{"id":27531,"date":"2024-10-27T14:41:39","date_gmt":"2024-10-27T14:41:39","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=27531"},"modified":"2024-11-26T07:17:31","modified_gmt":"2024-11-26T07:17:31","slug":"c-%ec%bd%94%eb%94%a9%ed%85%8c%ec%8a%a4%ed%8a%b8-%ea%b0%95%ec%a2%8c-ax-by-c-2","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/27531\/","title":{"rendered":"C++ \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, Ax + By = C"},"content":{"rendered":"

<\/p>\n

\n \ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 C++ \uc5b8\uc5b4\ub97c \uc774\uc6a9\ud558\uc5ec Ax + By = C<\/strong> \ud615\ud0dc\uc758 \ubc29\uc815\uc2dd\uc744 \ud478\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc54c\uc544\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.
\n \uc774 \ubb38\uc81c\ub294 \ucf54\ub529\ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc790\uc8fc \uc811\ud560 \uc218 \uc788\ub294 \ub0b4\uc6a9\uc73c\ub85c, \uc218\ud559\uc801 \uc774\ud574\uc640 \uc54c\uace0\ub9ac\uc998 \uc124\uacc4\ub97c \ud544\uc694\ub85c \ud569\ub2c8\ub2e4.\n<\/p>\n

\ubb38\uc81c \uc815\uc758<\/h2>\n

\n \uc8fc\uc5b4\uc9c4 \uc815\uc218 A, B, C\uac00 \uc788\uc744 \ub54c, \ubc29\uc815\uc2dd Ax + By = C<\/strong>\ub97c \ub9cc\uc871\ud558\ub294 \uc815\uc218 x\uc640 y\uc758 \ubaa8\ub4e0 \uc870\ud569\uc744 \uad6c\ud558\ub294 \ubb38\uc81c\uc785\ub2c8\ub2e4.
\n \uc8fc\uc758\ud560 \uc810\uc740 x\uc640 y\uac00 \uc815\uc218\uc5ec\uc57c \ud55c\ub2e4\ub294 \uac83\uc785\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4 A=2, B=3, C=6\uc77c \ub54c,
\n (x, y) = (0, 2), (3, 0), (1, 1)\uc640 \uac19\uc740 \uc815\uc218 \uc30d\uc774 \uc788\uc2b5\ub2c8\ub2e4.\n<\/p>\n

\ubb38\uc81c \ud574\uacb0\uc744 \uc704\ud55c \uae30\ucd08 \uc218\ud559 \uac1c\ub150<\/h2>\n

\n \uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574\uc11c\ub294 \ub514\uc624\ud310\ud2f4 \ubc29\uc815\uc2dd(Diophantine Equation)<\/strong> \uac1c\ub150\uc744 \uc54c\uc544\uc57c \ud569\ub2c8\ub2e4.
\n \ub514\uc624\ud310\ud2f4 \ubc29\uc815\uc2dd\uc740 \uc815\uc218 \uacc4\uc218\ub97c \uac00\uc9c4 \ub2e4\ud56d \ubc29\uc815\uc2dd\uc5d0\uc11c \uc815\uc218 \ud574\ub97c \ucc3e\ub294 \ubb38\uc81c\uc785\ub2c8\ub2e4.
\n Ax + By = C \ud615\ud0dc\uc758 \ubc29\uc815\uc2dd\uc774 \uc77c\uad00\ub41c \ud574\ub97c \uac00\uc9c0\ub824\uba74, gcd(A, B)<\/strong>\uac00 C<\/strong>\uc758 \uc57d\uc218\uc5ec\uc57c \ud569\ub2c8\ub2e4.\n<\/p>\n

\uc54c\uace0\ub9ac\uc998 \uc124\uacc4<\/h2>\n

\n 1. \uba3c\uc800 A, B, C\uc758 GCD\ub97c \uacc4\uc0b0\ud569\ub2c8\ub2e4.
\n 2. GCD\uac00 C\uc758 \uc57d\uc218\uc778\uc9c0 \ud655\uc778\ud569\ub2c8\ub2e4.
\n 3. GCD\uac00 C\uc758 \uc57d\uc218\uc774\uba74, x\uc640 y\uc758 \uac00\ub2a5\ud55c \uc870\ud569\uc744 \ucc3e\uae30 \uc2dc\uc791\ud569\ub2c8\ub2e4.
\n 4. \uc815\uc218 \ud574\ub97c \ucc3e\uae30 \uc704\ud574 x\uc758 \uac12\uc740 0\ubd80\ud130 \uc2dc\uc791\ud558\uc5ec B\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \uac80\ud1a0\ud569\ub2c8\ub2e4.
\n 5. \uac01 x\uc5d0 \ub300\ud574 y\ub97c \uacc4\uc0b0\ud558\uc5ec \uc815\uc218 \ud574\ub97c \ucc3e\uc2b5\ub2c8\ub2e4.\n<\/p>\n

C++ \ucf54\ub4dc \uad6c\ud604<\/h2>\n

\n \uc544\ub798\ub294 \uc704 \uc54c\uace0\ub9ac\uc998\uc744 C++\ub85c \uad6c\ud604\ud55c \uc608\uc2dc \ucf54\ub4dc\uc785\ub2c8\ub2e4:\n<\/p>\n

\n# include <iostream>\n# include <vector>\n# include <numeric> \/\/ for std::gcd\nusing namespace std;\n\n\/\/ Ax + By = C \ubc29\uc815\uc2dd\uc744 \ub9cc\uc871\ud558\ub294 (x, y)\uc758 \ubaa8\ub4e0 \uc870\ud569\uc744 \uad6c\ud558\ub294 \ud568\uc218\nvoid findIntegerSolutions(int A, int B, int C) {\n    int gcd_ab = gcd(A, B);\n\n    \/\/ GCD\uac00 C\uc758 \uc57d\uc218\uc778\uc9c0 \ud655\uc778\n    if (C % gcd_ab != 0) {\n        cout << \"\ud574\uac00 \uc874\uc7ac\ud558\uc9c0 \uc54a\uc2b5\ub2c8\ub2e4.\" << endl;\n        return;\n    }\n\n    \/\/ A, B, C\ub97c GCD\ub85c \ub098\ub204\uc5b4 \uc815\uaddc\ud654\n    A \/= gcd_ab;\n    B \/= gcd_ab;\n    C \/= gcd_ab;\n\n    \/\/ x\uc758 \uac00\ub2a5\ud55c \ubc94\uc704\ub97c \uc124\uc815\n    for (int x = -100; x <= 100; ++x) {\n        \/\/ y\ub97c \uacc4\uc0b0\n        if ((C - A * x) % B == 0) {\n            int y = (C - A * x) \/ B;\n            cout << \"(x, y) = (\" << x << \", \" << y << \")\" << endl;\n        }\n    }\n}\n\nint main() {\n    int A, B, C;\n    cout << \"A, B, C \uac12\uc744 \uc785\ub825\ud558\uc138\uc694: \";\n    cin >> A >> B >> C;\n\n    findIntegerSolutions(A, B, C);\n    return 0;\n}\n<\/pre>\n
\ucf54\ub4dc \uc124\uba85<\/h2>\n
\n    – \uc785\ub825\uc73c\ub85c A, B, C\ub97c \ubc1b\uace0 findIntegerSolutions<\/strong> \ud568\uc218\ub97c \ud638\ucd9c\ud569\ub2c8\ub2e4.
\n    – A, B\uc758 GCD\ub97c \uacc4\uc0b0\ud558\uc5ec return\ud558\uace0, \uc774\ub97c \ud1b5\ud574 C\uac00 GCD\uc758 \uc57d\uc218\uc778\uc9c0 \uac80\uc0ac\ud569\ub2c8\ub2e4.
\n    – GCD\ub85c \ubaa8\ub4e0 \uc218\ub97c \ub098\ub208 \ud6c4, x\uc758 \uac12\uc744 -100\uc5d0\uc11c 100\uae4c\uc9c0 \ubcc0\ud654\uc2dc\ud0a4\uba70 y\ub97c \uacc4\uc0b0\ud569\ub2c8\ub2e4.
\n    – \ubc29\uc815\uc2dd\uc774 \uc131\ub9bd\ud558\ub294 \uacbd\uc6b0 x, y \uc30d\uc744 \ucd9c\ub825\ud569\ub2c8\ub2e4.\n<\/p>\n
\uacb0\uacfc \ubcf4\uae30<\/h2>\n
\n    \uc774\uc81c \ucf54\ub4dc \uc2e4\ud589 \uacb0\uacfc\ub97c \ud655\uc778\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4 A=2, B=3, C=6\uc778 \uacbd\uc6b0 \ub2e4\uc74c\uacfc \uac19\uc740 \uacb0\uacfc\ub97c \uc5bb\uc744 \uc218 \uc788\uc2b5\ub2c8\ub2e4:\n<\/p>\n
\nA, B, C \uac12\uc744 \uc785\ub825\ud558\uc138\uc694: 2 3 6\n(x, y) = (0, 2)\n(x, y) = (3, 0)\n(x, y) = (1, 1)\n<\/pre>\n
\uacb0\ub860<\/h2>\n
\n    \uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 Ax + By = C \ud615\ud0dc\uc758 \ubc29\uc815\uc2dd\uc744 C++\ub85c \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uc558\uc2b5\ub2c8\ub2e4.
\n    \uc774 \ubb38\uc81c\ub97c \ud1b5\ud574 \ub514\uc624\ud310\ud2f4 \ubc29\uc815\uc2dd\uc758 \uae30\ucd08 \uc774\ub860\uacfc, \uc774\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud55c \uc54c\uace0\ub9ac\uc998 \uc124\uacc4\ub97c \uc775\ud788\uac8c \ub418\uc5c8\uc2b5\ub2c8\ub2e4.
\n    \uc774\ub7ec\ud55c \ubb38\uc81c\ub294 \ucf54\ub529\ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc790\uc8fc \ucd9c\uc81c\ub418\ubbc0\ub85c, \ucda9\ubd84\ud788 \uc5f0\uc2b5\ud558\uc154\uc11c \uc790\uc2e0\ub9cc\uc758 \ud480\uc774 \ubc29\ubc95\uc744 \ucc3e\ub294 \uac83\uc774 \uc911\uc694\ud569\ub2c8\ub2e4.\n<\/p>\n
<\/body><\/p>\n","protected":false},"excerpt":{"rendered":"
\ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 C++ \uc5b8\uc5b4\ub97c \uc774\uc6a9\ud558\uc5ec Ax + By = C \ud615\ud0dc\uc758 \ubc29\uc815\uc2dd\uc744 \ud478\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc54c\uc544\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub294 \ucf54\ub529\ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc790\uc8fc \uc811\ud560 \uc218 \uc788\ub294 \ub0b4\uc6a9\uc73c\ub85c, \uc218\ud559\uc801 \uc774\ud574\uc640 \uc54c\uace0\ub9ac\uc998 \uc124\uacc4\ub97c \ud544\uc694\ub85c \ud569\ub2c8\ub2e4. \ubb38\uc81c \uc815\uc758 \uc8fc\uc5b4\uc9c4 \uc815\uc218 A, B, C\uac00 \uc788\uc744 \ub54c, \ubc29\uc815\uc2dd Ax + By = C\ub97c \ub9cc\uc871\ud558\ub294 \uc815\uc218 x\uc640 y\uc758 \ubaa8\ub4e0 \uc870\ud569\uc744 \uad6c\ud558\ub294 \ubb38\uc81c\uc785\ub2c8\ub2e4. \uc8fc\uc758\ud560 \uc810\uc740 … \ub354 \ubcf4\uae30 “C++ \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, Ax + By = C”<\/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":[25],"tags":[],"class_list":["post-27531","post","type-post","status-publish","format-standard","hentry","category-c---2"],"yoast_head":"\nC++ \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, Ax + By = C - 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