Else arr[minInd[ind]+1..i] has sum greater than k. Compare its length with maximum length found so far. P2 ) Given an array containing N integers and an integer K., Your task is to find the length of the longest Sub-Array with the sum of the elements equal to the given value K.Example 1: Input :A[] = {10, 5, 2, 7, 1, 9}K = 15Output : 4Explanation:The sub-array is {5, 2, 7, 1}.Example 2:Input : A[] = {-1, 2, 3}K = 6Output : 0Explanation: There is no such sub-array with sum 6.Your Task:This is a function problem. Expected Time Complexity: O (N) Expected Auxiliary Space: O (N) Constraints: 1<=n<=105 -105<=a [i]<=105 1<=k<=n Company Tags Topic Tags rev2023.7.17.43536. This article is being improved by another user right now. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Time Complexity : O(n), where n represents the size of the given array.Auxiliary Space: O(1), no extra space is required, so it is a constant. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. If minInd[ind] is greater than i, then no subarray exists having sum -x in range[0..i-1]. Is the DC of the Swarmkeeper ranger's Gathered Swarm feature affected by a Moon Sickle? Let this value be x. What could be the meaning of "doctor-testing of little girls" by Steinbeck? Specifically, I did not understand the following: What is the use of minInd in keeping track of largest subarray? Longest subarray with sum divisible by K Medium Accuracy: 33.72% Submissions: 43K+ Points: 4 Given an array containing N integers and a positive integer K, find the length of the longest sub array with sum of the elements divisible by the given value K. Example 1: How to calculate time complexity of a randomized search algorithm? Your Task: You don't need to read input or print anything. Why is that so many apps today require a MacBook with an M1 chip? acknowledge that you have read and understood our. What is the relational antonym of 'avatar'? If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. Asking for help, clarification, or responding to other answers. If yes then increment the length of the longest subarray by 1. rev2023.7.17.43536. This article is being improved by another user right now. MathJax reference. We will let left_p be the index of $p_i$ in left. If not then lets break this prefix array in two sub prefix sum array and add both of them in the queue. We can improve your code and speed it up from $O(n^2)$ to $O(n \cdot \log n)$ with one change. Stack Exchange network consists of 182 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. e.g: at index 2 in input array sum of all the elements before and including it : -2+3+1=2. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Now the problem is to find the largest $j-i$ such that $j>i$ and $p_j-p_i>k$. Companies Given an integer array nums, find the subarray with the largest sum, and return its sum. Create another array minInd[], in which minInd[i] stores the minimum index value in range [0..i] in sorted prefix sum vector. Start practicing on your own: https://practice.geeksforgeeks.org/explore/?page=1Follow us and stay updated on everything happening in the world of geeks:Twitter- https://twitter.com/geeksforgeeksLinkedIn- https://www.linkedin.com/company/geeksforgeeksFacebook- https://www.facebook.com/geeksforgeeks.orgInstagram- https://www.instagram.com/geeks_for_geeks/?hl=en#GFGPractice #GeeksforGeeks #PracticeProblems #CodingQuestions Submit your solutions here-: https://practice.geeksforgeeks.org/problems/longest-subarray-with-sum-divisible-by-k1259/1Free resources that can never be matched, presented to all our Geeks for free! Longest Subarray with given Sum K (Positives) Problem Statement: Given an array and a sum k, we need to print the length of the longest subarray that sums to k. Examples Practice: Solve Problem Disclaimer: Don't jump directly to the solution, try it out yourself first. Given an array of integers, our goal is to find the length of the largest subarray having the sum of its elements at most k where k>0. - Second part ( slight change) consisting of prefix sum array from start+1 to end. Not the answer you're looking for? Multiplication implemented in c++ with constant time, Bass line and chord mismatch - Afternoon in Paris, Rivers of London short about Magical Signature, Find out all the different files from two different paths efficiently in Windows (with Python). Time Complexity: O(n)Auxiliary Space: O(n). Method 2 (Efficient): An efficient approach is to use the sliding window technique. 53 upvotes. Let $p=(p_0, p_1, \cdots, p_n)$ be the array of the prefix sums, where $p_0=0$, $p_1=a_1$, $p_2=a_1+a_2$, etc. So increase count by the number of such subarrays. By clicking Post Your Answer, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct. If the sum is equal to the required sum, then increment the count of subarrays. Store their index too. Since the important index array forms a strictly decreasing subsequence we can perform binary search without any issue. Calculate prefix sum 2. for i in 1..n: for j in 1..i: if presum[i] - presum[j-1] > k: . To add x to sum, -x can be subtracted from it because sum- (-x) = sum + x. Suppose $(p_i,p_j)$ is a pair such that $j>i$ and $p_j-p_i>k$. Where to start with a large crack the lock puzzle like this? Subarray Sum Equals K Medium 18.9K 549 Companies Given an array of integers nums and an integer k, return the total number of subarrays whose sum equals to k. A subarray is a contiguous non-empty sequence of elements within an array. I was trying to understand the code at https://www.geeksforgeeks.org/largest-subarray-having-sum-greater-than-k/amp/. If the sum is less than or equal to k, then a value greater than or equal to k + 1 - sum has to be added to sum to make it at least k+1. largest sum of contiguous subarray No Larger than k, Length of longest subarray of sum less than or equal to k, Maximum sum of contiguous sub-sequence with length at most k, partition of array into k contiguous subarrays such that bitwise AND of sum of each subarray is maximum, Find maximum subarray using binary search, Multiplication implemented in c++ with constant time. 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Longest Subarray With Sum K . 75 % . 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What is the state of the art of splitting a binary file by size? This solution doesn't follow geeksforgeeks precisely but will give you O(N Log N) solution. Further optimization : you can use memoization to reduce branching . Otherwise, the current longest subarray is equal to 1. Start practicing on your own: https://practice.geeksforgeeks.org/explore/?utm_source=youtube\u0026utm_medium=courseteam_practice_desc\u0026utm_campaign=problem_of_the_day-----------------------------------------------------------------------------------------Follow us and stay updated on everything happening in the world of geeks: Twitter- https://twitter.com/geeksforgeeks LinkedIn- https://www.linkedin.com/company/geeksforgeeks Facebook- https://www.facebook.com/geeksforgeeks.org Instagram- https://www.instagram.com/geeks_for_geeks/?hl=en#GFGPractice #GeeksforGeeks #PracticeProblems #CodingQuestions By using our site, you Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Find out all the different files from two different paths efficiently in Windows (with Python). Starting the Prompt Design Site: A New Home in our Stack Exchange Neighborhood. Expected Time Complexity: O (N) Expected Auxiliary Space: O (1) Constraints: 1 <= N <= 105 -105 <= A [i] <= 105 Topic Tags Data Structure & Algorithm Classes (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Full Stack Development with React & Node JS(Live), Top 100 DSA Interview Questions Topic-wise, Top 20 Interview Questions on Greedy Algorithms, Top 20 Interview Questions on Dynamic Programming, Top 50 Problems on Dynamic Programming (DP), Commonly Asked Data Structure Interview Questions, Top 20 Puzzles Commonly Asked During SDE Interviews, Top 10 System Design Interview Questions and Answers, Business Studies - Paper 2019 Code (66-2-1), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Number of subsequences with positive product, Find the Maximum Alternate Subsequence Sum from a given array, Count of subsequences whose product is a difference of square of two integers, Find the count of subsequences where each element is divisible by K, Find maximum sum of subsequence after flipping signs of at most K elements in given Array, Find the minimum number of elements that should be removed to make an array good, Count of distinct GCDs among all the non-empty subsequences of given array, Number of Subsequences with Even and Odd Sum | Set 2, Maximize value of K such that a subsequence with sum i exists for each integer i in range [1, K], Count of all subsequence whose product is a Composite number, Print all subsequences in first decreasing then increasing by selecting N/2 elements from [1, N], Length of Longest Prime Subsequence in an Array, Count subsequence of length 4 having product of the first three elements equal to the fourth element, Number of Subsequences with Even and Odd Sum, Sum of minimum element of all sub-sequences of a sorted array, Cost of creating smallest subsequence with sum of difference between adjacent elements maximum, Check whether the product of every subsequence is a perfect square or not, Maximum Sum Subsequence made up of consecutive elements of different parity, Min and max length subarray having adjacent element difference atmost K, Range Queries for number of Armstrong numbers in an array with updates. Illustration with an example would be highly appreciated. Length of Longest Subarray with same elements in atmost K increments, Maximize length of longest subarray consisting of same elements by at most K decrements, Longest subarray with all even or all odd elements, Minimum cost to convert all elements of a K-size subarray to 0 from given Ternary Array with subarray sum as cost, Maximum length of subarray such that all elements are equal in the subarray, Maximize the subarray sum after multiplying all elements of any subarray with X, Longest subarray in which all elements are greater than K, Longest subarray in which all elements are a factor of K, Longest subarray in which all elements are smaller than K, Length of longest subarray in which elements greater than K are more than elements not greater than K, Mathematical and Geometric Algorithms - Data Structure and Algorithm Tutorials, Learn Data Structures with Javascript | DSA Tutorial, Introduction to Max-Heap Data Structure and Algorithm Tutorials, Introduction to Set Data Structure and Algorithm Tutorials, Introduction to Map Data Structure and Algorithm Tutorials, A-143, 9th Floor, Sovereign Corporate Tower, Sector-136, Noida, Uttar Pradesh - 201305, We use cookies to ensure you have the best browsing experience on our website. 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