So a prefix array arr[0..j] (ji$ and $p_j-p_i>k$. Find an array of size N having exactly K subarrays with sum S, Number of ways to select equal sized subarrays from two arrays having atleast K equal pairs of elements, Count of subarrays having exactly K distinct elements, Count of subarrays having exactly K prime numbers, Count of subarrays having exactly K perfect square numbers, Count subarrays made up of elements having exactly K set bits, Count subarrays having exactly K elements occurring at least twice, Count subarrays having at least X distinct elements that occur exactly Y times, Count subarrays having sum of elements at even and odd positions equal, Count of subarrays having sum equal to its length, 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. First precompute all prefix sum. Your task is to complete the function maxSumWithK () which takes the array A [], its size N and an integer K as inputs and returns the value of the largest sum of the subarray containing at least k numbers. In the second part you have to subtract the first element from each element present in the sub array (if you check the attached image it will become quite apparent). You will be notified via email once the article is available for improvement. This article is being improved by another user right now. Let $P_t$ = the sum of the first $t$ elements. We will let right_p be the index of $p_j$ in right. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. The trivial approach is to do it in O(N^2) time. By using our site, you 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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Hopefully it will be clearer from the diagram. What would a potion that increases resistance to damage actually do to the body? Notes/C++/Java/Python codes: Longest Subarray with sum K [positives]: https://takeuforward.org/data-structure/longest-subarray-with-given-sum-k/Longest Subarray with sum K [positives + negatives]: https://takeuforward.org/arrays/longest-subarray-with-sum-k-postives-and-negatives/Problem links.Longest Subarray with sum K [positives]: https://bit.ly/3GHyBOSLongest Subarray with sum K [positives + negatives]: http://bit.ly/3mNSZ9uWe have solved the above problems, and we have gone from brute force and ended with the most optimal solution.Full Course: https://bit.ly/tufA2ZYtYou can follow me across social media, all my handles are below: Linkedin/Instagram/Telegram: https://linktr.ee/takeUforward0:00 Introduction of course Find maximum sum contiguous subarray such that the length of the subarray is less than equal to k? The minimum element of the important index array will always be the last one. Not the answer you're looking for? How should a time traveler be careful if they decide to stay and make a family in the past? rev2023.7.17.43536. After this, start traversing array arr[] and store sum of subarray arr[0..i] in sum. Input: arr [] = {6, 8, 14, 9, 4, 11, 10}, K = 13 Output: 2 Longest subarray with sum divisible by K | Problem of the Day: 16/05/22 | Yash Dwivedi GeeksforGeeks Practice 57.3K subscribers Subscribe 2.1K views 11 months ago #GeeksforGeeks. 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 We can improve your code and speed it up from $O(n^2)$ to $O(n \cdot \log n)$ with one change. What is the relational antonym of 'avatar'? See your article appearing on the GeeksforGeeks main page and help other Geeks. If not then lets break this prefix array in two sub prefix sum array and add both of them in the queue. Smallest subarray whose sum is multiple of array size, Print all subarrays with sum in a given range, Maximize subarray sum by inverting sign of elements of any subarray at most twice, Largest sum contiguous increasing subarray, Find Maximum Sum Strictly Increasing Subarray, Count of subarray that does not contain any subarray with sum 0, Minimum cost to convert all elements of a K-size subarray to 0 from given Ternary Array with subarray sum as cost, Longest subsequence where every character appears at-least k times, 1 to n bit numbers with no consecutive 1s in binary representation. Edit: I have found a solution which works in $O(n\log n)$. This solution doesn't follow geeksforgeeks precisely but will give you O(N Log N) solution. Thanks for contributing an answer to Stack Overflow! To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Now if your last value in the prefix sum array is greater than or equal to K then the index you used to create this array is the answer. 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 That means, we need only to search for $(p_i,p_j)$ where $p_i$ is the smallest element in some prefix of $p$ and $p_j$ is the largest element in some suffix of $p$. The minimum index value in range[0..ind] is minInd[ind]. If the sum is greater than k, then-largest subarray having a sum greater than k is arr [0..i] having length i + 1. Subscribe now and start practicing today: https://www.youtube.com/c/GeeksforGeeksPractice/videosDaily solutions are also uploaded exclusively on our channel! . An efficient solution is to use prefix sum and binary search. Your Task: You don't need to read input or print anything. - Second part ( slight change) consisting of prefix sum array from start+1 to end. The above code does the same way, whenever there does not exist any subarray of length $mid$ it removes the other half and continues to search for an answer in the lower half by decreasing the $high$ to $mid-1$. 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. 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). To find the prefix sum, binary search can be performed on the prefix sum vector. acknowledge that you have read and understood our. 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 = 15 Output : 4 Explanation: The sub-array is {5, 2, 7, 1}. You will be notified via email once the article is available for improvement. Input: arr [] = {-5, 8, -14, 2, 4, 12}, k = -5 Output: 5 Recommended Problem Longest Sub-Array with Sum K sliding-window Arrays +4 more Amazon Also, update the longest subarray with equal elements at each step of the iteration.Below is the implementation of the above approach: You will be notified via email once the article is available for improvement. Given an unsorted array of integers, find the number of subarrays having a sum exactly equal to a given number k. Input : arr[] = {10, 2, -2, -20, 10}, k = -10Output : 3Explanation: Subarrays: arr[03], arr[14], arr[3..4] have a sum exactly equal to -10. This solution does a binary search on the length of the subarray and chooses the maximum length of the subarray satisfying the property. Given an array arr[] of size N, the task is to find the largest subarray which consists of all equal elements.Examples: Input: arr[] = {1, 1, 2, 2, 2, 3, 3};Output: 3Explanation:Longest subarray with equal elements is {2, 2, 2}Input: arr[] = {1, 1, 2, 2, 2, 3, 3, 3, 3};Output: 4Explanation:Longest subarray with equal elements is {3, 3, 3, 3}. With this in mind we can define an index $j$ important, if there is no index $k < j$ such that $P_k \leq P_j$, i.e. Time Complexity: O(n)Auxiliary Space: O(n). Take the first content ( prefix sum array) out of the queue. The problem is to find the length of the longest sub-array having sum equal to the given value k. Examples: Input: arr [] = { 10, 5, 2, 7, 1, 9 }, k = 15 Output: 4 Explanation: The sub-array is {5, 2, 7, 1}. Also, maintain the count of different values of currsum in a map. Why was there a second saw blade in the first grail challenge? My doubts: How does this algorithm discards the search space? If minInd[ind] is greater than i, then no subarray exists having sum -x in range[0..i-1]. Store their index too. What does "rooting for my alt" mean in Stranger Things? From the map, find the number of subarrays previously found having sum equal to currsum-sum. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to [email protected]. Maximum subarray sum of given length range.

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