\n \ubcf8\uae00\uc5d0\uc11c\ub294 ‘\ucd5c\uc18c \uacf5\ud1b5 \uc870\uc0c1(LCA; Lowest Common Ancestor)’ \uad6c\ud558\uae30 \ubb38\uc81c \uc911 \ud558\ub098\uc778 ‘\ucd5c\uc18c \uacf5\ud1b5 \uc870\uc0c1 \uad6c\ud558\uae30 2’\uc5d0 \ub300\ud574
\n \ud0d0\uad6c\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub294 \ud2b9\uc815 \ud2b8\ub9ac \uad6c\uc870\uc5d0\uc11c \ub450 \ub178\ub4dc\uc758 \ucd5c\uc18c \uacf5\ud1b5 \uc870\uc0c1\uc744 \ucc3e\ub294 \ubb38\uc81c\ub85c,
\n \ud2b9\ud788 \uc774\uc9c4 \ud2b8\ub9ac\uc5d0\uc11c \uc774\ub8e8\uc5b4\uc9d1\ub2c8\ub2e4. LCA \ubb38\uc81c\ub294 \ud2b8\ub9ac \ud0d0\uc0c9 \ubc0f \uc870\uc791\uacfc \uad00\ub828\ub41c \uae30\ubcf8\uc801\uc778 \ubb38\uc81c\ub85c,
\n \ucf54\ub529 \uc778\ud130\ubdf0 \ubc0f \uc54c\uace0\ub9ac\uc998 \uacbd\uc2dc\ub300\ud68c\uc5d0\uc11c\ub3c4 \uc790\uc8fc \ub4f1\uc7a5\ud569\ub2c8\ub2e4.\n<\/p>\n
\n \uc8fc\uc5b4\uc9c4 \uc774\uc9c4 \ud2b8\ub9ac\uac00 \uc788\uc744 \ub54c, \ub450 \ub178\ub4dc \n \ub178\ub4dc \n \uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574, \uba3c\uc800 \ud2b8\ub9ac\ub97c \uad6c\uc131\ud574\uc57c \ud569\ub2c8\ub2e4. \ud2b8\ub9ac\ub97c \ubc30\uc5f4\ub85c \ud45c\ud604\ud558\uac70\ub098 \uc5f0\uacb0 \ub9ac\uc2a4\ud2b8\ub85c \ud45c\ud604\ud560 \uc218 \uc788\uc9c0\ub9cc, \n \uc8fc\uc5b4\uc9c4 \uac04\uc120 \uc815\ubcf4\ub97c \ubc14\ud0d5\uc73c\ub85c \ub178\ub4dc\uc640 \uc790\uc2dd \uad00\uacc4\ub97c \uc124\uc815\ud569\ub2c8\ub2e4. \n \uae4a\uc774\ub97c \uae30\uc900\uc73c\ub85c \ub450 \ub178\ub4dc\uc758 \uc704\uce58\ub97c \ub9de\ucd98 \ud6c4, \uadf8\ub4e4\uc758 \ubd80\ubaa8\ub97c \ub530\ub77c \uc62c\ub77c\uac00\uba74\uc11c \n \uc704\uc758 \uc54c\uace0\ub9ac\uc998\uc758 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\ub294 O(n)\uc785\ub2c8\ub2e4. \ud2b8\ub9ac\ub97c \uad6c\uc131\ud558\uace0 \ud0d0\uc0c9\ud558\ub294 \uacfc\uc815\uc5d0\uc11c \n ‘\ucd5c\uc18c \uacf5\ud1b5 \uc870\uc0c1 \uad6c\ud558\uae30 2’ \ubb38\uc81c\ub294 \uc774\uc9c4 \ud2b8\ub9ac\uc758 \ud0d0\uc0c9 \ubc0f \uc870\uc791\uc758 \uae30\ucd08\ub97c \uc774\ud574\ud558\ub294 \ub370 \ub3c4\uc6c0\uc774 \ub418\uba70, <\/body><\/p>\n","protected":false},"excerpt":{"rendered":"u<\/code>\uc640 v<\/code>\uc758 \ucd5c\uc18c \uacf5\ud1b5 \uc870\uc0c1\uc744 \ucc3e\uc544\uc57c \ud569\ub2c8\ub2e4.
\n \uc774\uc9c4 \ud2b8\ub9ac\ub294 \uac01 \ub178\ub4dc\uac00 \ucd5c\ub300 2\uac1c\uc758 \uc790\uc2dd\uc744 \uac00\uc9c8 \uc218 \uc788\uc73c\uba70, \ub8e8\ud2b8 \ub178\ub4dc\ubd80\ud130 \uc2dc\uc791\ud558\uc5ec
\n \uac01\uac01\uc758 \ub178\ub4dc\ub294 \uace0\uc720\ud55c \uac12\uc744 \uac00\uc9d1\ub2c8\ub2e4.\n<\/p>\n\uc785\ub825 \ud615\uc2dd<\/h3>\n
\n
n<\/code> (1 \u2264 n \u2264 100,000)<\/li>\nu<\/code>, v<\/code><\/li>\n<\/ul>\n\ucd9c\ub825 \ud615\uc2dd<\/h3>\n
u<\/code>\uc640 v<\/code>\uc758 \ucd5c\uc18c \uacf5\ud1b5 \uc870\uc0c1\uc744 \ucd9c\ub825\ud569\ub2c8\ub2e4.\n<\/p>\n\uc608\uc81c<\/h2>\n
\n\uc785\ub825:\n7\n1 2\n1 3\n2 4\n2 5\n3 6\n3 7\n4 5\n\n\ucd9c\ub825:\n2\n<\/pre>\n
\ubb38\uc81c \uc811\uadfc \ubc29\ubc95<\/h2>\n
\n \uc5f0\uacb0 \ub9ac\uc2a4\ud2b8\ub97c \uc0ac\uc6a9\ud558\ub294 \uac83\uc774 \ub354 \ud6a8\uc728\uc801\uc785\ub2c8\ub2e4. \uc774\ud6c4 DFS(Depth First Search)\ub97c \ud1b5\ud574 \uac01 \ub178\ub4dc\uc758 \uae4a\uc774\ub97c \uae30\ub85d\ud558\uace0,
\n \ubd80\ubaa8 \ub178\ub4dc\ub97c \uc800\uc7a5\ud558\uc5ec \uc774\ud6c4 LCA\ub97c \uc27d\uac8c \ucc3e\uc744 \uc218 \uc788\uc2b5\ub2c8\ub2e4.\n<\/p>\n\ud2b8\ub9ac \uad6c\uc131<\/h2>\n
\n \ud30c\uc774\uc36c\uc758 \ub515\uc154\ub108\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \ubd80\ubaa8-\uc790\uc2dd \uad00\uacc4\ub97c \uc800\uc7a5\ud569\ub2c8\ub2e4.\n<\/p>\n\nfrom collections import defaultdict\n\ndef build_tree(edges):\n tree = defaultdict(list)\n for parent, child in edges:\n tree[parent].append(child)\n return tree\n<\/code><\/pre>\nDFS\ub97c \ud1b5\ud55c \uae4a\uc774 \ubc0f \ubd80\ubaa8 \ub178\ub4dc \uc815\ubcf4 \uc800\uc7a5<\/h2>\n
\ndef dfs(tree, node, parent, depth, depths, parents):\n depths[node] = depth\n parents[node] = parent\n for child in tree[node]:\n if child != parent:\n dfs(tree, child, node, depth + 1, depths, parents)\n<\/code><\/pre>\nLCA \ud568\uc218 \uad6c\ud604<\/h2>\n
\n \ub450 \ub178\ub4dc\uac00 \uac19\uc740 \ub178\ub4dc\uc5d0 \ub3c4\ub2ec\ud560 \ub54c\uae4c\uc9c0 \uc9c4\ud589\ud569\ub2c8\ub2e4.\n<\/p>\n\ndef lca(u, v, depths, parents):\n # Depth \ub9de\ucd94\uae30\n if depths[u] < depths[v]:\n u, v = v, u\n\n while depths[u] > depths[v]:\n u = parents[u]\n\n while u != v:\n u = parents[u]\n v = parents[v]\n\n return u\n<\/code><\/pre>\n\uc804\uccb4 \ucf54\ub4dc<\/h2>\n
\ndef main():\n n = int(input())\n edges = [tuple(map(int, input().split())) for _ in range(n - 1)]\n u, v = map(int, input().split())\n\n tree = build_tree(edges)\n depths = {}\n parents = {}\n\n # DFS\ub97c \ud1b5\ud574 \uae4a\uc774\uc640 \ubd80\ubaa8 \uc815\ubcf4 \uc218\uc9d1\n dfs(tree, 1, -1, 0, depths, parents)\n\n # \ucd5c\uc18c \uacf5\ud1b5 \uc870\uc0c1 \ucc3e\uae30\n ancestor = lca(u, v, depths, parents)\n print(ancestor)\n\nif __name__ == \"__main__\":\n main()\n<\/code><\/pre>\n\uc2dc\uac04 \ubcf5\uc7a1\ub3c4<\/h2>\n
\n \uac01 \ub178\ub4dc\ub97c \ud55c \ubc88\uc529 \ubc29\ubb38\ud558\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4.\n<\/p>\n\uacb0\ub860<\/h2>\n
\n \uc2e4\uc81c\ub85c \uc720\uc6a9\ud55c \uc54c\uace0\ub9ac\uc998\uc785\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \uacfc\uc815\uc5d0\uc11c \ud2b8\ub9ac\uc758 \uad6c\uc870\uc640 DFS\uc758 \uac1c\ub150\uc744 \uae4a\uc774 \uc788\uac8c \uc774\ud574\ud560 \uc218 \uc788\uac8c \ub429\ub2c8\ub2e4.
\n \uc774 \uc54c\uace0\ub9ac\uc998\uc740 \uc774\ud6c4 \ub2e4\uc591\ud55c \ubb38\uc81c\ub4e4\ub85c \ud655\uc7a5 \uac00\ub2a5\ud558\uba70, \ub2e4\ub978 \uc790\ub8cc\uad6c\uc870\uc640\uc758 \uc751\uc6a9\uc5d0\ub3c4 \ud070 \ub3c4\uc6c0\uc774 \ub429\ub2c8\ub2e4.\n<\/p>\n