\uc548\ub155\ud558\uc138\uc694! \uc774\ubc88 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 \ucd5c\uc18c \ube44\uc6a9 \uad6c\ud558\uae30<\/strong>\ub77c\ub294 \uc8fc\uc81c\ub85c C++ \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ub97c \ub2e4\ub904\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub294 \uc5ec\ub7ec \uc0c1\ud669\uc5d0\uc11c \ucd5c\uc801\uc758 \ud574\uacb0\ucc45\uc744 \ucc3e\ub294 \ub370 \uc720\uc6a9\ud558\uac8c \uc4f0\uc774\ub294 \uc54c\uace0\ub9ac\uc998 \uac1c\ub150\ub4e4\uc744 \uc0b4\ud3b4\ubcf4\ub294 \uc88b\uc740 \uae30\ud68c\uac00 \ub420 \uac83\uc785\ub2c8\ub2e4. \uc774 \uae00\uc744 \ud1b5\ud574 \uc6b0\ub9ac\ub294 \ubb38\uc81c\ubd84\uc11d, \uc54c\uace0\ub9ac\uc998 \uc120\ud0dd, \ucf54\ub4dc \uad6c\ud604, \ud14c\uc2a4\ud2b8, \uadf8\ub9ac\uace0 \ucd5c\uc801\ud654 \ubc29\ubc95\uae4c\uc9c0 \uc0c1\uc138\ud788 \uc54c\uc544\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n \uc6b0\ub9ac\uc5d0\uac8c\ub294 \uc5ec\ub7ec \uac1c\uc758 \ub3c4\uc2dc\uc640 \uc774\ub4e4 \uc0ac\uc774\uc758 \ub3c4\ub85c\uac00 \uc788\uc2b5\ub2c8\ub2e4. \uac01 \ub3c4\ub85c\ub294 \ud2b9\uc815 \ube44\uc6a9\uc744 \uac00\uc9c0\uace0 \uc788\uc2b5\ub2c8\ub2e4. \uc8fc\uc5b4\uc9c4 \uc5ec\ub7ec \ub3c4\uc2dc\ub4e4 \uac04\uc5d0 \uc774\ub3d9\ud560 \ub54c, \uc6b0\ub9ac\uc758 \ubaa9\ud45c\ub294 \uc2dc\uc791 \ub3c4\uc2dc\uc5d0\uc11c \ubaa9\ud45c \ub3c4\uc2dc\uae4c\uc9c0\uc758 \ucd5c\uc18c \uc774\ub3d9 \ube44\uc6a9\uc744 \uad6c\ud558\ub294 \uac83\uc785\ub2c8\ub2e4. \uc774\ub97c \ub2e4\uc775\uc2a4\ud2b8\ub77c \uc54c\uace0\ub9ac\uc998\uc744 \ud1b5\ud574 \ud574\uacb0\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n \ub2e4\uc74c\uc740 \ubb38\uc81c\uc758 \uc218\ud559\uc801 \uc815\uc758\uc785\ub2c8\ub2e4:<\/p>\n \ubaa9\ud45c \ub3c4\uc2dc\uae4c\uc9c0 \uac00\ub294 \ucd5c\uc18c \ube44\uc6a9\uc744 \ucd9c\ub825\ud569\ub2c8\ub2e4. \ub9cc\uc57d \ub3c4\ucc29\ud560 \uc218 \uc5c6\ub2e4\uba74 \uc774 \ubb38\uc81c\ub294 \uac00\uc911\uce58 \uadf8\ub798\ud504\uc5d0\uc11c \ucd5c\ub2e8 \uacbd\ub85c\ub97c \ucc3e\ub294 \ubb38\uc81c\ub85c, \ub300\ud45c\uc801\uc778 \uc54c\uace0\ub9ac\uc998\uc778 \ub2e4\uc775\uc2a4\ud2b8\ub77c \uc54c\uace0\ub9ac\uc998<\/strong>\uc744 \uc0ac\uc6a9\ud558\uc5ec \ud574\uacb0\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \ub2e4\uc775\uc2a4\ud2b8\ub77c \uc54c\uace0\ub9ac\uc998\uc740 \ub2e4\uc775\uc2a4\ud2b8\ub77c \uc54c\uace0\ub9ac\uc998\uc758 \uae30\ubcf8 \uc544\uc774\ub514\uc5b4\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n \uc8fc\uc5b4\uc9c4 \uc785\ub825\uc744 \ud1b5\ud574 \uadf8\ub798\ud504\ub97c \uad6c\uc131\ud558\uace0, \uac01 \ub3c4\uc2dc\uc5d0 \ub300\ud55c \ube44\uc6a9 \uc815\ubcf4\ub97c \uc800\uc7a5\ud560 \ub370\uc774\ud130 \uad6c\uc870\uac00 \ud544\uc694\ud569\ub2c8\ub2e4. \uc6b0\ub9ac\ub294 \uc778\uc811 \ub9ac\uc2a4\ud2b8\ub97c \uc0ac\uc6a9\ud560 \uac83\uc785\ub2c8\ub2e4.<\/p>\n \uc704 \ucf54\ub4dc\ub97c \ud1b5\ud574 \uc785\ub825\uc744 \ud14c\uc2a4\ud2b8\ud569\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \ub2e4\uc74c \uc785\ub825\uc744 \ud1b5\ud574 \ud14c\uc2a4\ud2b8\ub97c \ud574 \ubcfc \uc218 \uc788\uc2b5\ub2c8\ub2e4:<\/p>\n \uc704 \uc785\ub825\uc740 \ub3c4\uc2dc 5\uac1c\uc640 6\uac1c\uc758 \ub3c4\ub85c\uac00 \uc788\ub294 \uacbd\uc6b0\ub85c, \uc2dc\uc791 \ub3c4\uc2dc\uac00 1\ubc88, \ubaa9\ud45c \ub3c4\uc2dc\uac00 5\ubc88\uc785\ub2c8\ub2e4. \uc774 \uacbd\uc6b0 \uc54c\uace0\ub9ac\uc998\uc740 \ucd5c\uc18c \ube44\uc6a9\uc73c\ub85c 1\ubc88 \ub3c4\uc2dc\uc5d0\uc11c 5\ubc88 \ub3c4\uc2dc\uae4c\uc9c0 \uac00\ub294 \ubc29\ubc95\uc744 \ucd9c\ub825\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\n \ub2e4\uc775\uc2a4\ud2b8\ub77c \uc54c\uace0\ub9ac\uc998\uc740 \uc77c\ubc18\uc801\uc73c\ub85c Priority Queue\ub97c \uc0ac\uc6a9\ud558\uc5ec \uad6c\ud604\ud558\uc9c0\ub9cc, \uc81c\ud55c\uc774 \uc788\ub294 \uacbd\uc6b0\uc5d0\ub294 Fibonacci Heap \ub4f1\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uadf8\ub7ec\ub098 \uc774 \uae00\uc5d0\uc11c\ub294 \uc77c\ubc18\uc801\uc778 Priority Queue\ub97c \uc0ac\uc6a9\ud558\uc5ec \uac04\ub2e8\ud558\uace0 \ud6a8\uc728\uc801\uc778 \uad6c\ud604\uc744 \ubcf4\uc5ec\uc8fc\uc5c8\uc2b5\ub2c8\ub2e4.<\/p>\n \uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 C++\ub85c \ucd5c\uc18c \ube44\uc6a9 \uad6c\ud558\uae30 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uc558\uc2b5\ub2c8\ub2e4. \ub2e4\uc775\uc2a4\ud2b8\ub77c \uc54c\uace0\ub9ac\uc998\uc758 \uc6d0\ub9ac\ub97c \uc774\ud574\ud558\uace0 \uc774\ub97c \uc2e4\uc81c \ubb38\uc81c\uc5d0 \uc5b4\ub5bb\uac8c \uc801\uc6a9\ud558\ub294\uc9c0 \ub2e4\ub918\uc2b5\ub2c8\ub2e4. \uc774\ub294 \ucf54\ub529 \ud14c\uc2a4\ud2b8\ub97c \ub300\ube44\ud558\ub294 \ub370 \ub3c4\uc6c0\uc774 \ub420 \uac83\uc785\ub2c8\ub2e4.<\/p>\n \uacc4\uc18d\ud574\uc11c \ub354 \ub9ce\uc740 \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc744 \ubc30\uc6b0\uace0 \uc5f0\uc2b5\ud558\uc2dc\uae38 \ubc14\ub78d\ub2c8\ub2e4. \uac10\uc0ac\ud569\ub2c8\ub2e4!<\/p>\n <\/body><\/p>\n","protected":false},"excerpt":{"rendered":"\ubb38\uc81c \uc124\uba85<\/h2>\n
\ubb38\uc81c \uc815\uc758<\/h3>\n
\n
n<\/code> (1 \uc774\uc0c1 10,000 \uc774\ud558)<\/li>\nm<\/code> (1 \uc774\uc0c1 100,000 \uc774\ud558)<\/li>\nu<\/code>, v<\/code>, cost<\/code>\uc758 \ud615\ud0dc\ub85c \uc785\ub825\ub429\ub2c8\ub2e4. \uc774\ub294 \ub3c4\uc2dc u<\/code>\uc5d0\uc11c \ub3c4\uc2dc v<\/code>\ub85c \uac00\ub294 \ube44\uc6a9\uc774 cost<\/code>\ub77c\ub294 \uac83\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4.<\/li>\nstart<\/code>\uc640 \ubaa9\ud45c \ub3c4\uc2dc end<\/code>\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4.<\/li>\n<\/ul>\n\uc785\ub825<\/h3>\n
\n n m\n u1 v1 cost1\n u2 v2 cost2\n ...\n um vm costm\n start end\n <\/code><\/pre>\n\ucd9c\ub825<\/h3>\n
-1<\/code>\uc744 \ucd9c\ub825\ud569\ub2c8\ub2e4.<\/p>\n\uc54c\uace0\ub9ac\uc998 \uc120\ud0dd<\/h2>\n
O((n + m) log n)<\/code>\uc758 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\ub97c \uac00\uc9c0\ubbc0\ub85c, \ucd5c\ub300 \uc785\ub825 \uc870\uac74\uc5d0\uc11c\ub3c4 \ud6a8\uc728\uc801\uc73c\ub85c \ub3d9\uc791\ud569\ub2c8\ub2e4.<\/p>\n\ub2e4\uc775\uc2a4\ud2b8\ub77c \uc54c\uace0\ub9ac\uc998 \uac1c\uc694<\/h3>\n
\n
\ubb38\uc81c \ud574\uacb0 \uacfc\uc815<\/h2>\n
1\ub2e8\uacc4: \ubb38\uc81c \ubd84\uc11d<\/h3>\n
2\ub2e8\uacc4: \ucf54\ub4dc \uad6c\ud604<\/h3>\n
\n#include <iostream>\n#include <vector>\n#include <queue>\n#include <utility>\n#include <limits>\n\nusing namespace std;\n\nconst int INF = numeric_limits<int>::max();\n\nvector<pair<int, int>> graph[10001];\n\nvoid dijkstra(int start, int n) {\n vector<int> cost(n + 1, INF);\n priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;\n\n cost[start] = 0;\n pq.push(make_pair(0, start));\n\n while (!pq.empty()) {\n int currentCost = pq.top().first;\n int currentNode = pq.top().second;\n pq.pop();\n\n if (currentCost > cost[currentNode]) continue;\n\n for (auto &edge : graph[currentNode]) {\n int nextNode = edge.first;\n int nextCost = edge.second;\n\n if (cost[currentNode] + nextCost < cost[nextNode]) {\n cost[nextNode] = cost[currentNode] + nextCost;\n pq.push(make_pair(cost[nextNode], nextNode));\n }\n }\n }\n\n for (int i = 1; i <= n; ++i) {\n if (cost[i] == INF) {\n cout << -1 << endl; \/\/ \ub3c4\ub2ec\ud560 \uc218 \uc5c6\ub294 \uacbd\uc6b0\n } else {\n cout << cost[i] << endl;\n }\n }\n}\n\nint main() {\n int n, m;\n cin >> n >> m;\n\n for (int i = 0; i < m; ++i) {\n int u, v, cost;\n cin >> u >> v >> cost;\n graph[u].push_back(make_pair(v, cost));\n graph[v].push_back(make_pair(u, cost)); \/\/ \uc591\ubc29\ud5a5 \ub3c4\ub85c \uac00\uc815\n }\n\n int start, end;\n cin >> start >> end;\n\n dijkstra(start, n);\n \n return 0;\n}\n <\/code><\/pre>\n3\ub2e8\uacc4: \ucf54\ub4dc \ud14c\uc2a4\ud2b8<\/h3>\n
\n5 6\n1 2 1\n1 3 4\n2 3 2\n2 4 5\n3 4 1\n4 5 3\n1 5\n <\/code><\/pre>\n4\ub2e8\uacc4: \ucd5c\uc801\ud654<\/h3>\n
\uacb0\ub860<\/h2>\n