{"id":27752,"date":"2024-10-27T14:43:34","date_gmt":"2024-10-27T14:43:34","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=27752"},"modified":"2024-11-26T07:15:31","modified_gmt":"2024-11-26T07:15:31","slug":"c-%ec%bd%94%eb%94%a9%ed%85%8c%ec%8a%a4%ed%8a%b8-%ea%b0%95%ec%a2%8c-%ec%b5%9c%ec%86%8c-%ec%8b%a0%ec%9e%a5-%ed%8a%b8%eb%a6%ac-%ea%b5%ac%ed%95%98%ea%b8%b0-2","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/27752\/","title":{"rendered":"C++ \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac \uad6c\ud558\uae30"},"content":{"rendered":"

\ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac(Minimum Spanning Tree, MST)\uc5d0 \ub300\ud574 \ubc30\uc6cc\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\ub294 \uac00\uc911\uce58\uac00 \uc788\ub294 \uadf8\ub798\ud504\uc5d0\uc11c \ubaa8\ub4e0 \uc815\uc810\uc744 \ud3ec\ud568\ud558\uba74\uc11c\ub3c4 \uac00\uc911\uce58\uc758 \ucd1d\ud569\uc774 \ucd5c\uc18c\uac00 \ub418\ub3c4\ub85d \ud558\ub294 \ud2b8\ub9ac\uc785\ub2c8\ub2e4. \uc774\ub7ec\ud55c \ubb38\uc81c\ub294 \uc5ec\ub7ec \ubd84\uc57c\uc5d0\uc11c \uc751\uc6a9 \uac00\ub2a5\ud558\uba70, \ud2b9\ud788 \ub124\ud2b8\uc6cc\ud06c \uc124\uacc4, \ub3c4\ub85c \uac74\uc124, \ud1b5\uc2e0\ub9dd \uad6c\ucd95 \ub4f1\uc5d0\uc11c \uc911\uc694\ud55c \uc5ed\ud560\uc744 \ud569\ub2c8\ub2e4.<\/p>\n

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

\ub2e4\uc74c\uacfc \uac19\uc740 \uac00\uc911\uce58\uac00 \uc788\ub294 \ubb34\ubc29\ud5a5 \uadf8\ub798\ud504\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\ub97c \uad6c\ud558\uc2dc\uc624.<\/p>\n

\uc785\ub825:\n\uccab \uc904\uc5d0 \uc815\uc810\uc758 \uc218 V<\/em>\uc640 \uac04\uc120\uc758 \uc218 E<\/em>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 \u2264 V<\/em> \u2264 1000, 1 \u2264 E<\/em> \u2264 10000)\n\ub2e4\uc74c E<\/em>\uc904\uc5d0\ub294 \uac01\uac01\uc758 \uac04\uc120 \uc815\ubcf4 u, v, w<\/em>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 \uc815\uc810 u<\/em>\uc640 \uc815\uc810 v<\/em>\ub97c \uc5f0\uacb0\ud558\ub294 \uac04\uc120\uc758 \uac00\uc911\uce58\uac00 w<\/em>\ub77c\ub294 \uc758\ubbf8\uc774\ub2e4.\n\n\ucd9c\ub825:\n\ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\uc758 \uac00\uc911\uce58 \ucd1d\ud569\uc744 \ucd9c\ub825\ud558\uc2dc\uc624.<\/code><\/pre>\n
\uc608\uc81c \uc785\ub825<\/h2>\n
3 3\n1 2 1\n2 3 2\n1 3 3\n<\/code><\/pre>\n
\uc608\uc81c \ucd9c\ub825<\/h2>\n
3\n<\/code><\/pre>\n
\ud574\uacb0 \ubc29\ubc95<\/h2>\n
\uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574 Prim \uc54c\uace0\ub9ac\uc998 \ub610\ub294 Kruskal \uc54c\uace0\ub9ac\uc998\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc5ec\uae30\uc11c\ub294 Kruskal \uc54c\uace0\ub9ac\uc998\uc744 \uc0ac\uc6a9\ud558\uc5ec \ud480\uc774\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n
Kruskal \uc54c\uace0\ub9ac\uc998 \uc124\uba85<\/h3>\n
Kruskal \uc54c\uace0\ub9ac\uc998\uc740 \uac04\uc120 \uae30\ubc18\uc758 \uc54c\uace0\ub9ac\uc998\uc73c\ub85c, \ub2e4\uc74c\uacfc \uac19\uc740 \ub2e8\uacc4\ub85c \uc9c4\ud589\ub429\ub2c8\ub2e4:<\/p>\n
    \n
  1. \ubaa8\ub4e0 \uac04\uc120\uc744 \uac00\uc911\uce58\uc758 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub82c\ud55c\ub2e4.<\/li>\n
  2. \uc815\uc810 \uc9d1\ud569\uc744 \ucd08\uae30\ud654\ud55c\ub2e4. (Union-Find \uc790\ub8cc\uad6c\uc870\ub97c \uc0ac\uc6a9)<\/li>\n
  3. \uac04\uc120\uc744 \ud558\ub098\uc529 \uc120\ud0dd\ud558\uc5ec \ub450 \uc815\uc810\uc774 \uc11c\ub85c \uc5f0\uacb0\ub418\uc5b4 \uc788\uc9c0 \uc54a\uc73c\uba74 \uc774 \uac04\uc120\uc744 \uc120\ud0dd\ud55c\ub2e4. \uc774\ub7f0 \uacfc\uc815\uc744 \ubc18\ubcf5\ud558\uc5ec \ubaa8\ub4e0 \uc815\uc810\uc744 \uc5f0\uacb0\ud558\ub294 \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\ub97c \ub9cc\ub4e0\ub2e4.<\/li>\n<\/ol>\n
    \ucf54\ub4dc \uad6c\ud604<\/h3>\n
    \uc774\uc81c C++\ub85c Kruskal \uc54c\uace0\ub9ac\uc998\uc744 \uad6c\ud604\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n
    #include <iostream>\n#include <vector>\n#include <algorithm>\n\nusing namespace std;\n\nstruct Edge {\n    int u, v, weight;\n};\n\nbool compare(Edge a, Edge b) {\n    return a.weight < b.weight;\n}\n\nint find(int parent[], int x) {\n    if (parent[x] != x) {\n        parent[x] = find(parent, parent[x]);\n    }\n    return parent[x];\n}\n\nvoid unionSet(int parent[], int rank[], int x, int y) {\n    int rootX = find(parent, x);\n    int rootY = find(parent, y);\n\n    if (rootX != rootY) {\n        if (rank[rootX] < rank[rootY]) {\n            parent[rootX] = rootY;\n        } else if (rank[rootX] > rank[rootY]) {\n            parent[rootY] = rootX;\n        } else {\n            parent[rootY] = rootX;\n            rank[rootX]++;\n        }\n    }\n}\n\nint kruskal(int V, vector& edges) {\n    sort(edges.begin(), edges.end(), compare);\n    int parent[V + 1];\n    int rank[V + 1];\n    for (int i = 0; i <= V; i++) {\n        parent[i] = i;\n        rank[i] = 0;\n    }\n\n    int totalWeight = 0;\n    for (Edge edge : edges) {\n        if (find(parent, edge.u) != find(parent, edge.v)) {\n            totalWeight += edge.weight;\n            unionSet(parent, rank, edge.u, edge.v);\n        }\n    }\n    return totalWeight;\n}\n\nint main() {\n    int V, E;\n    cin >> V >> E;\n    vector edges(E);\n    for (int i = 0; i < E; i++) {\n        cin >> edges[i].u >> edges[i].v >> edges[i].weight;\n    }\n    cout << kruskal(V, edges) << endl;\n    return 0;\n}\n<\/edge><\/edge><\/code><\/pre>\n
    \ucf54\ub4dc \uc124\uba85<\/h2>\n
    \uba3c\uc800, Edge \uad6c\uc870\uccb4\ub97c \uc815\uc758\ud558\uace0 \ube44\uad50 \ud568\uc218\ub85c \uac00\uc911\uce58\ub97c \uae30\uc900\uc73c\ub85c \uc815\ub82c\ud569\ub2c8\ub2e4.<\/p>\n
    find<\/b> \ud568\uc218\ub294 \uacbd\ub85c \uc555\ucd95 \uae30\ubc95\uc744 \uc0ac\uc6a9\ud558\uc5ec \ud6a8\uc728\uc801\uc73c\ub85c \ubd80\ubaa8 \ub178\ub4dc\ub97c \ucc3e\uc2b5\ub2c8\ub2e4. unionSet<\/b> \ud568\uc218\ub294 \ub450 \uc815\uc810\uc758 \uc9d1\ud569\uc744 \ud569\uce58\ub294 \uc5ed\ud560\uc744 \ud558\uba70, \ub7ad\ud06c\ub97c \uc0ac\uc6a9\ud558\uc5ec \ud2b8\ub9ac\uac00 \ub108\ubb34 \ucee4\uc9c0\uc9c0 \uc54a\ub3c4\ub85d \ud569\ub2c8\ub2e4.<\/p>\n
    \uba54\uc778 \ud568\uc218\uc5d0\uc11c\ub294 \uc785\ub825\uc744 \ubc1b\uace0 Kruskal \uc54c\uace0\ub9ac\uc998\uc744 \ud1b5\ud574 \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\uc758 \uac00\uc911\uce58 \ucd1d\ud569\uc744 \uad6c\ud558\uc5ec \ucd9c\ub825\ud569\ub2c8\ub2e4.<\/p>\n
    \ubcf5\uc7a1\ub3c4 \ubd84\uc11d<\/h2>\n
    Kruskal \uc54c\uace0\ub9ac\uc998\uc758 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\ub294 O(E log E)\uc785\ub2c8\ub2e4. \uc774\ub294 \uac04\uc120 \uc815\ub82c\uc5d0 \uc18c\uc694\ub418\ub294 \uc2dc\uac04\uc785\ub2c8\ub2e4. Union-Find\uc758 \uc5f0\uc0b0\uc744 \ucd5c\uc801\ud654\ud560 \uacbd\uc6b0 \ub9e4\uc6b0 \ud6a8\uc728\uc801\uc778 \uc54c\uace0\ub9ac\uc998\uc73c\ub85c \uc791\ub3d9\ud569\ub2c8\ub2e4.<\/p>\n
    \uacb0\ub860<\/h2>\n
    \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\ub294 \ub9ce\uc740 \uc2e4\uc81c \ubb38\uc81c\uc5d0\uc11c \uc0ac\uc6a9\ub418\ubbc0\ub85c \uc774\ub97c \uccb4\uacc4\uc801\uc73c\ub85c \uc774\ud574\ud558\ub294 \uac83\uc774 \uc911\uc694\ud569\ub2c8\ub2e4. \ubcf8 \uc608\uc81c\ub97c \ud1b5\ud574 Kruskal \uc54c\uace0\ub9ac\uc998\uc744 \uc801\uc6a9\ud558\uc5ec MST\ub97c \ucc3e\ub294 \ubc29\ubc95\uc744 \ud559\uc2b5\ud558\uc600\uc73c\uba70, \ub2e4\uc591\ud55c \ubcc0\ud615 \ubb38\uc81c\uc5d0\ub3c4 \uc801\uc6a9\ud560 \uc218 \uc788\ub294 \uae30\ubc18 \uc774\ub860\uc744 \uc2b5\ub4dd\ud558\uac8c \ub418\uc5c8\uc2b5\ub2c8\ub2e4. \ucd94\uac00\uc801\uc73c\ub85c Prim \uc54c\uace0\ub9ac\uc998\ub3c4 \uc2e4\uc2b5\ud574\ubcf4\uc2dc\uae38 \uad8c\uc7a5\ud569\ub2c8\ub2e4.<\/p>\n
    \ub2e4\uc74c \uac15\uc88c\uc5d0\uc11c\ub294 \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\uc5d0 \ub300\ud55c \ub2e4\ub978 \uc54c\uace0\ub9ac\uc998\uc774\ub098 \ub2e4\uc591\ud55c \ubb38\uc81c \ud480\uae30\ub97c \ub2e4\ub8f0 \uc608\uc815\uc774\ub2c8 \ub9ce\uc740 \uae30\ub300 \ubc14\ub78d\ub2c8\ub2e4.<\/p>\n","protected":false},"excerpt":{"rendered":"
    \ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac(Minimum Spanning Tree, MST)\uc5d0 \ub300\ud574 \ubc30\uc6cc\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\ub294 \uac00\uc911\uce58\uac00 \uc788\ub294 \uadf8\ub798\ud504\uc5d0\uc11c \ubaa8\ub4e0 \uc815\uc810\uc744 \ud3ec\ud568\ud558\uba74\uc11c\ub3c4 \uac00\uc911\uce58\uc758 \ucd1d\ud569\uc774 \ucd5c\uc18c\uac00 \ub418\ub3c4\ub85d \ud558\ub294 \ud2b8\ub9ac\uc785\ub2c8\ub2e4. \uc774\ub7ec\ud55c \ubb38\uc81c\ub294 \uc5ec\ub7ec \ubd84\uc57c\uc5d0\uc11c \uc751\uc6a9 \uac00\ub2a5\ud558\uba70, \ud2b9\ud788 \ub124\ud2b8\uc6cc\ud06c \uc124\uacc4, \ub3c4\ub85c \uac74\uc124, \ud1b5\uc2e0\ub9dd \uad6c\ucd95 \ub4f1\uc5d0\uc11c \uc911\uc694\ud55c \uc5ed\ud560\uc744 \ud569\ub2c8\ub2e4. \ubb38\uc81c \uc124\uba85 \ub2e4\uc74c\uacfc \uac19\uc740 \uac00\uc911\uce58\uac00 \uc788\ub294 \ubb34\ubc29\ud5a5 \uadf8\ub798\ud504\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\ub97c … \ub354 \ubcf4\uae30 “C++ \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac \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":[25],"tags":[],"class_list":["post-27752","post","type-post","status-publish","format-standard","hentry","category-c---2"],"yoast_head":"\nC++ \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac \uad6c\ud558\uae30 - 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