{"id":26880,"date":"2024-10-27T11:53:25","date_gmt":"2024-10-27T11:53:25","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=26880"},"modified":"2024-11-26T07:27:20","modified_gmt":"2024-11-26T07:27:20","slug":"%ec%9e%90%eb%b0%94-%ec%bd%94%eb%94%a9%ed%85%8c%ec%8a%a4%ed%8a%b8-%ea%b0%95%ec%a2%8c-%ec%9e%84%ea%b3%84-%ea%b2%bd%eb%a1%9c-%ea%b5%ac%ed%95%98%ea%b8%b0","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/26880\/","title":{"rendered":"\uc790\ubc14 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uc784\uacc4 \uacbd\ub85c \uad6c\ud558\uae30"},"content":{"rendered":"<div class=\"post\">\n<h2>\uc11c\ub860<\/h2>\n<p>\n        \uc18c\ud504\ud2b8\uc6e8\uc5b4 \uac1c\ubc1c\uacfc \uad00\ub828\ub41c \ub9ce\uc740 \uae30\uc5c5\uc5d0\uc11c \ucf54\ub529 \ud14c\uc2a4\ud2b8\ub294 \ud544\uc218\uc801\uc778 \ucc44\uc6a9 \uacfc\uc815\uc73c\ub85c \uc790\ub9ac \uc7a1\uace0 \uc788\uc2b5\ub2c8\ub2e4.<br \/>\n        \ud2b9\ud788, \uc790\ubc14\ub294 \ub9ce\uc740 \uae30\uc5c5\uc5d0\uc11c \uc120\ud638\ub418\ub294 \ud504\ub85c\uadf8\ub798\ubc0d \uc5b8\uc5b4 \uc911 \ud558\ub098\uc785\ub2c8\ub2e4.<br \/>\n        \uc774\ubc88 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 \uc790\ubc14\ub97c \uc0ac\uc6a9\ud558\uc5ec &#8216;\uc784\uacc4 \uacbd\ub85c \uad6c\ud558\uae30&#8217; \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<br \/>\n        \uc784\uacc4 \uacbd\ub85c\ub294 \uc720 directed graph\uc5d0\uc11c \uac00\uc7a5 \uae34 \uacbd\ub85c\ub97c \ucc3e\ub294 \uac83\uc744 \uc758\ubbf8\ud558\uba70, \ud2b9\ud788 \ud504\ub85c\uc81d\ud2b8 \uad00\ub9ac \ub3c4\uad6c\uc5d0\uc11c \uc77c\uc815 \uacc4\ud68d\uc744 \uc138\uc6b0\ub294 \ub370 \uc911\uc694\ud55c \uc5ed\ud560\uc744 \ud569\ub2c8\ub2e4.\n    <\/p>\n<h2>\ubb38\uc81c \uc124\uba85<\/h2>\n<p>\n        \uc8fc\uc5b4\uc9c4 \ubc29\ud5a5 \uadf8\ub798\ud504\uc5d0\uc11c \uac01 \ub178\ub4dc\ub294 \uc791\uc5c5\uc744 \uc758\ubbf8\ud558\uace0, \uac01 \uac04\uc120\uc740 \uc791\uc5c5 \uac04\uc758 \uc758\uc874\uc131\uc744 \ub098\ud0c0\ub0c5\ub2c8\ub2e4.<br \/>\n        \uc5ec\uae30\uc11c \ubc29\ud5a5 \uadf8\ub798\ud504\uc758 \ub178\ub4dc\ub97c \uc2dc\uc791\uc73c\ub85c \ud558\uc5ec \ucd5c\uc885 \ub178\ub4dc\uae4c\uc9c0 \ub3c4\ub2ec\ud558\ub294 \uac00\uc7a5 \uae34 \uacbd\ub85c\ub97c \ucc3e\ub294 \uac83\uc774 \uc6b0\ub9ac\uc758 \ubaa9\ud45c\uc785\ub2c8\ub2e4.<br \/>\n        \uc608\ub97c \ub4e4\uc5b4, \uac01 \uc791\uc5c5\uc758 \uc218\ud589 \uc2dc\uac04\ub3c4 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ud504\ub85c\uc81d\ud2b8 \uc644\ub8cc\uae4c\uc9c0 \uac78\ub9ac\ub294 \ucd5c\ub300 \uc2dc\uac04\uc744 \uad6c\ud558\ub77c\ub294 \uac83\uc774 \ubb38\uc81c\uc758 \uc694\uc9c0\uc785\ub2c8\ub2e4.\n    <\/p>\n<h3>\uc785\ub825 \ud615\uc2dd<\/h3>\n<ul>\n<li>\uc815\uc218 N: \uc791\uc5c5\uc758 \uac1c\uc218 (1 \u2264 N \u2264 10,000)<\/li>\n<li>\uc815\uc218 M: \uc758\uc874\uc131\uc758 \uac1c\uc218 (1 \u2264 M \u2264 100,000)<\/li>\n<li>\uac01 \uc791\uc5c5\uc758 \uc218\ud589 \uc2dc\uac04: \ubc30\uc5f4\uc758 \ud615\ud0dc\ub85c \uc8fc\uc5b4\uc9d0<\/li>\n<li>\uc758\uc874\uc131 \uc815\ubcf4: \ubc30\uc5f4\uc758 \ud615\ud0dc\ub85c \uc8fc\uc5b4\uc9d0 (a \u2192 b: \uc791\uc5c5 a\ub294 \uc791\uc5c5 b\uac00 \uc644\ub8cc\ub41c \ud6c4\uc5d0 \uc218\ud589 \uac00\ub2a5)<\/li>\n<\/ul>\n<h3>\ucd9c\ub825 \ud615\uc2dd<\/h3>\n<p>\n        \ucd5c\uc885 \uc791\uc5c5\uc744 \uc644\ub8cc\ud558\ub294 \ub370 \uac78\ub9ac\ub294 \ucd5c\ub300 \uc2dc\uac04\uc744 \ucd9c\ub825\ud569\ub2c8\ub2e4.\n    <\/p>\n<h2>\uc608\uc81c<\/h2>\n<pre>\n        **\uc785\ub825**:\n        5 4\n        [2, 3, 4, 1, 5]\n        [\n            (0, 1),\n            (1, 2),\n            (1, 3),\n            (3, 4)\n        ]\n        \n        **\ucd9c\ub825**:\n        10\n    <\/pre>\n<p>\n        \uc774 \uc608\uc81c\uc5d0\uc11c\ub294 \ucd5c\ub300 \uacbd\ub85c\uac00 2(0\uc5d0\uc11c 1\ub85c) + 3(1\uc5d0\uc11c 2\ub85c) + 5(3\uc5d0\uc11c 4\ub85c)\ub85c None\uc758 \uc5f0\uc18d\uc131\uc744 \uc704\ud55c \uac83\uc744 \uae30\ubc18\uc73c\ub85c \ud55c\ub2e4\uba74 \ucd5c\uc885 \uc791\uc5c5\uc744 \uc644\ub8cc\ud558\ub294 \ub370 10\uc758 \uc2dc\uac04\uc774 \uc18c\uc694\ub429\ub2c8\ub2e4.\n    <\/p>\n<h2>\ubb38\uc81c \uc811\uadfc \ubc29\ubc95<\/h2>\n<p>\n        &#8216;\uc784\uacc4 \uacbd\ub85c \uad6c\ud558\uae30&#8217; \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574\uc11c\ub294 \uadf8\ub798\ud504 \ud0d0\uc0c9 \uc54c\uace0\ub9ac\uc998\uc744 \ud65c\uc6a9\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<br \/>\n        \uc77c\ubc18\uc801\uc73c\ub85c Topological Sort\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc791\uc5c5\uc758 \uc21c\uc11c\ub97c \uc815\ud55c \ud6c4, \uac01 \ub178\ub4dc\uc5d0 \ub300\ud574 \ub204\uc801 \uc2dc\uac04\uc744 \uacc4\uc0b0\ud558\uc5ec \ucd5c\uc885 \uc2dc\uac04\uc744 \uacb0\uc815\ud558\uac8c \ub429\ub2c8\ub2e4.<br \/>\n        \uc804\uccb4\uc801\uc778 \ud480\uc774\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ub2e8\uacc4\ub85c \uc9c4\ud589\ub429\ub2c8\ub2e4:\n    <\/p>\n<ol>\n<li>\uadf8\ub798\ud504 \uc0dd\uc131: \uac01 \uc791\uc5c5\uacfc \uadf8 \uc791\uc5c5\uc5d0 \uc758\uc874\uc801\uc778 \uc791\uc5c5\uc744 \uc5f0\uacb0\ud558\ub294 \ubc29\ud5a5 \uadf8\ub798\ud504\ub97c \uc0dd\uc131\ud569\ub2c8\ub2e4.<\/li>\n<li>\ud0d1\uc624\ub85c\uc9c0 \uc815\ub82c: \uc758\uc874\uc131\uc774 \uc788\ub294 \uc791\uc5c5\uc744 \uc815\ub82c\ud558\uc5ec \uc21c\uc11c\ub300\ub85c \uc791\uc5c5\uc744 \uc218\ud589\ud560 \uc218 \uc788\ub3c4\ub85d \ud569\ub2c8\ub2e4.<\/li>\n<li>\uc2dc\uac04 \uacc4\uc0b0: \uac01 \uc791\uc5c5\uc744 \uc218\ud589\ud558\ub294 \ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\uc744 \ub204\uc801\ud558\uc5ec \ucd5c\uc885 \ubaa9\ud45c \uc791\uc5c5\uc758 \uc2dc\uac04\uc744 \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n<h3>1\ub2e8\uacc4: \uadf8\ub798\ud504 \uc0dd\uc131<\/h3>\n<p>\n        \uc785\ub825\ub41c \uc758\uc874\uc131 \uc815\ubcf4\ub97c \uc0ac\uc6a9\ud558\uc5ec \uadf8\ub798\ud504\ub97c \uc0dd\uc131\ud569\ub2c8\ub2e4.<br \/>\n        \uac01 \uc791\uc5c5\uc744 \uc815\uc810\uc73c\ub85c \ubcf4\uace0, \uc758\uc874\uc131\uc5d0 \ub300\ud574 \uac04\uc120\uc73c\ub85c \uc5f0\uacb0\ud569\ub2c8\ub2e4.<br \/>\n        \uc790\ubc14\uc5d0\uc11c\ub294 ArrayList\ub97c \uc0ac\uc6a9\ud558\uc5ec \uadf8\ub798\ud504\ub97c \ud45c\ud604\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.\n    <\/p>\n<pre>\n        List<list<integer>&gt; graph = new ArrayList&lt;&gt;();\n        int[] indegree = new int[N];\n        int[] time = new int[N];\n\n        for (int i = 0; i &lt; N; i++) {\n            graph.add(new ArrayList&lt;&gt;());\n        }\n\n        \/\/ \uc758\uc874\uc131 \uc815\ubcf4\ub97c \uae30\ubc18\uc73c\ub85c \uadf8\ub798\ud504 \uad6c\uc131\n        \/\/ (a, b)\ub97c \ud1b5\ud574 a \u2192 b\ub85c \uac04\uc120 \ucd94\uac00\n        for (int[] dep : dependencies) {\n            graph.get(dep[0]).add(dep[1]);\n            indegree[dep[1]]++;\n            time[dep[0]] = taskTimes[dep[0]];\n        }\n    <\/list<integer><\/pre>\n<h3>2\ub2e8\uacc4: \ud0d1\uc624\ub85c\uc9c0 \uc815\ub82c<\/h3>\n<p>\n        \uadf8\ub798\ud504\uac00 \ub9cc\ub4e4\uc5b4\uc9c0\uba74, \ucc28\uc218(indegree)\uac00 0\uc778 \ub178\ub4dc\ubd80\ud130 \uc2dc\uc791\ud558\uc5ec \uc704\uc0c1 \uc815\ub82c\uc744 \ud1b5\ud574 \uc815\uc810\uc744 \ud0d0\uc0c9\ud569\ub2c8\ub2e4.<br \/>\n        \uc8fc\ub85c \ud050\ub97c \uc0ac\uc6a9\ud558\uc5ec \uad6c\ud604\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.\n    <\/p>\n<pre>\n        Queue<integer> queue = new LinkedList&lt;&gt;();\n        for (int i = 0; i &lt; N; i++) {\n            if (indegree[i] == 0) {\n                queue.offer(i);\n            }\n        }\n\n        int[] dp = new int[N]; \/\/ \uac01 \uc791\uc5c5 \uc644\ub8cc \uc2dc\uac04 \uc800\uc7a5\n        while (!queue.isEmpty()) {\n            int u = queue.poll();\n            dp[u] = Math.max(dp[u], time[u]);\n\n            for (int v : graph.get(u)) {\n                indegree[v]--;\n                dp[v] = Math.max(dp[v], dp[u] + time[v]);\n                if (indegree[v] == 0) {\n                    queue.offer(v);\n                }\n            }\n        }\n    <\/integer><\/pre>\n<h3>3\ub2e8\uacc4: \uc2dc\uac04 \uacc4\uc0b0<\/h3>\n<p>\n        \ub9c8\uc9c0\ub9c9 \uc791\uc5c5\uae4c\uc9c0 \ub3c4\ub2ec\ud588\uc744 \ub54c, dp \ubc30\uc5f4\uc758 \ucd5c\ub313\uac12\uc774 \ubc14\ub85c \ud504\ub85c\uc81d\ud2b8 \uc644\ub8cc\uc5d0 \uac78\ub9ac\ub294 \ucd5c\ub300 \uc2dc\uac04\uc744 \ub098\ud0c0\ub0c5\ub2c8\ub2e4.\n    <\/p>\n<pre>\n        int result = 0;\n        for (int t : dp) {\n            result = Math.max(result, t);\n        }\n        System.out.println(result);\n    <\/pre>\n<h2>\uc790\ubc14 \ucf54\ub4dc<\/h2>\n<pre>\n        import java.util.*;\n\n        public class CriticalPath {\n            public static void main(String[] args) {\n                \/\/ \uc785\ub825 \ucc98\ub9ac\n                Scanner sc = new Scanner(System.in);\n                int N = sc.nextInt();\n                int M = sc.nextInt();\n                int[] taskTimes = new int[N];\n                for (int i = 0; i &lt; N; i++) {\n                    taskTimes[i] = sc.nextInt();\n                }\n                List<list<integer>&gt; graph = new ArrayList&lt;&gt;();\n                int[] indegree = new int[N];\n\n                for (int i = 0; i &lt; N; i++) {\n                    graph.add(new ArrayList&lt;&gt;());\n                }\n\n                for (int i = 0; i &lt; M; i++) {\n                    int a = sc.nextInt();\n                    int b = sc.nextInt();\n                    graph.get(a).add(b);\n                    indegree[b]++;\n                }\n\n                \/\/ \uc704\uc0c1 \uc815\ub82c \ubc0f \uc2dc\uac04 \uacc4\uc0b0\n                Queue<integer> queue = new LinkedList&lt;&gt;();\n                for (int i = 0; i &lt; N; i++) {\n                    if (indegree[i] == 0) {\n                        queue.offer(i);\n                    }\n                }\n\n                int[] dp = new int[N];\n                while (!queue.isEmpty()) {\n                    int u = queue.poll();\n                    dp[u] = Math.max(dp[u], taskTimes[u]);\n\n                    for (int v : graph.get(u)) {\n                        indegree[v]--;\n                        dp[v] = Math.max(dp[v], dp[u] + taskTimes[v]);\n                        if (indegree[v] == 0) {\n                            queue.offer(v);\n                        }\n                    }\n                }\n\n                \/\/ \ucd5c\ub300 \uc2dc\uac04 \uacc4\uc0b0\n                int result = Arrays.stream(dp).max().getAsInt();\n                System.out.println(result);\n            }\n        }\n    <\/integer><\/list<integer><\/pre>\n<h2>\uacb0\ub860<\/h2>\n<p>\n        \uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 \uc790\ubc14\ub97c \uc774\uc6a9\ud55c \uc784\uacc4 \uacbd\ub85c \uad6c\ud558\uae30 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \uacfc\uc815\uc744 \ub2e4\ub918\uc2b5\ub2c8\ub2e4.<br \/>\n        \uadf8\ub798\ud504 \uc774\ub860\uc744 \ud65c\uc6a9\ud558\uc5ec \uac01 \uc791\uc5c5\uc758 \uc758\uc874\uc131\uc744 \ub098\ud0c0\ub0b4\uace0, \ucd5c\uc885 \uc791\uc5c5\uc758 \uc644\ub8cc \uc2dc\uac04\uc744 \uacc4\uc0b0\ud558\ub294 \ubc29\ubc95\uc744 \ubc30\uc6e0\uc2b5\ub2c8\ub2e4.<br \/>\n        \uc774\ucc98\ub7fc \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \uacfc\uc815\uc5d0\uc11c \ub2e8\uacc4\uc801\uc778 \uc811\uadfc\uc774 \uc911\uc694\ud558\uba70, \uc774\ub97c \ud1b5\ud574 \uc2e4\uc81c \ucf54\ub529 \ud14c\uc2a4\ud2b8\uc5d0\uc11c\ub3c4 \uc88b\uc740 \uc131\uacfc\ub97c \ub0bc \uc218 \uc788\uc2b5\ub2c8\ub2e4.<br \/>\n        \uc55e\uc73c\ub85c\ub3c4 \ub2e4\uc591\ud55c \uc54c\uace0\ub9ac\uc998\uc744 \ub2e4\ub8e8\ub294 \uae00\uc744 \uc9c0\uc18d\uc801\uc73c\ub85c \uc791\uc131\ud560 \uc608\uc815\uc774\ub2c8 \ub9ce\uc740 \uad00\uc2ec \ubd80\ud0c1\ub4dc\ub9bd\ub2c8\ub2e4.\n    <\/p>\n<h2>\ucc38\uace0 \uc790\ub8cc<\/h2>\n<ul>\n<li>\n<a href=\"https:\/\/en.wikipedia.org\/wiki\/Longest_path_problem\">Longest Path Problem (Wikipedia)<\/a>\n<\/li>\n<li>\n<a href=\"https:\/\/www.geeksforgeeks.org\/find-longest-path-directed-acyclic-graph\/\">Find Longest Path in a Directed Acyclic Graph (GeeksforGeeks)<\/a>\n<\/li>\n<li>\n<a href=\"https:\/\/www.coursera.org\/learn\/algorithms-part1\">Coursera Algorithms Course<\/a>\n<\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc11c\ub860 \uc18c\ud504\ud2b8\uc6e8\uc5b4 \uac1c\ubc1c\uacfc \uad00\ub828\ub41c \ub9ce\uc740 \uae30\uc5c5\uc5d0\uc11c \ucf54\ub529 \ud14c\uc2a4\ud2b8\ub294 \ud544\uc218\uc801\uc778 \ucc44\uc6a9 \uacfc\uc815\uc73c\ub85c \uc790\ub9ac \uc7a1\uace0 \uc788\uc2b5\ub2c8\ub2e4. \ud2b9\ud788, \uc790\ubc14\ub294 \ub9ce\uc740 \uae30\uc5c5\uc5d0\uc11c \uc120\ud638\ub418\ub294 \ud504\ub85c\uadf8\ub798\ubc0d \uc5b8\uc5b4 \uc911 \ud558\ub098\uc785\ub2c8\ub2e4. \uc774\ubc88 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 \uc790\ubc14\ub97c \uc0ac\uc6a9\ud558\uc5ec &#8216;\uc784\uacc4 \uacbd\ub85c \uad6c\ud558\uae30&#8217; \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc784\uacc4 \uacbd\ub85c\ub294 \uc720 directed graph\uc5d0\uc11c \uac00\uc7a5 \uae34 \uacbd\ub85c\ub97c \ucc3e\ub294 \uac83\uc744 \uc758\ubbf8\ud558\uba70, \ud2b9\ud788 \ud504\ub85c\uc81d\ud2b8 \uad00\ub9ac \ub3c4\uad6c\uc5d0\uc11c \uc77c\uc815 \uacc4\ud68d\uc744 \uc138\uc6b0\ub294 \ub370 &hellip; <a href=\"https:\/\/atmokpo.com\/w\/26880\/\" class=\"more-link\">\ub354 \ubcf4\uae30<span class=\"screen-reader-text\"> &#8220;\uc790\ubc14 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uc784\uacc4 \uacbd\ub85c 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property=\"og:title\" content=\"\uc790\ubc14 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uc784\uacc4 \uacbd\ub85c \uad6c\ud558\uae30 - \ub77c\uc774\ube0c\uc2a4\ub9c8\ud2b8\" \/>\n<meta property=\"og:description\" content=\"\uc11c\ub860 \uc18c\ud504\ud2b8\uc6e8\uc5b4 \uac1c\ubc1c\uacfc \uad00\ub828\ub41c \ub9ce\uc740 \uae30\uc5c5\uc5d0\uc11c \ucf54\ub529 \ud14c\uc2a4\ud2b8\ub294 \ud544\uc218\uc801\uc778 \ucc44\uc6a9 \uacfc\uc815\uc73c\ub85c \uc790\ub9ac \uc7a1\uace0 \uc788\uc2b5\ub2c8\ub2e4. \ud2b9\ud788, \uc790\ubc14\ub294 \ub9ce\uc740 \uae30\uc5c5\uc5d0\uc11c \uc120\ud638\ub418\ub294 \ud504\ub85c\uadf8\ub798\ubc0d \uc5b8\uc5b4 \uc911 \ud558\ub098\uc785\ub2c8\ub2e4. \uc774\ubc88 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 \uc790\ubc14\ub97c \uc0ac\uc6a9\ud558\uc5ec &#8216;\uc784\uacc4 \uacbd\ub85c \uad6c\ud558\uae30&#8217; \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc784\uacc4 \uacbd\ub85c\ub294 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