\uc548\ub155\ud558\uc138\uc694! \uc624\ub298\uc740 \ucf54\ud2c0\ub9b0\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc774\ud56d\uacc4\uc218\ub97c \uad6c\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc54c\uc544\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc774\ud56d\uacc4\uc218\ub294 \uc870\ud569(combination)\uc5d0\uc11c \uc911\uc694\ud55c \uac1c\ub150\uc73c\ub85c, \uc8fc\uc5b4\uc9c4 n\uac1c\uc758 \uac1d\uccb4 \uc911 k\uac1c\uc758 \uac1d\uccb4\ub97c \uc120\ud0dd\ud558\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4. \uc774 \ud56d\ubaa9\uc740 \ucf54\ub529\ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc790\uc8fc \ucd9c\uc81c\ub418\ubbc0\ub85c \ubc18\ub4dc\uc2dc \uc219\uc9c0\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\n
\uc5b4\ub5a4 \uc815\uc218 n\uacfc k\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, nCk (n choose k)\ub97c \uacc4\uc0b0\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc774\ud56d\uacc4\uc218\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uc218\uc2dd\uc73c\ub85c \uc815\uc758\ub429\ub2c8\ub2e4:<\/p>\n
\nC(n, k) = n! \/ (k! * (n - k)!)\n<\/pre>\n\uc5ec\uae30\uc11c n!\uc740 n\uc758 \ud329\ud1a0\ub9ac\uc5bc\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4. \ud329\ud1a0\ub9ac\uc5bc\uc740 1\ubd80\ud130 n\uae4c\uc9c0\uc758 \ubaa8\ub4e0 \uc790\uc5f0\uc218\uc758 \uacf1\uc785\ub2c8\ub2e4.<\/p>\n
\uc785\ub825 \ud615\uc2dd<\/h2>\n
\uccab \ubc88\uc9f8 \uc904\uc5d0 \uc815\uc218 n(0 \u2264 n \u2264 30)\uacfc k(0 \u2264 k \u2264 n)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\n
\ucd9c\ub825 \ud615\uc2dd<\/h2>\n
nCk\uc758 \uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\n
\uc608\uc81c \uc785\ub825<\/h2>\n
\n5 2\n<\/pre>\n\uc608\uc81c \ucd9c\ub825<\/h2>\n
\n10\n<\/pre>\n\ubb38\uc81c \ud574\uacb0 \ubc29\ubc95<\/h2>\n
\uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574\uc11c\ub294 \ub2e4\uc74c\uc758 \ub450 \uac00\uc9c0 \ubc29\ubc95\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4:<\/p>\n
\n
- \uc7ac\uadc0\ub97c \uc774\uc6a9\ud55c \ud329\ud1a0\ub9ac\uc5bc \uacc4\uc0b0<\/li>\n
- \ub3d9\uc801 \ud504\ub85c\uadf8\ub798\ubc0d\uc744 \uc774\uc6a9\ud55c \uc774\ud56d\uacc4\uc218 \uacc4\uc0b0<\/li>\n<\/ol>\n
1. \uc7ac\uadc0\ub97c \uc774\uc6a9\ud55c \ud329\ud1a0\ub9ac\uc5bc \uacc4\uc0b0<\/h3>\n
\uac00\uc7a5 \uae30\ubcf8\uc801\uc778 \ubc29\ubc95\uc740 \uc7ac\uadc0\ub97c \uc774\uc6a9\ud558\uc5ec \ud329\ud1a0\ub9ac\uc5bc\uc744 \uacc4\uc0b0\ud558\ub294 \uac83\uc785\ub2c8\ub2e4. \uc774 \ubc29\ubc95\uc740 \uc774\ud574\ud558\uae30 \uc27d\uc9c0\ub9cc n\uc774 \ucee4\uc9c8\uc218\ub85d \ube44\ud6a8\uc728\uc801\uc77c \uc218 \uc788\uc2b5\ub2c8\ub2e4. \ub2e4\uc74c\uc740 \ud329\ud1a0\ub9ac\uc5bc\uc744 \uc7ac\uadc0\uc801\uc73c\ub85c \uacc4\uc0b0\ud558\ub294 \ucf54\ud2c0\ub9b0 \uc608\uc81c\uc785\ub2c8\ub2e4:<\/p>\n
\nfun factorial(n: Int): Long {\n return if (n == 0 || n == 1) 1 else n * factorial(n - 1)\n}\n<\/pre>\n2. \ub3d9\uc801 \ud504\ub85c\uadf8\ub798\ubc0d\uc744 \uc774\uc6a9\ud55c \uc774\ud56d\uacc4\uc218 \uacc4\uc0b0<\/h3>\n
\uc774\ud56d\uacc4\uc218\ub97c \ud6a8\uc728\uc801\uc73c\ub85c \uacc4\uc0b0\ud558\uae30 \uc704\ud574\uc11c\ub294 \ub3d9\uc801 \ud504\ub85c\uadf8\ub798\ubc0d\uc744 \ud65c\uc6a9\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ud56d\uacc4\uc218\ub294 Pascal\uc758 \uc0bc\uac01\ud615\uc758 \uc131\uc9c8\uc744 \ud1b5\ud574 \uacc4\uc0b0\ud560 \uc218 \uc788\uc73c\uba70, \ub2e4\uc74c\uc758 \uc810\ud654\uc2dd\uc73c\ub85c \uc815\uc758\ub429\ub2c8\ub2e4:<\/p>\n
\nC(n, k) = C(n - 1, k - 1) + C(n - 1, k)\n<\/pre>\n\uae30\uc800 \uc0ac\ub840\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n
\n
- C(n, 0) = 1 (n >= 0)<\/li>\n
- C(n, n) = 1 (n >= 0)<\/li>\n<\/ul>\n
Pascal\uc758 \uc0bc\uac01\ud615\uc5d0 \ub530\ub77c \ub3d9\uc801 \ud504\ub85c\uadf8\ub798\ubc0d \ubc30\uc5f4\uc744 \ud1b5\ud574 \uc774\ud56d\uacc4\uc218\ub97c \uacc4\uc0b0\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4:<\/p>\n
\nfun binomialCoefficient(n: Int, k: Int): Long {\n val dp = Array(n + 1) { LongArray(k + 1) }\n for (i in 0..n) {\n for (j in 0..minOf(i, k)) {\n if (j == 0 || j == i) {\n dp[i][j] = 1\n } else {\n dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j]\n }\n }\n }\n return dp[n][k]\n}\n<\/pre>\n\ucf54\ub4dc \ud1b5\ud569 \uc608\uc81c<\/h2>\n
\uc704\uc758 \ubc29\ubc95\ub4e4\uc744 \ubc14\ud0d5\uc73c\ub85c \ucd5c\uc885 \ucf54\ub4dc\ub97c \uc791\uc131\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4:<\/p>\n
\nfun main() {\n val input = readLine()!!.split(\" \").map { it.toInt() }\n val n = input[0]\n val k = input[1]\n \n println(binomialCoefficient(n, k))\n}\n\nfun binomialCoefficient(n: Int, k: Int): Long {\n val dp = Array(n + 1) { LongArray(k + 1) }\n for (i in 0..n) {\n for (j in 0..minOf(i, k)) {\n if (j == 0 || j == i) {\n dp[i][j] = 1\n } else {\n dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j]\n }\n }\n }\n return dp[n][k]\n}\n<\/pre>\n\uacb0\ub860<\/h2>\n
\uc774\ud56d\uacc4\uc218\ub97c \uacc4\uc0b0\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc54c\uc544\ubcf4\uc558\uc2b5\ub2c8\ub2e4. \uc7ac\uadc0\uc640 \ub3d9\uc801 \ud504\ub85c\uadf8\ub798\ubc0d\uc744 \ud1b5\ud574 \uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud560 \uc218 \uc788\uc73c\uba70, \uac01 \ubc29\ubc95\uc758 \uc7a5\ub2e8\uc810\uc744 \uc774\ud574\ud558\ub294 \uac83\uc774 \uc911\uc694\ud569\ub2c8\ub2e4. \uc774\ud56d\uacc4\uc218\ub294 \uc870\ud569\ub860\ubfd0\ub9cc \uc544\ub2c8\ub77c \ub9ce\uc740 \ubd84\uc57c\uc5d0\uc11c \uc751\uc6a9\ub420 \uc218 \uc788\uc73c\ub2c8, \uc774 \uac1c\ub150\uc744 \ud655\uc2e4\ud788 \uc774\ud574\ud574 \ub450\ub294 \uac83\uc774 \uc88b\uc2b5\ub2c8\ub2e4.<\/p>\n
\uc55e\uc73c\ub85c\ub3c4 \ucf54\ud2c0\ub9b0\uc744 \uc774\uc6a9\ud55c \ub2e4\uc591\ud55c \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ud480\uc774 \uacfc\uc815\uc744 \uc9c0\uc18d\uc801\uc73c\ub85c \ud0d0\uad6c\ud558\uae38 \ubc14\ub78d\ub2c8\ub2e4. \uac10\uc0ac\ud569\ub2c8\ub2e4!<\/p>\n
<\/body><\/p>\n","protected":false},"excerpt":{"rendered":"