uc18c\ub97c \uadf8 \uc790\uccb4\ub85c \ucd08\uae30\ud654\ud569\ub2c8\ub2e4. phi[i]\ub294 i\ub97c \ucd08\uae30\uac12\uc73c\ub85c \uac00\uc9d1\ub2c8\ub2e4.<\/li>\n<li>2\ubd80\ud130 n\uae4c\uc9c0 \ubc18\ubcf5\ud558\uba74\uc11c, \uac01 \uc218 p\uac00 \uc18c\uc218\uc778\uc9c0 \uac80\uc0ac\ud569\ub2c8\ub2e4. \uc774\ub97c \uc704\ud574, phi[p]\uac00 p\uc640 \uac19\uc740 \uacbd\uc6b0 \uc18c\uc218\ub85c \uac04\uc8fc\ud569\ub2c8\ub2e4.<\/li>\n<li>p\uac00 \uc18c\uc218\uc77c \uacbd\uc6b0, p\uc758 \ubc30\uc218\ub97c \ucc3e\uc544 phi[k] \uac12\uc744 \uc5c5\ub370\uc774\ud2b8\ud569\ub2c8\ub2e4. \uc5c5\ub370\uc774\ud2b8\ub294 \ud835\udf19(k) = \ud835\udf19(k) * (1 &#8211; 1\/p)\ub85c \uc218\ud589\ud569\ub2c8\ub2e4.<\/li>\n<li>\ucd5c\uc885\uc801\uc73c\ub85c, phi[n] \uac12\uc744 \ubc18\ud658\ud558\uc5ec n\uc5d0 \ub300\ud55c \uc624\uc77c\ub7ec \ud53c \ud568\uc218\uc758 \uac12\uc744 \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n<h2>\ubcf5\uc7a1\ub3c4 \ubd84\uc11d<\/h2>\n<p>\uc704 \ucf54\ub4dc\uc758 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\ub294 O(n log log n)\uc785\ub2c8\ub2e4. \uc774\ub294 \uc5d0\ub77c\ud1a0\uc2a4\ud14c\ub124\uc2a4\uc758 \uccb4\ub97c \uc0ac\uc6a9\ud558\ub294 \ubc29\ubc95 \ub54c\ubb38\uc785\ub2c8\ub2e4. \uacf5\uac04 \ubcf5\uc7a1\ub3c4\ub294 O(n)\uc785\ub2c8\ub2e4, \ubc30\uc5f4 phi\ub97c \uc800\uc7a5\ud558\uae30 \uc704\ud574 n\uc758 \ud06c\uae30\ub9cc\ud07c\uc758 \uacf5\uac04\uc774 \ud544\uc694\ud569\ub2c8\ub2e4.<\/p>\n<h2>\uacb0\ub860<\/h2>\n<p>\uc9c0\uae08\uae4c\uc9c0 \uc790\ubc14\uc2a4\ud06c\ub9bd\ud2b8\ub85c \uc624\uc77c\ub7ec \ud53c \ud568\uc218\ub97c \uad6c\ud604\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc54c\uc544\ubcf4\uc558\uc2b5\ub2c8\ub2e4. \uc774 \ubc29\ubc95\uc740 \uc54c\uace0\ub9ac\uc998 \ud14c\uc2a4\ud2b8 \ubc0f \uc218\ub860\uc5d0 \ub9e4\uc6b0 \uc720\uc6a9\ud558\uba70, \ud6a8\uc728\uc801\uc73c\ub85c \uc624\uc77c\ub7ec \ud53c \uac12\uc744 \uacc4\uc0b0\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774 \ucf54\ub4dc\ub97c \ud65c\uc6a9\ud558\uc5ec \ub2e4\uc591\ud55c \ubb38\uc81c\ub97c \ud574\uacb0\ud574 \ubcf4\uc2dc\uae30 \ubc14\ub78d\ub2c8\ub2e4.<\/p>\n<h2>\ub354 \ub098\uc544\uac00\uae30<\/h2>\n<p>\ube44\uc2b7\ud55c \ubb38\uc81c\ub97c \ud480\uc5b4\ubcf4\uace0 \uc2f6\ub2e4\uba74, \ucd5c\ub300\uacf5\uc57d\uc218\ub098 \ucd5c\uc18c\uacf5\ubc30\uc218\ub97c \uc0ac\uc6a9\ud558\ub294 \ubb38\uc81c\ub97c \ud574\uacb0\ud574\ubcf4\ub294 \uac83 \ub610\ud55c \uc88b\uc740 \uc5f0\uc2b5\uc774 \ub420 \uac83\uc785\ub2c8\ub2e4. \ub610\ud55c \uc218\ub860\uc758 \ub2e4\ub978 \uac1c\ub150\uc778 \uc18c\uc218 \ud310\ubcc4, \uc18c\uc218 \uc0dd\uc131\uae30 \ub4f1\uc744 \uc5f0\uad6c\ud574\ubcf4\ub294 \uac83\ub3c4 \ucd94\ucc9c\ub4dc\ub9bd\ub2c8\ub2e4. \uc218\ud559\uc801 \uc0ac\uace0\ub97c \ud1b5\ud574 \uc54c\uace0\ub9ac\uc998\uc5d0 \ub300\ud55c \uc774\ud574\ub3c4\ub97c \ub192\uc5ec\ubcf4\uc138\uc694!<\/p>\n<h2>\ucc38\uace0 \uc790\ub8cc<\/h2>\n<ul>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Euler%27s_totient_function\">\uc704\ud0a4\ud53c\ub514\uc544 &#8211; \uc624\uc77c\ub7ec \ud53c \ud568\uc218<\/a><\/li>\n<li><a href=\"https:\/\/cp-algorithms.com\/algebra\/euler_phi.html\">CP-Algorithms &#8211; \uc624\uc77c\ub7ec \ud53c \ud568\uc218<\/a><\/li>\n<\/ul>\n<footer>\n<p>\uc774 \ud3ec\uc2a4\ud305\uc774 \ub3c4\uc6c0\uc774 \ub418\uc168\uae30\ub97c \ubc14\ub78d\ub2c8\ub2e4. \uad81\uae08\ud55c \uc810\uc774\ub098 \ucd94\uac00\uc801\uc778 \uc9c8\ubb38\uc774 \uc788\uc73c\uc2dc\ub2e4\uba74 \ub313\uae00\ub85c \ub0a8\uaca8\uc8fc\uc138\uc694! \uac10\uc0ac\ud569\ub2c8\ub2e4!<\/p>\n<\/footer>\n","protected":false},"excerpt":{"rendered":"<p>\uc548\ub155\ud558\uc138\uc694, \uc5ec\ub7ec\ubd84! \uc624\ub298\uc740 \uc790\ubc14\uc2a4\ud06c\ub9bd\ud2b8\ub85c \uc624\uc77c\ub7ec \ud53c \ud568\uc218(\ud835\udf19(n))\ub97c \uad6c\ud604\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc124\uba85\ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4. \uc624\uc77c\ub7ec \ud53c \ud568\uc218\ub294 \uc8fc\uc5b4\uc9c4 \uc815\uc218 n\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc815\uc218 \uc911 n\uacfc \uc11c\ub85c \uc18c\uc778 \uc815\uc218\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub294 \uc218\ub860 \uad00\ub828 \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\uc5d0\uc11c \ub9e4\uc6b0 \uc790\uc8fc \ub4f1\uc7a5\ud558\uba70, \ub2e4\uc591\ud55c \ucf54\ub529 \ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc720\uc6a9\ud558\uac8c \ud65c\uc6a9\ub420 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc624\uc77c\ub7ec \ud53c \ud568\uc218\ub780? \uc624\uc77c\ub7ec \ud53c \ud568\uc218 \ud835\udf19(n)\uc740 n\uacfc \uc11c\ub85c \uc18c\uc778 1\ubd80\ud130 &hellip; <a href=\"https:\/\/atmokpo.com\/w\/27863\/\" class=\"more-link\">\ub354 \ubcf4\uae30<span class=\"screen-reader-text\"> &#8220;\uc790\ubc14\uc2a4\ud06c\ub9bd\ud2b8 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uc624\uc77c\ub7ec \ud53c \ud568\uc218 \uad6c\ud604\ud558\uae30&#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":[26],"tags":[],"class_list":["post-27863","post","type-post","status-publish","format-standard","hentry","category-26"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\uc790\ubc14\uc2a4\ud06c\ub9bd\ud2b8 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uc624\uc77c\ub7ec \ud53c \ud568\uc218 \uad6c\ud604\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\/27863\/\" \/>\n<meta property=\"og:locale\" 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