{"id":27750,"date":"2024-10-27T14:43:33","date_gmt":"2024-10-27T14:43:33","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=27750"},"modified":"2024-11-26T07:15:34","modified_gmt":"2024-11-26T07:15:34","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-2","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/27750\/","title":{"rendered":"C++ \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac"},"content":{"rendered":"<p><body><\/p>\n<p>\uc548\ub155\ud558\uc138\uc694! \uc774\ubc88 \ube14\ub85c\uadf8 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 C++\uc744 \uc774\uc6a9\ud55c \ucf54\ub529 \ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc790\uc8fc \ucd9c\uc81c\ub418\ub294 \ubb38\uc81c \uc911 \ud558\ub098\uc778 <strong>\ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac(Minimum Spanning Tree)<\/strong>\uc5d0 \ub300\ud574 \ub2e4\ub904\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc6b0\ub9ac\ub294 Prim \uc54c\uace0\ub9ac\uc998\uacfc Kruskal \uc54c\uace0\ub9ac\uc998\uc744 \uc0ac\uc6a9\ud560 \uac83\uc774\uba70, \uad6c\uccb4\uc801\uc778 \ubb38\uc81c\ub97c \ud480\uc5b4\ubcf4\uba70 \uc774\ub860\uc744 \uc815\ub9ac\ud560 \uac83\uc785\ub2c8\ub2e4.<\/p>\n<h2>\ubb38\uc81c \uc124\uba85<\/h2>\n<p>\ub2e4\uc74c\uacfc \uac19\uc740 \uadf8\ub798\ud504\uac00 \uc8fc\uc5b4\uc9c8 \ub54c, \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\ub97c \uad6c\ud558\uc2dc\uc624. \ucd5c\uc885\uc801\uc73c\ub85c \ud2b8\ub9ac\uc758 \uac00\uc911\uce58\uc758 \ud569\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\n<pre>\n\uc785\ub825:\n5 7\n1 2 3\n1 3 4\n2 3 2\n2 4 6\n3 4 1\n3 5 5\n4 5 2\n\n\ucd9c\ub825:\n6\n<\/pre>\n<p>\uc5ec\uae30\uc11c \uc785\ub825\uc758 \uad6c\uc870\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n<ul>\n<li>\uccab \ubc88\uc9f8 \uc904: \uc815\uc810\uc758 \uc218 <code>V<\/code>\uc640 \uac04\uc120\uc758 \uc218 <code>E<\/code><\/li>\n<li>\uadf8 \ub2e4\uc74c <code>E<\/code>\uac1c\uc758 \uc904: \uac01 \uac04\uc120\uc758 \uc815\ubcf4 (\uc815\uc8101, \uc815\uc8102, \uac00\uc911\uce58)<\/li>\n<\/ul>\n<h2>\ubb38\uc81c \ud574\uacb0 \ubc29\ubc95<\/h2>\n<p>\uc704\uc758 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574 Prim \uc54c\uace0\ub9ac\uc998\uacfc Kruskal \uc54c\uace0\ub9ac\uc998\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc5ec\uae30\uc11c\ub294 Prim \uc54c\uace0\ub9ac\uc998\uc744 \uc0ac\uc6a9\ud558\uc5ec \ubb38\uc81c\ub97c \ud480\uc5b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. Prim \uc54c\uace0\ub9ac\uc998\uc740 \uc784\uc758\uc758 \uc815\uc810\uc5d0\uc11c \uc2dc\uc791\ud574, \uac00\uc7a5 \uc791\uc740 \uac00\uc911\uce58\uc758 \uac04\uc120\uc744 \uc120\ud0dd\ud558\uc5ec \uc810\ucc28 \uadf8\ub798\ud504\ub97c \ud655\uc7a5\ud558\ub294 \ubc29\uc2dd\uc785\ub2c8\ub2e4.<\/p>\n<h3>1. Prim \uc54c\uace0\ub9ac\uc998 \uac1c\uc694<\/h3>\n<p>Prim \uc54c\uace0\ub9ac\uc998\uc740 \ub2e4\uc74c\uc758 \ub2e8\uacc4\ub85c \uc774\ub8e8\uc5b4\uc9d1\ub2c8\ub2e4:<\/p>\n<ol>\n<li>\uc2dc\uc791 \uc815\uc810\uc744 \uc120\ud0dd\ud558\uace0, \uc774\uc5d0 \uc5f0\uacb0\ub41c \uac04\uc120 \uc911\uc5d0\uc11c \ucd5c\uc18c \uac00\uc911\uce58\uc758 \uac04\uc120\uc744 \uc120\ud0dd\ud569\ub2c8\ub2e4.<\/li>\n<li>\uc120\ud0dd\ud55c \uac04\uc120\uc5d0 \uc5f0\uacb0\ub41c \uc815\uc810\uc744 \ud3ec\ud568\uc2dc\ud0b5\ub2c8\ub2e4.<\/li>\n<li>\uc704\uc758 \uacfc\uc815\uc744 \ubc18\ubcf5\ud558\uc5ec \ubaa8\ub4e0 \uc815\uc810\uc744 \ud3ec\ud568\ud560 \ub54c\uae4c\uc9c0 \uc9c4\ud589\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n<h3>2. C++\ub85c Prim \uc54c\uace0\ub9ac\uc998 \uad6c\ud604\ud558\uae30<\/h3>\n<p>\uc774\uc81c Prim \uc54c\uace0\ub9ac\uc998\uc744 C++\ub85c \uad6c\ud604\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc774 \uad6c\ud604\uc744 \ud1b5\ud574 \uc2e4\uc81c \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \uacfc\uc815\uc744 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<pre><code>\n#include <iostream>\n#include <vector>\n#include <queue>\n#include <utility>\n#include <algorithm>\nusing namespace std;\n\nconst int MAX_V = 100; \/\/ \ucd5c\ub300 \uc815\uc810 \uc218\nconst int INF = 1e9; \/\/ \ubb34\ud55c\ub300 \ud45c\uc2dc\n\nvector<pair<int, int=\"\">&gt; graph[MAX_V]; \/\/ \uc778\uc811 \ub9ac\uc2a4\ud2b8\nint key[MAX_V]; \/\/ \ucd5c\uc18c \uac00\uc911\uce58 \ubc30\uc5f4\nbool inMST[MAX_V]; \/\/ MST \ud3ec\ud568 \uc5ec\ubd80\n\nint prim(int start, int V) {\n    priority_queue<pair<int, int=\"\">, vector<pair<int, int=\"\">&gt;, greater<pair<int, int=\"\">&gt;&gt; pq;\n    fill(key, key + V, INF);\n    fill(inMST, inMST + V, false);\n\n    key[start] = 0; \/\/ \uc2dc\uc791 \uc815\uc810\uc758 \ud0a4 \uac12\uc740 0\n    pq.push({0, start}); \/\/ (\uac00\uc911\uce58, \uc815\uc810)\n\n    int totalWeight = 0; \/\/ \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac\uc758 \ucd1d \uac00\uc911\uce58\n\n    while (!pq.empty()) {\n        int u = pq.top().second;\n        pq.pop();\n\n        if (inMST[u]) continue; \/\/ \uc774\ubbf8 MST\uc5d0 \ud3ec\ud568\ub41c \uacbd\uc6b0\n\n        totalWeight += key[u]; \/\/ \ucd1d \uac00\uc911\uce58\uc5d0 \ud604\uc7ac \uc815\uc810\uc758 \ud0a4 \uac12\uc744 \ucd94\uac00\n        inMST[u] = true; \/\/ MST\uc5d0 \ucd94\uac00\n\n        for (auto&amp; edge : graph[u]) {\n            int v = edge.first;\n            int weight = edge.second;\n\n            \/\/ \ud604\uc7ac \uac04\uc120\uc774 MST\uc5d0 \ud3ec\ud568\ub418\uc9c0 \uc54a\uace0, \uac00\uc911\uce58\uac00 \ub354 \uc791\uc740 \uacbd\uc6b0\n            if (!inMST[v] &amp;&amp; weight &lt; key[v]) {\n                key[v] = weight; \/\/ \ucd5c\uc18c \uac00\uc911\uce58 \uc5c5\ub370\uc774\ud2b8\n                pq.push({key[v], v}); \/\/ \ud050\uc5d0 \ucd94\uac00\n            }\n        }\n    }\n\n    return totalWeight;\n}\n\nint main() {\n    int V, E;\n    cin &gt;&gt; V &gt;&gt; E;\n\n    for (int i = 0; i &lt; E; i++) {\n        int u, v, weight;\n        cin &gt;&gt; u &gt;&gt; v &gt;&gt; weight;\n        \/\/ 0-indexed\ub85c \uc800\uc7a5\n        graph[u - 1].push_back({v - 1, weight});\n        graph[v - 1].push_back({u - 1, weight});\n    }\n\n    cout &lt;&lt; prim(0, V) &lt;&lt; endl; \/\/ \uc2dc\uc791 \uc815\uc810 0\n    return 0;\n}\n<\/pair<int,><\/pair<int,><\/pair<int,><\/pair<int,><\/algorithm><\/utility><\/queue><\/vector><\/iostream><\/code><\/pre>\n<h4>3. \ucf54\ub4dc \uc124\uba85<\/h4>\n<p>\uc704 \ucf54\ub4dc\uc758 \uc124\uba85\uc740 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n<ul>\n<li>\uadf8\ub798\ud504\ub294 \uc778\uc811 \ub9ac\uc2a4\ud2b8\ub97c \uc0ac\uc6a9\ud558\uc5ec \ud45c\ud604\ud569\ub2c8\ub2e4. \uac01 \uc815\uc810\uc740 \uc5f0\uacb0\ub41c \uc815\uc810\uacfc \uadf8 \uac00\uc911\uce58\ub97c \uac00\uc9c0\ub294 \ub9ac\uc2a4\ud2b8\ub85c \ub418\uc5b4 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n<li>\uc6b0\uc120\uc21c\uc704 \ud050\ub97c \uc0ac\uc6a9\ud558\uc5ec \ud604\uc7ac \uc815\uc810\uc5d0\uc11c \uc5f0\uacb0\ub41c \uac04\uc120 \uc911 \ucd5c\uc18c \uac00\uc911\uce58\uc758 \uac04\uc120\uc744 \ud6a8\uc728\uc801\uc73c\ub85c \uc120\ud0dd\ud569\ub2c8\ub2e4.<\/li>\n<li>MST\uc5d0 \ud3ec\ud568\ub41c \uc815\uc810\uc740 <code>inMST<\/code> \ubc30\uc5f4\ub85c \uad00\ub9ac\ud569\ub2c8\ub2e4.<\/li>\n<li>\ucd5c\uc885\uc801\uc73c\ub85c \ubaa8\ub4e0 \uc815\uc810\uc744 \ud3ec\ud568\ud55c MST\uc758 \ucd1d \uac00\uc911\uce58\ub97c \ubc18\ud658\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n<h4>4. \uc2e4\ud589 \uc608\uc2dc<\/h4>\n<p>\uc785\ub825 \ub370\uc774\ud130\ub97c \uc2e4\ud589\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc740 \uacb0\uacfc\uac00 \ub098\uc635\ub2c8\ub2e4:<\/p>\n<pre><code>\n5 7\n1 2 3\n1 3 4\n2 3 2\n2 4 6\n3 4 1\n3 5 5\n4 5 2\n<\/code><\/pre>\n<p>\ucd9c\ub825 \uacb0\uacfc:<\/p>\n<pre><code>\n6\n<\/code><\/pre>\n<h2>Kruskal \uc54c\uace0\ub9ac\uc998\uc744 \ud1b5\ud55c \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac \uad6c\ud558\uae30<\/h2>\n<p>Prim \uc54c\uace0\ub9ac\uc998\uc5d0 \uc774\uc5b4, Kruskal \uc54c\uace0\ub9ac\uc998\uc744 \uc0ac\uc6a9\ud558\uc5ec \ub3d9\uc77c\ud55c \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. Kruskal \uc54c\uace0\ub9ac\uc998\uc740 \uac04\uc120\uc744 \uae30\uc900\uc73c\ub85c \ub3d9\uc791\ud558\uba70, \ubaa8\ub4e0 \uac04\uc120\uc744 \uac00\uc911\uce58 \uae30\uc900\uc73c\ub85c \uc815\ub82c\ud55c \ud6c4 \uc791\uc740 \uac83\ubd80\ud130 \ucd94\uac00\ud558\ub294 \ubc29\uc2dd\uc785\ub2c8\ub2e4.<\/p>\n<h3>1. Kruskal \uc54c\uace0\ub9ac\uc998 \uac1c\uc694<\/h3>\n<p>Kruskal \uc54c\uace0\ub9ac\uc998\uc740 \ub2e4\uc74c\uc758 \ub2e8\uacc4\ub85c \uc774\ub8e8\uc5b4\uc9d1\ub2c8\ub2e4:<\/p>\n<ol>\n<li>\uac04\uc120\uc744 \uac00\uc911\uce58 \uae30\uc900\uc73c\ub85c \uc815\ub82c\ud569\ub2c8\ub2e4.<\/li>\n<li>\uac00\uc7a5 \uc791\uc740 \uac04\uc120\uc744 \uc120\ud0dd\ud558\uc5ec \uc0ac\uc774\ud074\uc774 \uc0dd\uae30\uc9c0 \uc54a\ub294 \uacbd\uc6b0 MST\uc5d0 \ucd94\uac00\ud569\ub2c8\ub2e4.<\/li>\n<li>\ubaa8\ub4e0 \uac04\uc120\uc744 \ucc98\ub9ac\ud560 \ub54c\uae4c\uc9c0 \ubc18\ubcf5\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n<h3>2. C++\ub85c Kruskal \uc54c\uace0\ub9ac\uc998 \uad6c\ud604\ud558\uae30<\/h3>\n<p>\uc774\uc81c Kruskal \uc54c\uace0\ub9ac\uc998\uc744 C++\ub85c \uad6c\ud604\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n<pre><code>\n#include <iostream>\n#include <vector>\n#include <algorithm>\nusing namespace std;\n\nstruct Edge {\n    int u, v, weight;\n};\n\nbool compare(Edge a, Edge b) {\n    return a.weight &lt; b.weight;\n}\n\nint find(int parent[], int u) {\n    if (parent[u] != u) {\n        parent[u] = find(parent, parent[u]); \/\/ \uacbd\ub85c \uc555\ucd95\n    }\n    return parent[u];\n}\n\nvoid unionSet(int parent[], int rank[], int u, int v) {\n    int root_u = find(parent, u);\n    int root_v = find(parent, v);\n    \n    if (root_u != root_v) {\n        if (rank[root_u] &gt; rank[root_v]) {\n            parent[root_v] = root_u;\n        } else if (rank[root_u] &lt; rank[root_v]) {\n            parent[root_u] = root_v;\n        } else {\n            parent[root_v] = root_u;\n            rank[root_u]++;\n        }\n    }\n}\n\nint kruskal(int V, vector<edge>&amp; edges) {\n    sort(edges.begin(), edges.end(), compare);\n    int parent[V], rank[V];\n    for (int i = 0; i &lt; V; i++) {\n        parent[i] = i;\n        rank[i] = 0;\n    }\n\n    int totalWeight = 0; \/\/ MST\uc758 \ucd1d \uac00\uc911\uce58\n    for (Edge edge : edges) {\n        int u = edge.u, v = edge.v;\n        \n        \/\/ \uc0ac\uc774\ud074\uc774 \ubc1c\uc0dd\ud558\uc9c0 \uc54a\ub294 \uacbd\uc6b0 MST\uc5d0 \ucd94\uac00\n        if (find(parent, u) != find(parent, v)) {\n            unionSet(parent, rank, u, v);\n            totalWeight += edge.weight; \/\/ \uac00\uc911\uce58 \ucd94\uac00\n        }\n    }\n    \n    return totalWeight;\n}\n\nint main() {\n    int V, E;\n    cin &gt;&gt; V &gt;&gt; E;\n    vector<edge> edges(E);\n\n    for (int i = 0; i &lt; E; i++) {\n        cin &gt;&gt; edges[i].u &gt;&gt; edges[i].v &gt;&gt; edges[i].weight;\n        edges[i].u--; \/\/ 0-indexed\n        edges[i].v--; \/\/ 0-indexed\n    }\n\n    cout &lt;&lt; kruskal(V, edges) &lt;&lt; endl; \/\/ MST\uc758 \ucd1d \uac00\uc911\uce58 \ucd9c\ub825\n    return 0;\n}\n<\/edge><\/edge><\/algorithm><\/vector><\/iostream><\/code><\/pre>\n<h4>3. \ucf54\ub4dc \uc124\uba85<\/h4>\n<p>\uc704 \ucf54\ub4dc\uc758 \uc124\uba85\uc740 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n<ul>\n<li>\uac04\uc120\uc744 \uc800\uc7a5\ud558\ub294 \uad6c\uc870\uccb4 <code>Edge<\/code>\ub97c \uc815\uc758\ud569\ub2c8\ub2e4.<\/li>\n<li>\uac04\uc120\uc744 \uac00\uc911\uce58 \uae30\uc900\uc73c\ub85c \uc815\ub82c\ud569\ub2c8\ub2e4.<\/li>\n<li>\uc720\ub2c8\uc628-\ud30c\uc778\ub4dc(Union-Find) \uc790\ub8cc\uad6c\uc870\ub97c \uc774\uc6a9\ud574 \uc0ac\uc774\ud074\uc744 \uccb4\ud06c\ud558\uace0, \uc0ac\uc774\ud074\uc774 \ubc1c\uc0dd\ud558\uc9c0 \uc54a\uc73c\uba74 \uac04\uc120\uc744 MST\uc5d0 \ucd94\uac00\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n<h4>4. \uc2e4\ud589 \uc608\uc2dc<\/h4>\n<p>\uc785\ub825 \ub370\uc774\ud130\ub97c \uc2e4\ud589\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc740 \uacb0\uacfc\uac00 \ub098\uc635\ub2c8\ub2e4:<\/p>\n<pre><code>\n5 7\n1 2 3\n1 3 4\n2 3 2\n2 4 6\n3 4 1\n3 5 5\n4 5 2\n<\/code><\/pre>\n<p>\ucd9c\ub825 \uacb0\uacfc:<\/p>\n<pre><code>\n6\n<\/code><\/pre>\n<h2>\uacb0\ub860<\/h2>\n<p>\uc774\ubc88 \uc2dc\uac04\uc5d0\ub294 \ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac \ubb38\uc81c\ub97c Prim \uc54c\uace0\ub9ac\uc998\uacfc Kruskal \uc54c\uace0\ub9ac\uc998\uc744 \ud1b5\ud574 \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \ubc30\uc6b0\uc558\uc2b5\ub2c8\ub2e4. \uac01 \uc54c\uace0\ub9ac\uc998\uc758 \ud2b9\uc9d5\uacfc \uc2e4\uc81c \uad6c\ud604 \ubc29\uc2dd\uc744 \uc774\ud574\ud558\ub294 \uac83\uc774 \uc911\uc694\ud558\uba70, \ub2e4\uc591\ud55c \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574 \uc774\ub7ec\ud55c \uc54c\uace0\ub9ac\uc998\uc744 \uc219\uc9c0\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\n<p>\ucd5c\uc18c \uc2e0\uc7a5 \ud2b8\ub9ac \ubb38\uc81c\ub294 \uadf8\ub798\ud504 \uc774\ub860\uc758 \uae30\ubcf8 \uac1c\ub150 \uc911 \ud558\ub098\uc774\uba70, \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\uc5d0\uc11c\ub3c4 \uc790\uc8fc \ub4f1\uc7a5\ud569\ub2c8\ub2e4. \uc704\uc758 \uad6c\ud604\uc744 \ud65c\uc6a9\ud558\uc5ec \ub2e4\uc591\ud55c \uadf8\ub798\ud504 \ubb38\uc81c\ub97c \ud6a8\uc728\uc801\uc73c\ub85c \ud574\uacb0\ud560 \uc218 \uc788\ub3c4\ub85d \uc5f0\uc2b5\ud558\uc2dc\uae30 \ubc14\ub78d\ub2c8\ub2e4.<\/p>\n<p>\ubdf0\uc5b4 \uc5ec\ub7ec\ubd84\uaed8\uc11c\ub3c4 \uc774 \uac15\uc88c\uac00 \ub3c4\uc6c0\uc774 \ub418\uc5c8\uae30\ub97c \ubc14\ub77c\uba70, \ucd94\uac00\uc801\uc778 \uc9c8\ubb38\uc774 \uc788\uc73c\uba74 \ub313\uae00\ub85c \ub0a8\uaca8\uc8fc\uc138\uc694. \ub2e4\uc74c \ud3ec\uc2a4\ud2b8\uc5d0\ub294 \ub610 \ub2e4\ub978 \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ub97c \ub2e4\ub8f0 \uc608\uc815\uc785\ub2c8\ub2e4. \uac10\uc0ac\ud569\ub2c8\ub2e4!<\/p>\n<p><\/body><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc548\ub155\ud558\uc138\uc694! \uc774\ubc88 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