1 \u2264 i \u2264 j \u2264 N<\/li>\n<\/ul>\n<\/blockquote>\nInput Example<\/h2>\n
The input format is as follows:<\/p>\n
\n 5 3\n 1 2 3 4 5\n 1 3\n 2 4\n 1 5\n <\/pre>\nIn the above input, the first line represents the size of the array N and the number of queries M. The second line contains the elements of the array A. The subsequent M lines represent each query.<\/p>\n
Output Example<\/h2>\n
The sum for each of the queries from the input should be output.<\/p>\n
\n 6\n 9\n 15\n <\/pre>\nProblem Solving Method<\/h2>\n
A efficient way to solve this problem is to use prefix sums<\/strong>. That is, by calculating the prefix sums of array A in advance, we can determine the sum of each query in constant time.<\/p>\nStep 1: Calculate Prefix Sums<\/h3>\n
Create a prefix sum array prefixSum<\/code> such that prefixSum[i]<\/code> stores the sum of the first element of array A up to the i-th element.<\/p>\n\n let N = 5\n let A = [1, 2, 3, 4, 5]\n var prefixSum = [Int](repeating: 0, count: N + 1)\n\n for i in 1...N {\n prefixSum[i] = prefixSum[i - 1] + A[i - 1]\n }\n <\/pre>\nStep 2: Process Queries<\/h3>\n
When processing the queries, use prefixSum[j] - prefixSum[i - 1]<\/code> to obtain the sum from i to j. This allows the time complexity for each query to be O(1).<\/p>\n\n let queries = [(1, 3), (2, 4), (1, 5)]\n for query in queries {\n let i = query.0\n let j = query.1\n let result = prefixSum[j] - prefixSum[i - 1]\n print(result)\n }\n <\/pre>\nComplete Code<\/h2>\n
Combining the above explanations, the complete code is as follows.<\/p>\n
\n let firstLine = readLine()!.split(separator: \" \").map { Int($0)! }\n let N = firstLine[0] \/\/ Size of the array\n let M = firstLine[1] \/\/ Number of queries\n\n let A = readLine()!.split(separator: \" \").map { Int($0)! }\n var prefixSum = [Int](repeating: 0, count: N + 1)\n\n for i in 1...N {\n prefixSum[i] = prefixSum[i - 1] + A[i - 1]\n }\n\n for _ in 0..\nTime Complexity<\/h2>\n
The time complexity of this algorithm is O(N + M). Here, N is the size of array A, and M is the number of queries. This is due to the O(N) for summing all elements of A and O(M) for processing M queries combined.<\/p>\n
Conclusion<\/h2>\n
In this lecture, we learned how to use prefix sums to solve the range sum problem. This method can significantly improve performance. I encourage you to apply this technique when solving similar problems in the future.<\/p>\n
<\/m><\/body><\/p>\n","protected":false},"excerpt":{"rendered":"
In this lecture, we will learn how to solve the range sum problem using Swift. Problem Description Let’s consider the following problem. An array A consisting of N integers and M queries are given. Each query is provided as two integers i and j, and we need to calculate the sum from A[i] to A[j]. … \ub354 \ubcf4\uae30 “Swift Coding Test Course, Finding the Sum of Intervals 3”<\/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":[129],"tags":[],"class_list":["post-34688","post","type-post","status-publish","format-standard","hentry","category-swift-coding-test"],"yoast_head":"\nSwift Coding Test Course, Finding the Sum of Intervals 3 - \ub77c\uc774\ube0c\uc2a4\ub9c8\ud2b8<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/atmokpo.com\/w\/34688\/\" \/>\n<meta property=\"og:locale\" content=\"ko_KR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Swift Coding Test Course, Finding the Sum of Intervals 3 - \ub77c\uc774\ube0c\uc2a4\ub9c8\ud2b8\" \/>\n<meta property=\"og:description\" content=\"In this lecture, we will learn how to solve the range sum problem using Swift. 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