{"id":28409,"date":"2024-10-27T16:10:59","date_gmt":"2024-10-27T16:10:59","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=28409"},"modified":"2024-11-26T07:03:02","modified_gmt":"2024-11-26T07:03:02","slug":"%ec%bd%94%ed%8b%80%eb%a6%b0-%ec%bd%94%eb%94%a9%ed%85%8c%ec%8a%a4%ed%8a%b8-%ea%b0%95%ec%a2%8c-%ea%b8%b0%ed%95%98-%ec%95%8c%ec%95%84%eb%b3%b4%ea%b8%b0","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/28409\/","title":{"rendered":"\ucf54\ud2c0\ub9b0 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uae30\ud558 \uc54c\uc544\ubcf4\uae30"},"content":{"rendered":"

<\/p>\n

\n \uae30\ud558\ud559\uc740 \ucef4\ud4e8\ud130 \uacfc\ud559\uc5d0\uc11c \ub9ce\uc740 \ubd84\uc57c\uc5d0\uc11c \ud65c\uc6a9\ub418\uba70, \ucf54\ub529\ud14c\uc2a4\ud2b8\uc5d0\uc11c\ub3c4 \uc790\uc8fc \ucd9c\uc81c\ub418\ub294 \uc8fc\uc81c\uc785\ub2c8\ub2e4.
\n \uc774\ubc88 \ud3ec\uc2a4\ud305\uc5d0\uc11c\ub294 \uae30\ud558 \uc0ac\uc6a9\uc790 \ubb38\uc81c\ub97c \ub2e4\ub8e8\uace0, \ucf54\ud2c0\ub9b0\uc744 \uc0ac\uc6a9\ud558\uc5ec \ud6a8\uc728\uc801\uc73c\ub85c \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc744
\n \uc124\uba85\ud558\uaca0\uc2b5\ub2c8\ub2e4.\n <\/p>\n

\ubb38\uc81c \uc124\uba85<\/h2>\n

\n\ubb38\uc81c:<\/strong> \uc8fc\uc5b4\uc9c4 N\uac1c\uc758 \uc810\uc774 2\ucc28\uc6d0 \ud3c9\uba74\uc5d0 \uc788\uc744 \ub54c, \uc774\ub4e4 \uc810 \uc911\uc5d0\uc11c \ubcfc\ub85d \uaecd\uc9c8(Convex Hull)\uc744
\n \uc774\ub8e8\ub294 \uc810\ub4e4\uc758 \uc88c\ud45c\ub97c \uc2dc\uacc4 \ubc29\ud5a5\uc73c\ub85c \ucd9c\ub825\ud558\uc2dc\uc624.\n <\/p>\n

\n \ubcfc\ub85d \uaecd\uc9c8\uc774\ub780, \ud3c9\uba74\uc0c1\uc758 \uc810\ub4e4 \uc911\uc5d0\uc11c \ubaa8\ub4e0 \uc810\uc744 \ud3ec\ud568\ud558\ub294 \uac00\uc7a5 \uc791\uc740 \ubcfc\ub85d \ub2e4\uac01\ud615\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4.
\n \uc774 \ubb38\uc81c\ub294 \ud754\ud788 \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ub85c \uc790\uc8fc \ucd9c\uc81c\ub418\uba70, \ud6a8\uc728\uc801\uc778 \uc54c\uace0\ub9ac\uc998\uc73c\ub85c\ub294 \uadf8\ub808\uc774\uc5c4 \uc2a4\uce94(Graham’s scan)
\n \uc774\ub098 \uc794\ub514\ubc2d \ubc29\uc2dd(Jarvis March) \ub4f1\uc774 \uc788\uc2b5\ub2c8\ub2e4.\n <\/p>\n

\uc785\ucd9c\ub825 \ud615\uc2dd<\/h2>\n

\n\uc785\ub825:<\/strong> \uccab \ubc88\uc9f8 \uc904\uc5d0 \uc815\uc218 N(1 \u2264 N \u2264 100,000)\uc774 \uc8fc\uc5b4\uc9c0\uace0,
\n \ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0 \uac01 \uc810\uc758 x, y \uc88c\ud45c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.
\n (x, y\ub294 -10^9 \uc774\uc0c1, 10^9 \uc774\ud558\uc758 \uc815\uc218\ub2e4.)\n <\/p>\n

\n\ucd9c\ub825:<\/strong> \ubcfc\ub85d \uaecd\uc9c8\uc744 \uad6c\uc131\ud558\ub294 \uc810\ub4e4\uc758 \uc88c\ud45c\ub97c
\n \uc2dc\uacc4 \ubc29\ud5a5\uc73c\ub85c \ucd9c\ub825\ud558\uace0, \uac01 \uc88c\ud45c\ub294 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud55c\ub2e4.\n <\/p>\n

\ubb38\uc81c \ud480\uc774 \uacfc\uc815<\/h2>\n

\n \ubb38\uc81c\ub97c \ud480\uae30 \uc704\ud574\uc11c\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ub2e8\uacc4\ub4e4\uc744 \uac70\uccd0\uc57c \ud569\ub2c8\ub2e4:\n <\/p>\n

    \n
  1. \n\uc785\ub825 \ub370\uc774\ud130 \ucc98\ub9ac:<\/strong>
    \n \uc810\uc758 \uc88c\ud45c\ub97c \uc785\ub825\ubc1b\uc544 \ub9ac\uc2a4\ud2b8\uc5d0 \uc800\uc7a5\ud569\ub2c8\ub2e4.
    \n \uc774\ub54c, \uac01 \uc810\uc744 Pair \uac1d\uccb4\ub85c \uc800\uc7a5\ud558\uba74 \ud3b8\ub9ac\ud569\ub2c8\ub2e4.\n <\/li>\n
  2. \n\uc88c\ud45c \uc815\ub82c:<\/strong>
    \n \uadf9\uac01\ub3c4\ub97c \uae30\uc900\uc73c\ub85c \uc810\ub4e4\uc744 \uc815\ub82c\ud569\ub2c8\ub2e4.
    \n \uac00\uc7a5 \uc67c\ucabd \uc544\ub798(\ub610\ub294 \uc704) \uc810\uc744 \uae30\uc900\uc73c\ub85c \uc0bc\uace0, \ub098\uba38\uc9c0 \uc810\ub4e4\uc744 \uadf9\uac01\ub3c4\uc5d0 \ub530\ub77c \uc815\ub82c\ud569\ub2c8\ub2e4.\n <\/li>\n
  3. \n\ubcfc\ub85d \uaecd\uc9c8 \uc0dd\uc131:<\/strong>
    \n \uadf8\ub808\uc774\uc5c4 \uc2a4\uce94 \uc54c\uace0\ub9ac\uc998\uc744 \uc0ac\uc6a9\ud558\uc5ec \ubcfc\ub85d \uaecd\uc9c8\uc758 \uc810\ub4e4\uc744 \ucc3e\uc2b5\ub2c8\ub2e4.\n <\/li>\n
  4. \n\ucd9c\ub825 \ud615\uc2dd\uc5d0 \ub9de\uac8c \ud3ec\ub9f7\ud305:<\/strong>
    \n \uacb0\uacfc\ub97c \uc2dc\uacc4 \ubc29\ud5a5\uc73c\ub85c \uc815\ub9ac\ud558\uace0, \uc694\uad6c\ud558\ub294 \ud615\uc2dd\uc73c\ub85c \ucd9c\ub825\ud569\ub2c8\ub2e4.\n <\/li>\n<\/ol>\n

    \ucf54\ub4dc \uad6c\ud604<\/h2>\n
    \n        \n            import kotlin.math.atan2\n            \n            data class Point(val x: Int, val y: Int)\n            \n            fun convexHull(points: List): List {\n                val sortedPoints = points.sortedWith(compareBy({ it.x }, { it.y }))\n                val hull = mutableListOf()\n                \n                \/\/ \uc544\ub798\ucabd \ubd80\ubd84\n                for (point in sortedPoints) {\n                    while (hull.size >= 2 && cross(hull[hull.size - 2], hull[hull.size - 1], point) <= 0)\n                        hull.removeAt(hull.size - 1)\n                    hull.add(point)\n                }\n                \n                val lowerSize = hull.size\n                \n                \/\/ \uc704\ucabd \ubd80\ubd84\n                for (i in sortedPoints.size - 1 downTo 0) {\n                    val point = sortedPoints[i]\n                    while (hull.size > lowerSize && cross(hull[hull.size - 2], hull[hull.size - 1], point) <= 0)\n                        hull.removeAt(hull.size - 1)\n                    hull.add(point)\n                }\n                \n                hull.removeAt(hull.size - 1) \/\/ \ub9c8\uc9c0\ub9c9 \uc810\uc740 \uc911\ubcf5\ub418\ubbc0\ub85c \uc81c\uac70\n                \n                return hull\n            }\n            \n            fun cross(o: Point, a: Point, b: Point): Int {\n                return (a.x - o.x) * (b.y - o.y) - (a.y - o.y) * (b.x - o.x)\n            }\n            \n            fun main() {\n                val n = readLine()!!.toInt()\n                val points = List(n) {\n                    val (x, y) = readLine()!!.split(\" \").map { it.toInt() }\n                    Point(x, y)\n                }\n                val hull = convexHull(points)\n                hull.forEach { println(\"${it.x} ${it.y}\") }\n            }\n        <\/point><\/point><\/point><\/code>\n    <\/pre>\n
    \uacb0\ub860<\/h2>\n
    \n        \uc774\ubc88 \ud3ec\uc2a4\ud305\uc5d0\uc11c\ub294 \ubcfc\ub85d \uaecd\uc9c8\uc744 \uad6c\ud558\ub294 \ubb38\uc81c\uc5d0 \ub300\ud574 \uc124\uba85\ud558\uc600\uc2b5\ub2c8\ub2e4.
    \n        \uae30\ud558\ud559\uc801\uc778 \ubb38\uc81c\ub294 \uc2e4\uc804 \ucf54\ub529\ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc790\uc8fc \ucd9c\uc81c\ub418\ubbc0\ub85c
    \n        \ucda9\ubd84\ud788 \uc5f0\uc2b5\ud558\uace0 \ub2e4\uc591\ud55c \uc720\ud615\uc758 \ubb38\uc81c\ub97c \ud480\uc5b4\ubcf4\ub294 \uac83\uc774 \uc911\uc694\ud569\ub2c8\ub2e4.
    \n        \uc774 \uc678\uc5d0\ub3c4 \ub2e4\ub978 \uae30\ud558\ud559\uc801 \ubb38\uc81c\ub97c \ud1b5\ud574 \ubb38\uc81c \ud574\uacb0 \ub2a5\ub825\uc744 \ud0a4\uc6cc\ub098\uac00\uc2dc\uae30 \ubc14\ub78d\ub2c8\ub2e4.\n    <\/p>\n
    \ucd94\uac00 \ud559\uc2b5 \uc790\ub8cc<\/h2>\n
    \n        \ucf54\ud2c0\ub9b0\uc744 \ub354 \uae4a\uc774 \uc788\uac8c \ubc30\uc6b0\uace0 \uc2f6\uc73c\uc2dc\ub2e4\uba74 \ub2e4\uc74c\uc758 \uc790\ub8cc\ub4e4\uc744 \ucd94\ucc9c\ub4dc\ub9bd\ub2c8\ub2e4:<\/p>\n