\uc548\ub155\ud558\uc138\uc694! \uc774\ubc88 \uae00\uc5d0\uc11c\ub294 \ucf54\ud2c0\ub9b0\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc(Union-Find) \uc54c\uace0\ub9ac\uc998\uc5d0 \ub300\ud574 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc\ub294 \uc9d1\ud569 \ub370\uc774\ud130 \uad6c\uc870\ub97c \ud6a8\uc728\uc801\uc73c\ub85c \uad00\ub9ac\ud558\ub294 \ubc29\ubc95\uc73c\ub85c, \uc8fc\ub85c \uc5f0\uacb0\ub41c \ucef4\ud3ec\ub10c\ud2b8\ub97c \ucc3e\uace0 \uacb0\ud569\ud558\ub294 \ub370 \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \uc774 \uc54c\uace0\ub9ac\uc998\uc740 \uadf8\ub798\ud504 \uc774\ub860\uacfc \uad00\ub828\ub41c \ubb38\uc81c\uc5d0\uc11c \uc885\uc885 \uc0ac\uc6a9\ub418\ub294 \uc911\uc694\ud55c \uac1c\ub150\uc785\ub2c8\ub2e4.<\/p>\n
\ub2e4\uc74c\uc740 \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc\ub97c \uc774\uc6a9\ud558\uc5ec \ud574\uacb0\ud560 \uc218 \uc788\ub294 \ubb38\uc81c\uc785\ub2c8\ub2e4. \uc5f0\uacb0\ub41c \ucef4\ud3ec\ub10c\ud2b8\uc758 \uac1c\uc218 \uc138\uae30<\/strong> \ubb38\uc81c\ub97c \ud1b5\ud574 \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc\uc758 \uc911\uc694\uc131\uc744 \uc774\ud574\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n \ub2f9\uc2e0\uc740 N\uac1c\uc758 \ub178\ub4dc\uc640 M\uac1c\uc758 \uac04\uc120\uc774 \uc788\ub294 \uadf8\ub798\ud504\ub97c \uac00\uc9c0\uace0 \uc788\uc2b5\ub2c8\ub2e4. \uac01 \ub178\ub4dc\ub294 1\ubd80\ud130 N\uae4c\uc9c0 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\uc2b5\ub2c8\ub2e4. \ub2e4\uc74c\uacfc \uac19\uc774 M\uac1c\uc758 \uac04\uc120\uc774 \uc8fc\uc5b4\uc9c8 \ub54c, \uc5f0\uacb0\ub41c \ucef4\ud3ec\ub10c\ud2b8\uc758 \uac1c\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc138\uc694.<\/p>\n \uc5ec\uae30\uc11c \uc5f0\uacb0\ub41c \ucef4\ud3ec\ub10c\ud2b8\uc758 \uac1c\uc218\ub97c \ud55c \uc904\uc5d0 \ucd9c\ub825\ud569\ub2c8\ub2e4.<\/p>\n \uc608\uc81c\uc5d0\uc11c \uc8fc\uc5b4\uc9c4 \uadf8\ub798\ud504\ub97c \uc0b4\ud3b4\ubcf4\uba74, \ub178\ub4dc 1, 2, 3\uc774 \ud558\ub098\uc758 \uc5f0\uacb0\ub41c \ucef4\ud3ec\ub10c\ud2b8\ub97c \uc774\ub8e8\uace0, \ub178\ub4dc 4, 5\uac00 \ub610 \ud558\ub098\uc758 \uc5f0\uacb0\ub41c \ucef4\ud3ec\ub10c\ud2b8\ub97c \uc774\ub8e8\ubbc0\ub85c \ucd1d 2\uac1c\uc758 \uc5f0\uacb0\ub41c \ucef4\ud3ec\ub10c\ud2b8\uac00 \uc874\uc7ac\ud569\ub2c8\ub2e4.<\/p>\n \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc(Union-Find) \ub610\ub294 \ubd84\ub9ac \uc9d1\ud569(Disjoint Set Union) \uc790\ub8cc \uad6c\uc870\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ub450 \uac00\uc9c0 \uc8fc\uc694 \uc5f0\uc0b0\uc744 \uc9c0\uc6d0\ud569\ub2c8\ub2e4:<\/p>\n \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc\ub294 \uc8fc\ub85c \ube44\uc5f0\uacb0 \uadf8\ub798\ud504\uc758 \uc5f0\uacb0\uc131\uc744 \uad00\ub9ac\ud558\uae30 \uc704\ud574 \uc0ac\uc6a9\ub418\uba70, \ud6a8\uc728\uc131\uc744 \uc704\ud574 \uacbd\ub85c \uc555\ucd95(Path Compression)\uacfc \ud569\uce58\uae30 \uae30\uc900(Union by Rank) \uae30\ubc95\uc744 \uc0ac\uc6a9\ud569\ub2c8\ub2e4. \uc774\ub7ec\ud55c \uae30\ubc95\ub4e4\uc740 \ud569\uce5c \ud6c4\uc5d0 \ud2b8\ub9ac \ud615\ud0dc\ub85c \uad6c\uc870\ub97c \uc720\uc9c0\ud568\uc73c\ub85c\uc368 ‘Find’ \uc5f0\uc0b0\uc744 \ube60\ub974\uac8c \uc218\ud589\ud560 \uc218 \uc788\ub3c4\ub85d \ub3d5\uc2b5\ub2c8\ub2e4.<\/p>\n \uc774\uc81c \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc\ub97c \ucf54\ud2c0\ub9b0\uc73c\ub85c \uad6c\ud604\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc544\ub798\ub294 \uc704 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud55c \ucf54\ub4dc\uc785\ub2c8\ub2e4.<\/p>\n \uc704 \ucf54\ub4dc\ub294 \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc \uc790\ub8cc \uad6c\uc870\ub97c \uad6c\ud604\ud55c \uac83\uc785\ub2c8\ub2e4. \uac01 \ub178\ub4dc\uc758 \ubd80\ubaa8\ub97c \uc800\uc7a5\ud558\uae30 \uc704\ud574 1. Find<\/strong> \uba54\uc11c\ub4dc\ub294 \uacbd\ub85c \uc555\ucd95\uc744 \ud1b5\ud574 \ud574\ub2f9 \ub178\ub4dc\uc758 \ub8e8\ud2b8\ub97c \uc7ac\uadc0\uc801\uc73c\ub85c \ucc3e\uc544\uac11\ub2c8\ub2e4. \uc774 \uacfc\uc815\uc5d0\uc11c \ubaa8\ub4e0 \ub178\ub4dc\uac00 \uc9c1\uc811 \ub8e8\ud2b8\ub97c \uac00\ub9ac\ud0a4\uac8c \ud558\uc5ec \ud5a5\ud6c4 \ud0d0\uc0c9\uc744 \ube60\ub974\uac8c \ud569\ub2c8\ub2e4.<\/p>\n 2. Union<\/strong> \uba54\uc11c\ub4dc\ub294 \ub450 \uac1c\uc758 \ub178\ub4dc\uc758 \ub8e8\ud2b8\ub97c \ucc3e\uc544, \ub7ad\ud06c\ub97c \ube44\uad50\ud558\uc5ec \ub354 \ub0ae\uc740 \ub7ad\ud06c\ub97c \uac00\uc9c4 \uc9d1\ud569\uc774 \ub192\uc740 \ub7ad\ud06c\ub97c \uac00\uc9c4 \uc9d1\ud569\uc5d0 \uc5f0\uacb0\ub418\ub3c4\ub85d \ud569\ub2c8\ub2e4. \ub9cc\uc57d \ub7ad\ud06c\uac00 \ub3d9\uc77c\ud55c \uacbd\uc6b0, \ud558\ub098\uc758 \uc9d1\ud569\uc744 \ub2e4\ub978 \uc9d1\ud569\uc758 \ub8e8\ud2b8\uc5d0 \uc5f0\uacb0\ud558\uace0 \ub7ad\ud06c\ub97c \uc99d\uac00\uc2dc\ud0b5\ub2c8\ub2e4.<\/p>\n 3. countComponents<\/strong> \uba54\uc11c\ub4dc\ub294 \ubaa8\ub4e0 \ub178\ub4dc\uc5d0 \ub300\ud574 \ub8e8\ud2b8\ub97c \ucc3e\uc544 \uc720\uc77c\ud55c \ub8e8\ud2b8\uc758 \uac1c\uc218\ub97c \uacc4\uc0b0\ud568\uc73c\ub85c\uc368 \uc5f0\uacb0\ub41c \ucef4\ud3ec\ub10c\ud2b8\uc758 \uac1c\uc218\ub97c \ubc18\ud658\ud569\ub2c8\ub2e4.<\/p>\n \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc\uc758 \uac01 \uc5f0\uc0b0\uc740 \ub9e4\uc6b0 \ube60\ub974\uba70, \uac70\uc758 \uc0c1\uc218 \uc2dc\uac04\uc5d0 \uc218\ud589\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774 \uc54c\uace0\ub9ac\uc998\uc758 \ud3c9\uade0 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n \uc774\ubc88 \uae00\uc5d0\uc11c\ub294 \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc \uc54c\uace0\ub9ac\uc998\uc758 \uae30\ucd08 \uac1c\ub150\uacfc \ud65c\uc6a9\uc744 \ud1b5\ud574, \uc5f0\uacb0\ub41c \uadf8\ub798\ud504\uc758 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \ubc30\uc6e0\uc2b5\ub2c8\ub2e4. \ucf54\ud2c0\ub9b0\uc744 \uc774\uc6a9\ud55c \uad6c\ud604\uc744 \ud1b5\ud574 \uc774\ub860\ubfd0\ub9cc \uc544\ub2c8\ub77c \uc2e4\uc2b5\ub3c4 \ubcd1\ud589\ud560 \uc218 \uc788\uc5c8\ub294\ub370, \uc774\ub294 \ucf54\ub529 \ud14c\uc2a4\ud2b8 \uc900\ube44\uc5d0 \ud070 \ub3c4\uc6c0\uc774 \ub420 \uac83\uc785\ub2c8\ub2e4.<\/p>\n \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc\ub294 \ub2e4\uc591\ud55c \ubd84\uc57c\uc5d0\uc11c \uc0ac\uc6a9\ub420 \uc218 \uc788\ub294 \uc911\uc694\ud55c \uc54c\uace0\ub9ac\uc998\uc774\ubbc0\ub85c, \ubc18\ub4dc\uc2dc \uc219\uc9c0\ud558\uc2dc\uae30\ub97c \uad8c\uc7a5\ud569\ub2c8\ub2e4. \ucd94\ud6c4 \ub2e4\ub978 \uc54c\uace0\ub9ac\uc998\uacfc \uc790\ub8cc \uad6c\uc870\uc5d0 \ub300\ud55c \uac15\uc88c\ub3c4 \uc774\uc5b4\uc9c8 \uc608\uc815\uc774\ub2c8 \ub9ce\uc740 \uad00\uc2ec \ubd80\ud0c1\ub4dc\ub9bd\ub2c8\ub2e4!<\/p>\n\ubb38\uc81c: \uc5f0\uacb0\ub41c \ucef4\ud3ec\ub10c\ud2b8\uc758 \uac1c\uc218<\/h3>\n
\uc785\ub825 \ud615\uc2dd<\/h4>\n
\nN M\nu1 v1\nu2 v2\n...\nuM vM\n <\/pre>\n
N<\/code>\uc740 \ub178\ub4dc\uc758 \uac1c\uc218, M<\/code>\uc740 \uac04\uc120\uc758 \uac1c\uc218\uc774\uba70, u_i<\/code>\uc640 v_i<\/code>\ub294 i\ubc88\uc9f8 \uac04\uc120\uc758 \uc591 \ub05d \uc810\uc744 \ub098\ud0c0\ub0c5\ub2c8\ub2e4.<\/p>\n\ucd9c\ub825 \ud615\uc2dd<\/h4>\n
\uc608\uc81c<\/h4>\n
\n\uc785\ub825:\n5 3\n1 2\n2 3\n4 5\n\n\ucd9c\ub825:\n2\n <\/pre>\n
\uc720\ub2c8\uc628 \ud30c\uc778\ub4dc \uc54c\uace0\ub9ac\uc998 \uc18c\uac1c<\/h2>\n
\n
\ucf54\ud2c0\ub9b0\uc73c\ub85c \uad6c\ud604\ud558\uae30<\/h2>\n
\nclass UnionFind(val size: Int) {\n private val parent = IntArray(size + 1) { it } \/\/ \uac01 \ub178\ub4dc\uc758 \ubd80\ubaa8\ub97c \uc790\uae30 \uc790\uc2e0\uc73c\ub85c \ucd08\uae30\ud654\n private val rank = IntArray(size + 1) { 1 } \/\/ \uac01 \uc9d1\ud569\uc758 \ub7ad\ud06c \ucd08\uae30\ud654\n\n \/\/ Find \uc5f0\uc0b0: \uacbd\ub85c \uc555\ucd95 \uae30\ubc95\n fun find(node: Int): Int {\n if (parent[node] != node) {\n parent[node] = find(parent[node]) \/\/ \ubd80\ubaa8\ub97c \uc7ac\uadc0\uc801\uc73c\ub85c \ucc3e\uc73c\uba74\uc11c \uacbd\ub85c\ub97c \uc555\ucd95\n }\n return parent[node]\n }\n\n \/\/ Union \uc5f0\uc0b0: \ub7ad\ud06c\ub97c \uae30\uc900\uc73c\ub85c \uc9d1\ud569\uc744 \ud569\uce68\n fun union(node1: Int, node2: Int) {\n val root1 = find(node1)\n val root2 = find(node2)\n\n if (root1 != root2) {\n if (rank[root1] > rank[root2]) {\n parent[root2] = root1\n } else if (rank[root1] < rank[root2]) {\n parent[root1] = root2\n } else {\n parent[root2] = root1\n rank[root1]++\n }\n }\n }\n\n \/\/ \uc5f0\uacb0\ub41c \ucef4\ud3ec\ub10c\ud2b8\uc758 \uac1c\uc218 \uc138\uae30\n fun countComponents(): Int {\n val rootSet = mutableSetOf\ucf54\ub4dc \uc124\uba85<\/h2>\n
parent<\/code> \ubc30\uc5f4\uc744 \uc0ac\uc6a9\ud558\uace0, \uac01 \uc9d1\ud569\uc758 \ub7ad\ud06c(\ub192\uc774)\ub97c \uc800\uc7a5\ud558\uae30 \uc704\ud574 rank<\/code> \ubc30\uc5f4\uc744 \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n\uc2dc\uac04 \ubcf5\uc7a1\ub3c4 \ubd84\uc11d<\/h2>\n
\n
\u03b1(N)<\/code>\ub294 \uc544\ucee4\ub9cc \ud568\uc218\uc758 \uc5ed\ud568\uc218\uc774\uba70, \uc774\ub294 \ub9e4\uc6b0 \ub290\ub9ac\uac8c \uc131\uc7a5\ud558\ub294 \ud568\uc218\uc785\ub2c8\ub2e4. \ub530\ub77c\uc11c \uc720\ub2c8\uc628 \ud30c\uc778\ub4dc\ub294 \ub300\uaddc\ubaa8 \ub370\uc774\ud130\uc5d0\uc11c\ub3c4 \ud6a8\uc728\uc801\uc73c\ub85c \uc791\ub3d9\ud569\ub2c8\ub2e4.<\/p>\n\ub9c8\ubb34\ub9ac<\/h2>\n