\ucf54\ub529\ud14c\uc2a4\ud2b8 \uc900\ube44\uc5d0 \uc788\uc5b4\uc11c \ub2e4\uc591\ud55c \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ub4e4\uc744 \ud480\uc5b4\ubcf4\ub294 \uac83\uc740 \ub9e4\uc6b0 \uc911\uc694\ud569\ub2c8\ub2e4. \uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 ‘\uc815\uc218\ub97c 1\ub85c \ub9cc\ub4e4\uae30’\ub77c\ub294 \ubb38\uc81c\ub97c \ud1b5\ud574 \uae30\ubcf8\uc801\uc778 \ubb38\uc81c \ud574\uacb0 \ub2a5\ub825\uc744 \uae30\ub974\uace0, \ud6a8\uc728\uc801\uc778 \uc54c\uace0\ub9ac\uc998\uc744 \uc124\uacc4\ud558\ub294 \uacfc\uc815\uc744 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub294 \uc8fc\uc5b4\uc9c4 \uc815\uc218\ub97c \uba87 \uac00\uc9c0 \uc5f0\uc0b0\uc744 \ud1b5\ud574 1\ub85c \ub9cc\ub4e4 \uc218 \uc788\ub294 \ucd5c\uc18c \ud69f\uc218\ub97c \ucc3e\ub294 \ubb38\uc81c\uc785\ub2c8\ub2e4.<\/p>\n
\uc8fc\uc5b4\uc9c4 \uc815\uc218 \ubaa9\ud45c\ub294 \uc774\ub7ec\ud55c \uc5f0\uc0b0\uc744 \ud1b5\ud574 \uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud55c \uba87 \uac00\uc9c0 \uc811\uadfc\ubc95\uc774 \uc788\uc2b5\ub2c8\ub2e4. \uc5ec\uae30\uc11c\ub294 DFS(Depth-First Search)\uc640 DP(Dynamic Programming) \ub450 \uac00\uc9c0 \ubc29\ubc95\uc744 \uc18c\uac1c\ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n \uba3c\uc800 DFS\ub97c \uc0ac\uc6a9\ud558\uc5ec \ubaa8\ub4e0 \uac00\ub2a5\ud55c \uacbd\ub85c\ub97c \ud0d0\uc0c9\ud558\ub294 \ubc29\ubc95\uc744 \uc0dd\uac01\ud574\ubcfc \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uadf8\ub7ec\ub098 \uc774 \ubc29\ubc95\uc740 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\uac00 \ub9e4\uc6b0 \ub192\uc544\uc9c8 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc0c1\uae30 \ucf54\ub4dc\ub294 \uc8fc\uc5b4\uc9c4 \ub530\ub77c\uc11c \ub354 \ud6a8\uc728\uc801\uc778 \ubc29\ubc95\uc740 DP\ub97c \uc0ac\uc6a9\ud558\ub294 \uac83\uc785\ub2c8\ub2e4. DP\ub97c \uc0ac\uc6a9\ud558\uba74 \uae30\uc874\uc5d0 \uacc4\uc0b0\ub41c \uacb0\uacfc\ub97c \uc800\uc7a5\ud558\uace0 \ud544\uc694\ud560 \ub54c \uc7ac\uc0ac\uc6a9\ud568\uc73c\ub85c\uc368 \ubd88\ud544\uc694\ud55c \uacc4\uc0b0\uc744 \uc904\uc77c \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n \uc0c1\uae30 DP \uad6c\ud604 \ucf54\ub4dc\ub294 \ubc30\uc5f4 DFS \uc811\uadfc\ubc95\uc740 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\uac00 \uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 \uc815\uc218\ub97c 1\ub85c \ub9cc\ub4e4\uae30 \uc704\ud55c \uc54c\uace0\ub9ac\uc998\uc758 \ub2e4\uc591\ud55c \uc811\uadfc\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uc558\uc73c\uba70, DFS\uc640 DP\ub97c \ud1b5\ud574 \ud6a8\uc728\uc801\uc778 \ubb38\uc81c \ud574\uacb0 \ubc29\uc2dd\uc744 \ubc30\uc6e0\uc2b5\ub2c8\ub2e4. \ucf54\ub529 \ud14c\uc2a4\ud2b8\ub97c \uc900\ube44\ud558\ub294 \ub370 \uc788\uc5b4 \uc2e4\uc81c \uc54c\uace0\ub9ac\uc998\uc744 \uc774\ud574\ud558\uace0, \uadf8\uac83\uc744 \uae30\ubc18\uc73c\ub85c \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ub2a5\ub825\uc744 \uae30\ub974\ub294 \uac83\uc774 \uc911\uc694\ud569\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ucc98\ub7fc \ubcf5\uc7a1\ud55c \ubb38\uc81c\ub4e4\uc744 \ud574\uacb0\ud558\uae30 \uc704\ud574 \uc5ec\ub7ec \uc811\uadfc\ubc95\uc744 \uc775\ud788\uace0, \ucd5c\uc801\ud654\ub41c \ubc29\ubc95\uc744 \uc120\ud0dd\ud558\ub294 \uc5f0\uc2b5\uc744 \uc9c0\uc18d\ud558\uc2dc\uae38 \ubc14\ub78d\ub2c8\ub2e4.<\/p>\n \uc544\ub798\uc758 \ucd94\uac00 \ubb38\uc81c\ub97c \ud480\uc5b4\ubcf4\uba70 \uc5f0\uc2b5\ud574\ubcf4\uc138\uc694:<\/p>\n \ubb38\uc81c\ub97c \ud480\uc5b4\ubcf4\uba74\uc11c \uac00\ub2a5\ud558\ub2e4\uba74, \ub2e4\uc591\ud55c \uc785\ub825\uac12\uc5d0 \ub300\ud574 \uacb0\uacfc\ub97c \ucd9c\ub825\ud574\ubcf4\uc138\uc694. \ucf54\ub529 \ud14c\uc2a4\ud2b8\ub294 \ub2e8\uc21c\ud788 \ubb38\uc81c\ub97c \ud478\ub294 \uac83\uc774 \uc544\ub2c8\ub77c, \ucd5c\uc801\uc758 \ud574\uacb0 \ubc29\ubc95\uc744 \ucc3e\uc544\ub0b4\ub294 \uac83\uc774 \uc911\uc694\ud569\ub2c8\ub2e4.<\/p>\n <\/body><\/p>\n","protected":false},"excerpt":{"rendered":"N<\/code>\uc774 \uc788\uc744 \ub54c, \uc544\ub798\uc758 \uc138 \uac00\uc9c0 \uc5f0\uc0b0 \uc911 \ud558\ub098\ub97c \uc120\ud0dd\ud558\uc5ec \uc22b\uc790\ub97c \ubcc0\ud615\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4:<\/p>\n\n
N - 1<\/code><\/li>\nN \/ 2<\/code> (\ub2e8, N\uc774 \uc9dd\uc218\uc77c \ub54c\ub9cc \uac00\ub2a5)<\/li>\nN \/ 3<\/code> (\ub2e8, N\uc774 3\uc73c\ub85c \ub098\ub204\uc5b4 \ub5a8\uc5b4\uc9c8 \ub54c\ub9cc \uac00\ub2a5)<\/li>\n<\/ul>\nN<\/code>\uc744 1\ub85c \ub9cc\ub4dc\ub294 \ucd5c\uc18c\uc758 \uc5f0\uc0b0 \ud69f\uc218\ub97c \uad6c\ud558\ub294 \uac83\uc785\ub2c8\ub2e4.<\/p>\n\uc608\uc81c \uc785\ub825 \ubc0f \ucd9c\ub825<\/h2>\n
\n
N = 10<\/code><\/li>\n3<\/code> (10 \u2192 9 \u2192 3 \u2192 1)<\/li>\n<\/ul>\n\ubb38\uc81c \ud574\uacb0\uc744 \uc704\ud55c \uc811\uadfc\ubc95<\/h2>\n
1. DFS (Depth-First Search)<\/h3>\n
N=10<\/code>\uc758 \uacbd\uc6b0 \ub098\uc62c \uc218 \uc788\ub294 \uacbd\ub85c\uc758 \uc218\uac00 \ub9ce\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4. \uadf8\ub7fc\uc5d0\ub3c4 \ubd88\uad6c\ud558\uace0 DFS\ub85c \uc811\uadfc\ud574\ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\nDFS \uad6c\ud604 \ucf54\ub4dc<\/h4>\n
\nimport java.util.HashMap;\n\npublic class Main {\n static int minSteps = Integer.MAX_VALUE;\n \n public static void main(String[] args) {\n int N = 10;\n findSteps(N, 0);\n System.out.println(\"Minimum steps to reach 1: \" + minSteps);\n }\n \n private static void findSteps(int N, int steps) {\n if (N == 1) {\n minSteps = Math.min(minSteps, steps);\n return;\n }\n \n findSteps(N - 1, steps + 1); \/\/ Decrement\n if (N % 2 == 0) {\n findSteps(N \/ 2, steps + 1); \/\/ Divide by 2\n }\n if (N % 3 == 0) {\n findSteps(N \/ 3, steps + 1); \/\/ Divide by 3\n }\n }\n}\n<\/pre>\n<\/div>\nN<\/code>\uc5d0\uc11c \uac00\ub2a5\ud55c \ubaa8\ub4e0 \uacbd\ub85c\ub97c \ud0d0\uc0c9\ud569\ub2c8\ub2e4. \uadf8\ub7ec\ub098 \uc774 \ubc29\ubc95\uc740 \uc911\ubcf5 \ud638\ucd9c \ubc0f \ube44\ud6a8\uc728\uc801\uc778 \uacbd\ub85c \ud0d0\uc0c9\uc73c\ub85c \uc778\ud574 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\uac00 O(3^N)<\/code>\uc785\ub2c8\ub2e4.<\/p>\n2. DP (Dynamic Programming)<\/h3>\n
DP \uad6c\ud604 \ucf54\ub4dc<\/h4>\n
\npublic class Main {\n public static void main(String[] args) {\n int N = 10;\n System.out.println(\"Minimum steps to reach 1: \" + minStepsDP(N));\n }\n\n private static int minStepsDP(int N) {\n int[] dp = new int[N + 1];\n dp[1] = 0; \/\/ 1\ub85c \uac00\ub294 \ucd5c\uc18c \uc5f0\uc0b0 \ud69f\uc218\ub294 0\n \n for (int i = 2; i <= N; i++) {\n dp[i] = dp[i - 1] + 1; \/\/ Decrement\n\n if (i % 2 == 0) {\n dp[i] = Math.min(dp[i], dp[i \/ 2] + 1); \/\/ Divide by 2\n }\n if (i % 3 == 0) {\n dp[i] = Math.min(dp[i], dp[i \/ 3] + 1); \/\/ Divide by 3\n }\n }\n \n return dp[N];\n }\n}\n<\/pre>\n<\/div>\ndp<\/code>\ub97c \uc0ac\uc6a9\ud558\uc5ec \uac01 \uc22b\uc790\uae4c\uc9c0 \uac00\uae30 \uc704\ud55c \ucd5c\uc18c \ub2e8\uacc4\ub97c \uc800\uc7a5\ud569\ub2c8\ub2e4. \uc54c\uace0\ub9ac\uc998\uc740 O(N)<\/code>\uc758 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\ub97c \uac00\uc9d1\ub2c8\ub2e4. \uac01\uac01\uc758 \uc22b\uc790\uc5d0 \ub300\ud574 \uc774\uc804 \uc22b\uc790\ub4e4\uc758 \uac12\uc744 \ucc38\uc870\ud558\uc5ec \ucd5c\uc18c \ub2e8\uacc4\ub97c \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/p>\n\uc2dc\uac04 \ubcf5\uc7a1\ub3c4 \ubd84\uc11d<\/h2>\n
O(3^N)<\/code>\ub85c \ub9e4\uc6b0 \ube44\ud6a8\uc728\uc801\uc785\ub2c8\ub2e4. \ubc18\uba74 DP \uc811\uadfc\ubc95\uc740 O(N)<\/code>\uc758 \uc2dc\uac04 \ubcf5\uc7a1\ub3c4\ub97c \uac00\uc9c0\uba70, \uc774\ub294 \ubaa8\ub4e0 \uc22b\uc790\uc5d0 \ub300\ud574 \ucd5c\ub300 \ud55c \ubc88\uc758 \uacc4\uc0b0\uc73c\ub85c \ucd5c\uc18c \ub2e8\uacc4\ub97c \ub3c4\ucd9c\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\uacb0\ub860<\/h2>\n
\uc5f0\uc2b5\ubb38\uc81c<\/h2>\n
\n
N = 15<\/code>\uc77c \ub54c, 1\ub85c \ub9cc\ub4e4\uae30 \uc704\ud55c \ucd5c\uc18c \uc5f0\uc0b0 \ud69f\uc218\ub97c \uad6c\ud558\uc138\uc694.<\/li>\nN = 25<\/code>\uc77c \ub54c, 1\ub85c \ub9cc\ub4e4\uae30 \uc704\ud55c \ucd5c\uc18c \uc5f0\uc0b0 \ud69f\uc218\ub97c \uad6c\ud558\uc138\uc694.<\/li>\n<\/ul>\n