\n This is a problem to find the K-th smallest number in a specific range when an array is given.
\n Given an integer array and two integers L and R, as well as K,
\n write an algorithm that returns the K-th smallest number among the numbers from L to R.\n <\/p>\n
\n - The first line contains N (1 \u2264 N \u2264 100,000) and Q (1 \u2264 Q \u2264 100,000).\n - The second line contains N integers A\u2081, A\u2082, ..., A\u2099 (-1,000,000,000 \u2264 A\u1d62 \u2264 1,000,000,000).\n - Following this, Q queries are given, each in the form of L, R, K.\n <\/pre>\nOutput Format<\/h2>\n
\n For each query, output the K-th smallest number.
\n Each output should be printed on a new line.\n <\/p>\nExample<\/h2>\n
\n Input\n 5 3\n 1 5 2 6 3\n 2 4 3\n 1 5 2\n 2 5 1\n\n Output\n 5\n 2\n 3\n <\/pre>\nProblem Solving Process<\/h2>\n
\n This problem fundamentally deals with interval queries.
\n While processing multiple queries, one must consider an optimal algorithm to find the K-th number each time in the interval.\n <\/p>\nStep 1: Problem Analysis<\/h3>\n
\n Given an array with N elements and Q queries,
\n each query must find the K-th number from the subarray of the array.
\n If the interval of the array is sorted every time to find the K-th number, it would take O(N * log(N)) time, which is
\n inefficient. The chances decrease as the number of queries increases.\n <\/p>\nStep 2: Designing a Solution Method<\/h3>\n
\n To solve this problem, the following methods can be used:
\n – **Peek Algorithm**: Sort the numbers in the interval to efficiently find the K-th number.
\n – **Counting Sort or Subarray Sorting**: Sort the subarray first and then find the K-th number.\n <\/p>\nStep 3: Algorithm Implementation<\/h3>\n
\n\n func kthSmallest(arr: [Int], l: Int, r: Int, k: Int) -> Int {\n var subArray = Array(arr[l...r]) \/\/ Create subarray\n subArray.sort() \/\/ Sort\n return subArray[k - 1] \/\/ Return K-th smallest number\n }\n\n func solveProblem(arr: [Int], queries: [(Int, Int, Int)]) {\n for query in queries {\n let (l, r, k) = query\n let answer = kthSmallest(arr: arr, l: l, r: r, k: k)\n print(answer)\n }\n }\n <\/pre>\n<\/div>\nStep 4: Time Complexity Analysis<\/h2>\n
\n The above algorithm takes O(N log N) time for each query, so
\n when processing Q queries, the worst-case time complexity is O(Q * N log N).
\n This is very large, so we need to solve this problem more efficiently.\n <\/p>\nEfficient Solution Method: Segment Tree or Fenwick Tree<\/h3>\n
\n An efficient method could utilize a segment tree or a Fenwick tree to find the K-th number
\n in each interval. However, this part will not be covered here.\n <\/p>\nStep 5: Conclusion<\/h2>\n
\n We have examined the process of solving the problem of finding the K-th number.
\n Although approached by sorting the interval for each query,
\n using a more efficient method can lead to faster query processing.
\n This will be covered in the next lecture.\n <\/p>\nConclusion<\/h2>\n
\n Understanding the problem accurately and designing an efficient algorithm is very important
\n in solving coding test problems.
\n Try various methods and establish your own approach.
\n The next lecture will cover more advanced topics such as the application of data structures.
\n Thank you!\n <\/p>\n<\/body><\/p>\n","protected":false},"excerpt":{"rendered":"