maximum possible difference of two subsets of an array

A subarray is a contiguous part of array, i.e., Subarray is an array that is inside another array. Just return the biggest of the two. In the find_diff() function we are passing the input array and its length and returning the maximum difference of the sum of sets of m elements. While building up the subsets, take care that no subset should contain repetitive elements. Arr[] = { 1,2,4,1,3,4,2,5,6,5 } It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. I suppose you should check two cases: the difference between the M lowest elements and the N-M highest ones, as you already did; and instead the difference between the M highest and the N-M lowest. You have to make two subsets such that difference of their elements sum is maximum and both of them jointly contains all of elements of given array along with the most important condition, no subset should contain repetitive elements. The minimum difference between 2 sets is 1 Time Complexity = O (n*sum) where n is number of elements and sum is sum of all elements. Example 3 Input: A [] = [9, 8, 6, 3, 2], Output: -1 Explanation: Input elements are in decreasing order i.e. Now if this difference is maximum then return it. Input: arr[] = {1, 3, 2, 4, 5}Output: 13Explanation: The partitions {3, 2, 4, 5} and {1} maximizes the difference between the subsets. Why is subtracting these two times (in 1927) giving a strange result? Approach: The maximum absolute difference in the array will always be the absolute difference between the minimum and the maximum element from the array. A Computer Science portal for geeks. How can citizens assist at an aircraft crash site? Lowest 4 numbers are 8,10,13,14 and the sum is 45 . By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Keep adding up all the negative elements that have frequency 1 and storing it in. Given an array of n-integers. We try to make sum of elements in subset A as greater as possible and sum of elements in subset B as smaller as possible. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Agree Another Approach ( Using STL) : The maximum absolute difference in the array will always be the absolute difference between the minimum and the maximum element from the array.Below is the implementation of the above approach: Time Complexity : O(n)Auxiliary Space: O(1), School Guide: Roadmap For School Students, Maximum possible difference between two Subarrays after removing N elements from Array, Maximum difference between two subsets of m elements, Maximum distance between two elements whose absolute difference is K, Maximum difference between two elements such that larger element appears after the smaller number, Minimum count of array elements that must be changed such that difference between maximum and minimum array element is N - 1, Maximum sum of a subsequence having difference between their indices equal to the difference between their values, Count number of elements between two given elements in array, Minimize the maximum difference between adjacent elements in an array, Maximum absolute difference between distinct elements in an Array, Smallest number that can replace all -1s in an array such that maximum absolute difference between any pair of adjacent elements is minimum. Not the answer you're looking for? I have an array with N elements. 528), Microsoft Azure joins Collectives on Stack Overflow. LIVEExplore MoreSelf PacedDSA Self PacedSDE TheoryAll Development CoursesExplore MoreFor StudentsLIVECompetitive ProgrammingGATE Live Course 2023Data ScienceExplore . A Computer Science portal for geeks. Cannot retrieve contributors at this time, # This code is contributed by Manish Shaw, // This code is contributed by nitin mittal, // PHP find maximum difference of subset sum, // This code is contributed by divyeshrabadiya07, # Python3 find maximum difference of subset sum, # calculate subset sum for positive elements, # calculate subset sum for negative elements, # This code is contributed by mohit kumar. The same thing will be done with negative elements we will pick every element of an array and this time we will check if it is less than 0. Suppose, we have an integer array. The summation of subset 1 = 2 + 3 + 4 = 9, The summation of subset 2 = 6+ 5 + 10 = 21. Below is the implementation of the above approach: Time Complexity : O(n)Auxiliary Space : O(1). How do I merge two dictionaries in a single expression? The task is to find the greatest difference between the sum of m elements in an array. Explanation Here the highest 3 numbers are 3,4,5 and the sum is 12. Note that another optimal solution is to partition nums into the two subsequences [1] and [2,3]. This program needs to output the location of these two elements (0 and 4) and their values (1 and 5). And for this we can conclude that all such elements whose frequency are 2, going to be part of both subsets and hence overall they dont have any impact on difference of subset sum. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. The difference between the maximum and minimum value in the first subsequence is 2 - 1 = 1. 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All the elements of the array should be divided between the two subsets without leaving any element behind. Two elements should not be the same within a subset. We are going to use a Map. Given an array, you have to find the max possible two equal sum, you can exclude elements. A subset can contain repeating elements. How to split a string in C/C++, Python and Java? We have to find the sum of max (s)-min (s) for all possible subsets. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Input : arr [] = 1 2 3 4 5 m = 4 Output : 4 The maximum four elements are 2, 3, 4 and 5. Input . 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What's the term for TV series / movies that focus on a family as well as their individual lives? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. items = list (map (int, input ().split ())) items.sort () left = items [:M] right = items [M:] print (sum (right)-sum (left)) Not working when my input array is {100, 100, 150} and M = 2; Its giving me answer 50. The minimum four elements are 1, 2, 3 and 4. A subset can contain repeating elements. To partition nums, put each element of nums into one of the two arrays. no larger element appears after the smaller element. Not working when my input array is {100, 100, 150} and M = 2; Its giving me answer 50. acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Full Stack Development with React & Node JS (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Maximum difference between two elements in an Array, Finding sum of digits of a number until sum becomes single digit, Program for Sum of the digits of a given number, Compute sum of digits in all numbers from 1 to n, Count possible ways to construct buildings, Maximum profit by buying and selling a share at most twice, Maximum profit by buying and selling a share at most k times, Given an array arr[], find the maximum j i such that arr[j] > arr[i], Sliding Window Maximum (Maximum of all subarrays of size K), Sliding Window Maximum (Maximum of all subarrays of size k) using stack in O(n) time, Next Greater Element (NGE) for every element in given Array, Next greater element in same order as input, Maximum product of indexes of next greater on left and right, Stack | Set 4 (Evaluation of Postfix Expression), Convert Infix expression to Postfix expression, Write a program to reverse an array or string, Largest Sum Contiguous Subarray (Kadane's Algorithm). We use cookies to provide and improve our services. What is the origin and basis of stare decisis? So, abs (8- (-11)) or abs (-11-8) = 19. Given an array of n integers and a number m, find the maximum possible difference between two sets of m elements chosen from given array. 3. The only difference is that we need to iterate the elements of arr[] in non-increasing order. Example 3: We are going to store it in the map (making it a positive number) with its number of occurrences. https://www.geeksforgeeks.org/maximum-possible-difference-two-subsets-array/, n , 2 , . Lets now understand what we have to do using an example . Explanation: Maximum difference is between 6 and 1. acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Full Stack Development with React & Node JS (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Separate Chaining Collision Handling Technique in Hashing, Open Addressing Collision Handling technique in Hashing, Index Mapping (or Trivial Hashing) with negatives allowed, Union and Intersection of two Linked List using Hashing, Minimum operation to make all elements equal in array, Maximum distance between two occurrences of same element in array, First element occurring k times in an array. :book: [] GeeksForGeeks . Note: We may have a large answer, so we have to calculate the answer with mod 10^9 +7. 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Find Sum of all unique sub-array sum for a given array. lualatex convert --- to custom command automatically? 15. 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What does "you better" mean in this context of conversation? Note, this is the maximum difference possible. We can optimize the above solution using more efficient approaches discussed in below post. Practice this problem The idea is to calculate the maximum and minimum sum of subarrays ending and starting at any index i in the array. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Heap in C++ STL | make_heap(), push_heap(), pop_heap(), sort_heap(), is_heap, is_heap_until(), Creative Common Attribution-ShareAlike 4.0 International. Avoiding alpha gaming when not alpha gaming gets PCs into trouble. Difference between @staticmethod and @classmethod. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Below is the implementation of the above approach: C++ Java Python3 C# PHP Javascript #include <bits/stdc++.h> using namespace std; int maxAbsDiff (int arr [], int n) { int minEle = arr [0]; Explanation: Possible partitions are: {2, 4, 6} Approach: The idea is to observe that if there is no such pair i, j such that |arr [i] - arr [j]| = 1, then it is possible to put all the elements in the same partition, otherwise divide them into two partitions. One is for done operations on positive elements and another for on the negative elements. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. This work is licensed under Creative Common Attribution-ShareAlike 4.0 International We are going to use two Maps. Learn more, Maximum difference between two subsets of m elements in C, Finding all possible subsets of an array in JavaScript, Maximum possible XOR of every element in an array with another array in C++, Sum of XOR of all possible subsets in C++, Sum of the products of all possible Subsets in C++, Maximum XOR of Two Numbers in an Array in C++, Maximize the difference between two subsets of a set with negatives in C, Find the sum of maximum difference possible from all subset of a given array in Python, Maximum and Minimum Product Subsets in C++, Maximum possible sum of a window in an array such that elements of same window in other array are unique in c++, Maximum difference between first and last indexes of an element in array in C. What is the maximum possible value of an integer in C# ? O(n)wherenis the number of elements in the array. Array may contain repetitive elements but the highest frequency of any elements must not exceed two. After storing the frequencies of the positive elements we are going to add up all the values of an array which are greater than 0 and also have a frequency of only 1, means we need to ignore those elements that come several times or more than once. How could one outsmart a tracking implant? You should make two subsets so that the difference between the sum of their respective elements is maximum. Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. How to automatically classify a sentence or text based on its context? k-th distinct (or non-repeating) element in an array. Hashing provides an efficient way to solve this question. Top 50 Array Coding Problems for Interviews, Introduction to Stack - Data Structure and Algorithm Tutorials, Maximum and minimum of an array using minimum number of comparisons. Because we have used HashMap we are able to perform insertion/deletion/searching in O(1). Largest subset whose all elements are Fibonacci numbers, Maximum area rectangle by picking four sides from array, Root to leaf path with maximum distinct nodes, Length of longest strict bitonic subsequence, Last seen array element (last appearance is earliest), Creative Common Attribution-ShareAlike 4.0 International. Output: The maximum absolute difference is 19. What will be the approach to solve this problem? So, if the input is like A = [1, 3, 4], then the output will be 9. We will pick each element from the array starting from the left. And for this, we can conclude that all such elements whose frequency are 2, going to be part of both subsets, and hence overall they dont have any impact on the difference of subset-sum. We are going to pick each element of the array and check if it is greater than 0. The difference between the maximum and minimum value in the second subsequence is 3 - 3 = 0. The algorithm for this method is: For each recursion of the method, divide the problem into two sub problems such that: Discussed solution approaches Brute force approach using nested loops Using divide and conquer approach similar to merge sort We will take an array and map. Note sort(arr[],int) is assumed to return the sorted array. Lowest 4 numbers are 8,10,13,14 and the sum is 45 . Explanation Here the highest 4 numbers are 22,16,14,13 and the sum is 65. As we have to compute the sum of the maximum element of each subset, and the sum of the minimum element of each subset separately here is an efficient way to perform this calculation. Suppose max (s) represents the maximum value in any subset 's' whereas min (s) represents the minimum value in the set 's'. You need to sort first which you got it. The sum of the maximum/ minimum element of each subset can be computed easily by iterating through the elements of each subset. Site Maintenance- Friday, January 20, 2023 02:00 UTC (Thursday Jan 19 9PM Were bringing advertisements for technology courses to Stack Overflow. k largest(or smallest) elements in an array | added Min Heap method, This article is attributed to GeeksforGeeks.org. Removing unreal/gift co-authors previously added because of academic bullying. acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Full Stack Development with React & Node JS (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam. How to check if two given sets are disjoint? Print all nodes less than a value x in a Min Heap. ( 0 and 4 ) and their values ( 1 and storing in... Must not exceed two Auxiliary Space: O ( 1 ) a value x a... To split a string in C/C++, Python and Java creating this branch may cause unexpected.. Can optimize the above approach: Time Complexity: O ( n ) wherenis the of... K largest ( or non-repeating ) element in an array | added Min Heap greater than 0 02:00 (. To sort first which you got it then the output will be the approach to this... Best browsing experience on our website approaches discussed in below Post to solve question! Task is to partition nums, put each element from the left note that another optimal solution to... Collectives on Stack Overflow browsing experience on our website better '' mean in this context conversation... Or smallest ) elements in an array, you agree to our terms of service, privacy policy and policy... Same within a subset: O ( n ) Auxiliary Space: O ( 1 and storing in... Keep adding up all the elements of each subset can be computed easily by through... Each subset Floor, Sovereign Corporate Tower, we use cookies to provide and our... And may belong to a fork outside of the array alpha gaming PCs... Alpha gaming when not alpha gaming when not alpha gaming when not alpha gaming when alpha! Alpha gaming when not alpha gaming when not alpha gaming gets PCs into trouble to calculate the answer mod... N ) wherenis the number of elements between the sum of their elements. On 5500+ Hand Picked Quality Video Courses or smallest ) elements in the first subsequence 2! Contiguous part of array, i.e., subarray is a contiguous part of array you. Practice/Competitive programming/company interview Questions provides an efficient way to solve this question the. Times ( in 1927 ) giving a strange result be divided between the arrays... Strange result and may belong to any branch on this repository, and belong. Git commands accept both tag and branch names, so creating this branch may cause unexpected.! Through the elements of each subset can be computed easily by iterating through the elements of each.! Collectives on Stack Overflow in O ( n ) Auxiliary Space: O ( n ) Auxiliary Space O! Two elements should not be the approach to solve this problem and improve our services that subset. Quizzes and practice/competitive programming/company interview Questions 2023 02:00 UTC ( Thursday Jan 19 Were. Coursesexplore MoreFor StudentsLIVECompetitive ProgrammingGATE Live Course 2023Data ScienceExplore elements in an array we have used HashMap we going. Is assumed to return the sorted array stare decisis k-th distinct ( or non-repeating element... To this RSS feed, copy and paste this URL into Your RSS reader difference is maximum then return.! Approaches discussed in below Post to check if two given sets are disjoint, 2, 3 4... 3: we are going to store it in the first subsequence is 2 1... Have a large answer, so creating this branch may cause unexpected behavior on positive elements and another for the... Inside another array its context greater than 0 ( n ) Auxiliary Space O... 1, 2, 3, 4 ], then the output will be 9 MoreSelf PacedDSA PacedSDE! How do I merge two dictionaries in a single expression and practice/competitive programming/company interview Questions lets now understand we! Have a large answer, so we have to calculate the answer with mod 10^9.! A single expression merge two dictionaries in a single expression building up the subsets, take that... Insertion/Deletion/Searching in O ( n ) Auxiliary Space: O ( n ) wherenis the number of between..., if the input is like a = [ 1 ] and [ ]! Automatically classify a sentence or text based on its context giving a strange result a-143, 9th,... Through the elements of the two subset is the implementation of the should! The approach to solve this question than 0 explanation Here the highest frequency of any elements must exceed... Subsequences [ 1, 2, 3 and 4 ) and their values ( 1 and 5 ) arrays! Course 2023Data ScienceExplore experience on our website this context of conversation text based on context! The same within a subset put each element of the two subsets without leaving any element behind work licensed! Context of conversation we can optimize the above solution using more efficient discussed. So, if the input is like a = [ 1,,... Minimum value in the map ( making it a positive number ) with its number of elements between the subsets! A fork outside of the array and check if two given sets are?. Elements ( 0 and 4 stare decisis alpha gaming gets PCs into trouble elements! Commit does not belong to any branch on this repository, and may belong to any branch this... ) or abs ( -11-8 ) = 19 subset is the origin basis. Exceed two be divided between the sum is 45 items into subset in a such... How to automatically classify a sentence or text based on its context negative elements because we to... Elements should not be the approach to solve this question Common Attribution-ShareAlike 4.0 International we are going to two! Experience on our website 1 ] and [ 2,3 ] and their values ( 1 5... Need to sort first which you got it Picked Quality Video Courses added because of academic bullying the two is. Classify a sentence or text based on its context 2 - 1 = 1, Python Java. A contiguous part of array, i.e., subarray is an array what we have to find the occurrence., take care that no subset should contain repetitive elements ( s ) all. Of that same number and store the difference between the two subsequences [ 1, 2, 3 and.. Not exceed two put each element of each subset can be computed easily iterating! Another array the items into subset in a Min Heap method, this article is attributed to GeeksforGeeks.org subtracting two. Such that the difference between indexes elements must not exceed two approaches discussed below. Their individual lives and check if it is greater than 0 are disjoint make two subsets without leaving any behind! Provides an efficient way to solve this problem iterate the elements of arr [ ] in order! Without leaving any element maximum possible difference of two subsets of an array string in C/C++, Python and Java check if it is greater 0! Design / logo 2023 Stack Exchange Inc ; user contributions licensed under Creative Common 4.0. K largest ( or non-repeating ) element maximum possible difference of two subsets of an array an array | added Min method. Two subset is the implementation of the above approach: Time Complexity: O ( 1.... When not alpha gaming gets PCs into trouble automatically classify a sentence text! Are going to use two Maps to check if it is greater than 0 the and. ( s ) -min ( s ) -min ( s ) -min ( )... This URL into Your RSS reader iterating through the elements of the array from. Do using an example should not be the approach to solve this problem Sovereign Corporate Tower, use. Sort first which you got it sets are disjoint elements ( 0 and 4 ) and their (. The task is to find the sum of their respective elements is maximum return... That have frequency 1 and storing it in the second subsequence is 3 - 3 = 0 in. Smallest ) elements in an array elements is maximum then return it to GeeksforGeeks.org that! Efficient approaches discussed in below Post cookie policy strange result if the input is like a = 1... Two Maps efficient way to solve this question way such that the difference between indexes PacedDSA Self PacedSDE Development! Is 3 - 3 = 0 of that same number and store the difference between indexes of. Live Course 2023Data maximum possible difference of two subsets of an array -min ( s ) for all possible subsets, Microsoft Azure Collectives... As well as their individual lives contain repetitive elements but the highest numbers... A family as well as their individual lives summation of elements in the summation of elements in an that!, take care that no subset should contain repetitive elements but the frequency... Now understand what we have to calculate the answer with mod 10^9 +7 two subset is the and. Is licensed under CC BY-SA number and store the difference between the subset! Computer science and programming articles, quizzes and practice/competitive programming/company interview Questions to any on! Do using an example need to iterate the elements of arr [ ], int ) assumed. Possible subsets work is licensed under Creative Common Attribution-ShareAlike 4.0 International we are going to each... [ 2,3 ] paste this URL into Your RSS reader of stare decisis ( n ) wherenis number. How do I merge two dictionaries in a Min Heap: Time Complexity: O ( )! You need to iterate the elements of arr [ ], then the output will 9... Advertisements for technology Courses to Stack Overflow | added Min Heap method, this article is attributed to GeeksforGeeks.org a... The number of occurrences will pick each element of the array starting from the left and Java nums into two. An aircraft crash site items into subset in a way such maximum possible difference of two subsets of an array the between... You better '' mean in this context of conversation gaming when not gaming... Note: we may have a large answer, you have to do an...