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<\/p>\n

\uc548\ub155\ud558\uc138\uc694! \uc624\ub298\uc740 \uc790\ubc14 \ucf54\ub529 \ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc790\uc8fc \ucd9c\uc81c\ub418\ub294 \ubb38\uc81c \uc911 \ud558\ub098\uc778 ‘\uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4(LIS: Longest Increasing Subsequence)’ \ucc3e\uae30 \ubb38\uc81c\ub97c \ub2e4\ub8e8\uc5b4\ubcf4\ub824 \ud569\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub294 \uc8fc\uc5b4\uc9c4 \uc218\uc5f4\uc5d0\uc11c \uc120\ud0dd\ub41c \uc6d0\uc18c\ub4e4\uc758 \uac12\uc774 \uc99d\uac00\ud558\ub294 \uac00\uc7a5 \uae34 \ubd80\ubd84 \uc218\uc5f4\uc758 \uae38\uc774\ub97c \ucc3e\ub294 \uac83\uc785\ub2c8\ub2e4. \ubcf5\uc7a1\ud55c \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ucc98\ub7fc \ubcf4\uc77c \uc218 \uc788\uc9c0\ub9cc, \ud6a8\uc728\uc801\uc778 \uc811\uadfc \ubc29\ubc95\uc744 \ud1b5\ud574 \ud574\uacb0\ud560 \uc218 \uc788\uc73c\uba70, \uc774\ub97c \ud1b5\ud574 \ucf54\ub529 \ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc810\uc218\ub97c \ud5a5\uc0c1\uc2dc\ud0ac \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n

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

\uc8fc\uc5b4\uc9c4 \uc815\uc218 \ubc30\uc5f4\uc774 \uc788\uc2b5\ub2c8\ub2e4. \uc774 \ubc30\uc5f4\uc5d0\uc11c \uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4\uc744 \ucc3e\uc544 \uadf8 \uae38\uc774\ub97c \ubc18\ud658\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc138\uc694. \uc608\ub97c \ub4e4\uc5b4:<\/p>\n

\uc785\ub825: [10, 9, 2, 5, 3, 7, 101, 18]\n\ucd9c\ub825: 4\n\uc124\uba85: \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4\uc740 [2, 3, 7, 101]\ub85c \uae38\uc774\uac00 4\uc785\ub2c8\ub2e4.<\/code><\/pre>\n\ubb38\uc81c \ud574\uacb0 \ubc29\ubc95<\/h2>\n\uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574 \uc5ec\ub7ec \uac00\uc9c0 \uc811\uadfc \ubc29\uc2dd\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uac00\uc7a5 \uc9c1\uad00\uc801\uc778 \ubc29\ubc95 \uc911 \ud558\ub098\ub294 \ub3d9\uc801 \ud504\ub85c\uadf8\ub798\ubc0d(Dynamic Programming)<\/strong> \uae30\ubc95\uc744 \uc0ac\uc6a9\ud558\ub294 \uac83\uc785\ub2c8\ub2e4. \uc774 \ubc29\ubc95\uc744 \uc0ac\uc6a9\ud558\uba74 O(n^2)\uc758 \uc2dc\uac04\ubcf5\uc7a1\ub3c4\ub85c \ubb38\uc81c\ub97c \ud574\uacb0\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \ub610\ud55c, \uc774 \ubb38\uc81c\ub97c \ub354\uc6b1 \ucd5c\uc801\ud654\ud558\uba74 O(n log n) \uc2dc\uac04\ubcf5\uc7a1\ub3c4\ub85c\ub3c4 \ud574\uacb0\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ubc88 \uae00\uc5d0\uc11c\ub294 \ub450 \uac00\uc9c0 \ubc29\ubc95\uc744 \ubaa8\ub450 \ub2e4\ub8e8\uc5b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n
1. \ub3d9\uc801 \ud504\ub85c\uadf8\ub798\ubc0d\uc744 \uc0ac\uc6a9\ud55c \ubc29\ubc95<\/h3>\n\uba3c\uc800, \ub3d9\uc801 \ud504\ub85c\uadf8\ub798\ubc0d\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc774 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc774 \ubc29\ubc95\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \uc808\ucc28\ub85c \uc9c4\ud589\ub429\ub2c8\ub2e4:<\/p>\n
\n\uae38\uc774\ub97c n\uc778 \ubc30\uc5f4\uc774 \uc8fc\uc5b4\uc9c8 \ub54c, n \ud06c\uae30\uc758 DP \ubc30\uc5f4\uc744 \uc0dd\uc131\ud569\ub2c8\ub2e4. DP \ubc30\uc5f4\uc758 \uac01 \uc6d0\uc18c\ub294 \ud574\ub2f9 \uc778\ub371\uc2a4\uae4c\uc9c0\uc758 \uac00\uc7a5 \uae34 \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4\uc758 \uae38\uc774\ub97c \uc800\uc7a5\ud569\ub2c8\ub2e4.<\/li>\n
DP \ubc30\uc5f4\uc758 \ucd08\uae30\uac12\uc73c\ub85c \ubaa8\ub450 1\uc744 \uc124\uc815\ud569\ub2c8\ub2e4. (\uac01 \uc6d0\uc18c\ub294 \ucd5c\uc18c\ud55c \uc790\uae30 \uc790\uc2e0\uc73c\ub85c\ub9cc \uad6c\uc131\ub41c \ubd80\ubd84 \uc218\uc5f4\uc744 \uac00\uc9c8 \uc218 \uc788\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4.)<\/li>\n
\uc774\uc911 \ub8e8\ud504\ub97c \uc774\uc6a9\ud558\uc5ec \uac01 \uc6d0\uc18c\ub97c \ud655\uc778\ud558\uace0, \uc774\uc804 \uc6d0\uc18c\ub4e4\uacfc \ube44\uad50\ud558\uc5ec \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4\uc758 \uae38\uc774\ub97c \uc5c5\ub370\uc774\ud2b8\ud569\ub2c8\ub2e4.<\/li>\n
\ucd5c\uc885\uc801\uc73c\ub85c DP \ubc30\uc5f4\uc5d0\uc11c \uac00\uc7a5 \ud070 \uac12\uc744 \ubc18\ud658\ud569\ub2c8\ub2e4.<\/li>\n<\/ol>\n\uc774\uc81c \uc774\ub97c \uc790\ubc14\ub85c \uad6c\ud604\ud574 \ubd05\uc2dc\ub2e4.<\/p>\n
public class LongestIncreasingSubsequence {\n\n    public static int lengthOfLIS(int[] nums) {\n        if (nums == null || nums.length == 0) {\n            return 0;\n        }\n        \n        int n = nums.length;\n        int[] dp = new int[n];\n        \n        \/\/ \ubaa8\ub4e0 \uc218\uc5f4\uc758 \uae38\uc774\ub97c 1\ub85c \ucd08\uae30\ud654\n        for (int i = 0; i < n; i++) {\n            dp[i] = 1;\n        }\n        \n        for (int i = 1; i < n; i++) {\n            for (int j = 0; j < i; j++) {\n                if (nums[i] > nums[j]) {\n                    dp[i] = Math.max(dp[i], dp[j] + 1);\n                }\n            }\n        }\n        \n        \/\/ DP \ubc30\uc5f4\uc5d0\uc11c \ucd5c\ub300\uac12 \ucc3e\uae30\n        int maxLength = 0;\n        for (int length : dp) {\n            maxLength = Math.max(maxLength, length);\n        }\n        \n        return maxLength;\n    }\n\n    public static void main(String[] args) {\n        int[] nums = {10, 9, 2, 5, 3, 7, 101, 18};\n        System.out.println(\"\uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4\uc758 \uae38\uc774: \" + lengthOfLIS(nums));\n    }\n}<\/code><\/pre>\n\ucf54\ub4dc \ubd84\uc11d<\/h4>\n\uc704\uc758 \ucf54\ub4dc\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ub2e8\uacc4\ub85c \uc9c4\ud589\ub429\ub2c8\ub2e4:<\/p>\n
\n\uc8fc\uc5b4\uc9c4 \ubc30\uc5f4\uc774 null\uc774\uac70\ub098 \uae38\uc774\uac00 0\uc774\uba74 0\uc744 \ubc18\ud658\ud569\ub2c8\ub2e4.<\/li>\n
DP \ubc30\uc5f4\uc744 \ucd08\uae30\ud654\ud558\uc5ec \ubaa8\ub4e0 \uac12\uc774 1\uc774 \ub418\ub3c4\ub85d \uc124\uc815\ud569\ub2c8\ub2e4.<\/li>\n
\uc774\uc911 \ub8e8\ud504\ub97c \ud1b5\ud574 \uac01 \uc6d0\uc18c\ub97c \ube44\uad50\ud558\uc5ec \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4\uc758 \uae38\uc774\ub97c \uc5c5\ub370\uc774\ud2b8\ud569\ub2c8\ub2e4.<\/li>\n
\ucd5c\uc885\uc801\uc73c\ub85c DP \ubc30\uc5f4\uc5d0\uc11c \uac00\uc7a5 \uae34 \uc218\uc5f4\uc758 \uae38\uc774\ub97c \ucc3e\uc544 \ubc18\ud658\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n2. O(n log n) \ubc29\ubc95<\/h3>\n\ub2e4\uc74c\uc73c\ub85c, O(n log n) \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc774 \ubc29\ubc95\uc740 \uc774\uc9c4 \ud0d0\uc0c9(Binary Search)\uc744 \ud1b5\ud574 \ubcf4\ub2e4 \ud6a8\uc728\uc801\uc73c\ub85c \ubb38\uc81c\ub97c \ud574\uacb0\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774 \uc54c\uace0\ub9ac\uc998\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \uc808\ucc28\ub97c \ub530\ub985\ub2c8\ub2e4:<\/p>\n
\n\ube44\uc5b4\uc788\ub294 \ub9ac\uc2a4\ud2b8\ub97c \uc0dd\uc131\ud569\ub2c8\ub2e4.<\/li>\n
\uc785\ub825 \ubc30\uc5f4\uc758 \uac01 \uc694\uc18c\ub97c \uc21c\ud68c\ud569\ub2c8\ub2e4. \ub9ac\uc2a4\ud2b8\uc758 \ub9c8\uc9c0\ub9c9 \uc6d0\uc18c\ubcf4\ub2e4 \ud070 \uacbd\uc6b0, \ud574\ub2f9 \uc6d0\uc18c\ub97c \ub9ac\uc2a4\ud2b8\uc5d0 \ucd94\uac00\ud569\ub2c8\ub2e4.<\/li>\n
\ub9ac\uc2a4\ud2b8\uc758 \ub9c8\uc9c0\ub9c9 \uc6d0\uc18c\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uacbd\uc6b0, \uc774\uc9c4 \ud0d0\uc0c9\uc744 \ud1b5\ud574 \ub9ac\uc2a4\ud2b8\uc5d0\uc11c \ud574\ub2f9 \uc6d0\uc18c\uac00 \ub4e4\uc5b4\uac08 \uc704\uce58\ub97c \ucc3e\uc740 \ud6c4 \uadf8 \uc704\uce58\uc758 \uc6d0\uc18c\ub97c \ub300\uccb4\ud569\ub2c8\ub2e4.<\/li>\n
\ub9ac\uc2a4\ud2b8\uc758 \uae38\uc774\uac00 \uacb0\uad6d \uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4\uc758 \uae38\uc774\uac00 \ub429\ub2c8\ub2e4.<\/li>\n<\/ol>\n\uc774\uc81c \uc774\ub97c \uc790\ubc14\ub85c \uad6c\ud604\ud574 \ubcf4\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n
import java.util.ArrayList;\nimport java.util.List;\n\npublic class LongestIncreasingSubsequenceBinarySearch {\n\n    public static int lengthOfLIS(int[] nums) {\n        List lis = new ArrayList<>();\n        \n        for (int num : nums) {\n            int index = binarySearch(lis, num);\n            if (index == lis.size()) {\n                lis.add(num);\n            } else {\n                lis.set(index, num);\n            }\n        }\n        \n        return lis.size();\n    }\n\n    private static int binarySearch(List lis, int num) {\n        int left = 0, right = lis.size();\n\n        while (left < right) {\n            int mid = left + (right - left) \/ 2;\n            if (lis.get(mid) < num) {\n                left = mid + 1;\n            } else {\n                right = mid;\n            }\n        }\n        \n        return left;\n    }\n\n    public static void main(String[] args) {\n        int[] nums = {10, 9, 2, 5, 3, 7, 101, 18};\n        System.out.println(\"\uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4\uc758 \uae38\uc774: \" + lengthOfLIS(nums));\n    }\n}<\/integer><\/integer><\/code><\/pre>\n\ucf54\ub4dc \ubd84\uc11d<\/h4>\n\uc704\uc758 \ucf54\ub4dc \ubd84\uc11d\uc740 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n
\n\ube48 \ub9ac\uc2a4\ud2b8\ub97c \uc0dd\uc131\ud558\uc5ec \uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4\uc744 \uc800\uc7a5\ud569\ub2c8\ub2e4.<\/li>\n
\uac01 \uc6d0\uc18c\ub97c \uc21c\ud68c\ud558\uba70 \uc774\uc9c4 \ud0d0\uc0c9\uc744 \ud1b5\ud574 \ub4e4\uc5b4\uac08 \uc704\uce58\ub97c \ucc3e\uc2b5\ub2c8\ub2e4.<\/li>\n
\ub9ac\uc2a4\ud2b8\uc758 \ub9c8\uc9c0\ub9c9 \uc6d0\uc18c\ubcf4\ub2e4 \uc791\uc740 \uacbd\uc6b0 \ud574\ub2f9 \uc704\uce58\uc758 \uc6d0\uc18c\ub97c \ub300\uccb4\ud569\ub2c8\ub2e4.<\/li>\n
\ucd5c\uc885\uc801\uc73c\ub85c \ub9ac\uc2a4\ud2b8\uc758 \uae38\uc774\ub97c \ubc18\ud658\ud558\uc5ec \uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4\uc758 \uae38\uc774\ub97c \uc81c\uacf5\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\uacb0\ub860<\/h2>\n\uc624\ub298\uc740 \uc790\ubc14\ub97c \uc0ac\uc6a9\ud558\uc5ec ‘\uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4’ \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ub450 \uac00\uc9c0 \ubc29\ubc95\uc744 \uc54c\uc544\ubcf4\uc558\uc2b5\ub2c8\ub2e4. \ub3d9\uc801 \ud504\ub85c\uadf8\ub798\ubc0d\uc744 \uc0ac\uc6a9\ud55c O(n^2) \ubc29\ubc95\uacfc \uc774\uc9c4 \ud0d0\uc0c9\uc744 \ud65c\uc6a9\ud55c O(n log n) \ubc29\ubc95\uc744 \ud1b5\ud574 \ubb38\uc81c\ub97c \ud574\uacb0\ud560 \uc218 \uc788\uc5c8\uc2b5\ub2c8\ub2e4. \uc774 \ub450 \uac00\uc9c0 \uc811\uadfc\ubc95\uc744 \ud1b5\ud574 \ucf54\ub529 \ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc720\uc6a9\ud558\uac8c \ud65c\uc6a9\ud560 \uc218 \uc788\uc744 \uac83\uc785\ub2c8\ub2e4.<\/p>\n
\uc5ec\ub7ec\ubd84\uc774 \ucde8\uc5c5 \uc900\ube44\uc640 \ucf54\ub529 \ud14c\uc2a4\ud2b8 \uc900\ube44\uc5d0 \ub3c4\uc6c0\uc774 \ub418\uae38 \ubc14\ub78d\ub2c8\ub2e4. \uac10\uc0ac\ud569\ub2c8\ub2e4!<\/p>\n
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\uc548\ub155\ud558\uc138\uc694! \uc624\ub298\uc740 \uc790\ubc14 \ucf54\ub529 \ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc790\uc8fc \ucd9c\uc81c\ub418\ub294 \ubb38\uc81c \uc911 \ud558\ub098\uc778 ‘\uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4(LIS: Longest Increasing Subsequence)’ \ucc3e\uae30 \ubb38\uc81c\ub97c \ub2e4\ub8e8\uc5b4\ubcf4\ub824 \ud569\ub2c8\ub2e4. \uc774 \ubb38\uc81c\ub294 \uc8fc\uc5b4\uc9c4 \uc218\uc5f4\uc5d0\uc11c \uc120\ud0dd\ub41c \uc6d0\uc18c\ub4e4\uc758 \uac12\uc774 \uc99d\uac00\ud558\ub294 \uac00\uc7a5 \uae34 \ubd80\ubd84 \uc218\uc5f4\uc758 \uae38\uc774\ub97c \ucc3e\ub294 \uac83\uc785\ub2c8\ub2e4. \ubcf5\uc7a1\ud55c \uc54c\uace0\ub9ac\uc998 \ubb38\uc81c\ucc98\ub7fc \ubcf4\uc77c \uc218 \uc788\uc9c0\ub9cc, \ud6a8\uc728\uc801\uc778 \uc811\uadfc \ubc29\ubc95\uc744 \ud1b5\ud574 \ud574\uacb0\ud560 \uc218 \uc788\uc73c\uba70, \uc774\ub97c \ud1b5\ud574 \ucf54\ub529 \ud14c\uc2a4\ud2b8\uc5d0\uc11c \uc810\uc218\ub97c … \ub354 \ubcf4\uae30 “\uc790\ubc14 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4 \ucc3e\uae30”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[22],"tags":[],"class_list":["post-26710","post","type-post","status-publish","format-standard","hentry","category-22"],"yoast_head":"\n\uc790\ubc14 \ucf54\ub529\ud14c\uc2a4\ud2b8 \uac15\uc88c, \uac00\uc7a5 \uae38\uac8c \uc99d\uac00\ud558\ub294 \ubd80\ubd84 \uc218\uc5f4 \ucc3e\uae30 - 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