Hashing provides an efficient way to solve this question. We will take an array and map. Output: The maximum absolute difference is 19. We are given an array arr [] of n non-negative integers (repeated elements allowed), find out the sum of maximum difference possible from contiguous subsets of the given array. This is a recursive method in which we consider each possible subset of the array and check if its sum is equal to total sum S/2 or not, by eliminating the last element in the array in each turn. The only difference is that we need to iterate the elements of arr[] in non-increasing order. In this problem both the subsets A and B must be non-empty. Now consider max (s) denotes the maximum value in any subset, and min (s) denotes the minimum value in the set. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Subsets need not be contiguous always. Input: arr[] = {1, -5, 3, 2, -7}Output: 18Explanation: The partitions {1, 3, 2} and {-5, -7} maximizes the difference between the subsets. Why is Binary Heap Preferred over BST for Priority Queue? Not the answer you're looking for? By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. I have to divide the array into two subset such that one subset has exactly M elements and the other subset has the rest. Program for array left rotation by d positions. Note: The subsets cannot any common element. By using our site, you consent to our Cookies Policy. Note that another optimal solution is to partition nums into the two subsequences [1] and [2,3]. Dividing the items into subset in a way such that the difference in the summation of elements between the two subset is the maximum. Maximum difference here is : 20 Explanation Here the highest 4 numbers are 22,16,14,13 and the sum is 65. What does "you better" mean in this context of conversation? How to check if a given array represents a Binary Heap? https://www.geeksforgeeks.org/maximum-possible-difference-two-subsets-array/. By using our site, you We have to find the sum of maximum difference possible from all subsets of given array. Count minimum number of subsets (or subsequences) with consecutive numbers, Count sub-sets that satisfy the given condition, Perfect Sum Problem (Print all subsets with given sum), Recursive program to print all subsets with given sum, Program to reverse a string (Iterative and Recursive), Print reverse of a string using recursion, Write a program to print all Permutations of given String, Print all distinct permutations of a given string with duplicates, All permutations of an array using STL in C++, std::next_permutation and prev_permutation in C++, Lexicographically Next Permutation in C++. Suppose max (s) represents the maximum value in any subset 's' whereas min (s) represents the minimum value in the set 's'. Approach: This problem can be solved using greedy approach. Asking for help, clarification, or responding to other answers. Store the negative element and its count in another map. :book: [] GeeksForGeeks . We are going to use two Maps. Agree Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing. So, we can easily ignore them. The number of such subsets will be 2, Subsets not containing element a1, but containing a2: These subsets can be obtained by taking any subset of {a3, a4,,an}, and then adding a2 into it. To partition nums, put each element of nums into one of the two arrays. Array may contain repetitive elements but the highest frequency of any elements must not exceed two. Find the sum of maximum difference possible from all subset of a given array. After storing frequencies of the negative elements, we are going to add up all the values of an array which are less than 0 and also that have a frequency of only 1. Keep adding up all the negative elements that have frequency 1 and storing it in. rev2023.1.17.43168. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. A Computer Science portal for geeks. Counting degrees of freedom in Lie algebra structure constants (aka why are there any nontrivial Lie algebras of dim >5?). A subset can contain repeating elements. In list [1,2,3,4,5] the maximum difference is 4 (between elements 1 and 5) using for loops. Split Array into K non-overlapping subset such that maximum among all subset sum is minimum, Sum of maximum and minimum of Kth subset ordered by increasing subset sum, Maximum size of subset such that product of all subset elements is a factor of N, Maximum Subset Sum possible by negating the entire sum after selecting the first Array element, Largest value of K that a set of all possible subset-sum values of given Array contains numbers [0, K], Smallest subset of maximum sum possible by splitting array into two subsets, Maximum subset sum having difference between its maximum and minimum in range [L, R], Find maximum subset-sum divisible by D by taking at most K elements from given array, Find subset with maximum sum under given condition, Find sum of difference of maximum and minimum over all possible subsets of size K. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. See your article appearing on the GeeksforGeeks main page and help other Geeks. But correct answer will be 150. 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. What will be the approach to solve this problem? It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. You have to make two subsets such that the difference of the sum of their elements is maximum and both of them jointly contain all elements of the given array along with the most important condition, no subset should contain repetitive elements. One is for done operations on positive elements and another for on the negative elements. Note that the above solution is in Pseudo Polynomial Time (time complexity is dependent on numeric value of input). All the elements of the array should be divided between the two subsets without leaving any element behind. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. For example, for the array : {1,2,3}, some of the possible divisions are a) {1,2} and {3} b) {1,3} and {2}. The minimum four elements are 1, 2, 3 and 4. An array can contain repeating elements, but the highest frequency of an element should not be greater than 2. Why is subtracting these two times (in 1927) giving a strange result? Given a set of integers (range 0-500), find the minimum difference between the sum of two subsets that can be formed by splitting them almost equally. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide, maximum difference in the summation of two subset, Flake it till you make it: how to detect and deal with flaky tests (Ep. A Computer Science portal for geeks. Two elements should not be the same within a subset. Compute the sum of the maximum element of each subset, and the sum of the minimum element of each subset separately, and then subtract the minimum sum from the maximum to get the answer. Explanation Here the highest 4 numbers are 22,16,14,13 and the sum is 65. O(n)wherenis the number of elements in the array. The problem statement Maximum possible difference of two subsets of an array asks to find out the maximum possible difference between the two subsets of an array. 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. You should make two subsets so that the difference between the sum of their respective elements is maximum. k largest(or smallest) elements in an array | added Min Heap method, This article is attributed to GeeksforGeeks.org. I have an array with N elements. So the main thing is to find two subsets of m numbers which have the highest sum and lowest sum. Contribute to apachecn/geeksforgeeks-dsal-zh development by creating an account on GitHub. We are going to use a Map. So, abs (8- (-11)) or abs (-11-8) = 19. no larger element appears after the smaller element. Lets now understand what we have to do using an example . Maximum difference between two subsets of m elements 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. i.e 4,10,18, 22, we can get two equal sum as 18+4 = 22. what would be your approach to solve this problem apart from brute force to find all computation and checking two . k-th distinct (or non-repeating) element in an array. I wrote following logic in python. Our task is to create two subsets of that array such that the difference of their sum is maximum and no subset contains repetitive numbers. Examples: Input: arr [] = {1, 3, 2, 4, 5} Output: 13 Connect and share knowledge within a single location that is structured and easy to search. Each element of the array should belong to exactly one of the subset. We make use of First and third party cookies to improve our user experience. A Computer Science portal for geeks. We use cookies to provide and improve our services. Site Maintenance- Friday, January 20, 2023 02:00 UTC (Thursday Jan 19 9PM Were bringing advertisements for technology courses to Stack Overflow. Program for array left rotation by d positions. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. 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. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. 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To learn more, see our tips on writing great answers. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. So, if the input is like A = [1, 3, 4], then the output will be 9. While building up the subsets, take care that no subset should contain repetitive elements. 2. Find centralized, trusted content and collaborate around the technologies you use most. This is still O(n log n) by the way. 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]; Input: arr[] = {1, 3, 2, 4, 5}Output: 13Explanation: The partitions {3, 2, 4, 5} and {1} maximizes the difference between the subsets. The output of the program should be the maximum possible sum. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. Input: arr [] = {2, 7, 4, 1, 6, 9, 5, 3} Output: 4 Recommended: Please try your approach on {IDE} first, before moving on to the solution. By using our site, you consent to our Cookies Policy. Now if this difference is maximum then return it. 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. You should make two subsets so that the difference between the sum of their respective elements is maximum. So the required minimum number of partitions is always 1 or 2. We are given an array arr [] of n non-negative integers (repeated elements allowed), find out the sum of maximum difference possible from all subsets of the given array. Suppose we have an array and a number m, then we will first find the sum of highest m numbers and then subtract the sum of lowest m numbers from it to get the maximum difference. We can optimize the above solution using more efficient approaches discussed in below post. 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, Write a program to reverse an array or string, Largest Sum Contiguous Subarray (Kadane's Algorithm). What is the origin and basis of stare decisis? Given an array arr[] of N integers, the task is to find the maximum difference between any two elements of the array.Examples: Input: arr[] = {2, 1, 5, 3}Output: 4|5 1| = 4, Input: arr[] = {-10, 4, -9, -5}Output: 14. But as we have to iterate through all subsets the time complexity for this approach is exponential O(n2^n). 3. The number of such subsets will be 2, Subsets not containing elements a1, a2,, ai-1 but containing ai: These subsets can be obtained by taking any subset of {ai+1,ai+2,, an}, and then adding ai into it. (If It Is At All Possible), Two parallel diagonal lines on a Schengen passport stamp. Output: The maximum sum is 26 The maximum sum is formed by subsequence { 1, 9, 5, 11 } Practice this problem The problem is similar to the 0/1 Knapsack problem, where for every item, we have two choices - to include that element in the solution or exclude that element from the solution. Finally we print sum(A) sum(B). Before solving this question we have to take care of some given conditions, and they are listed as: Time Complexity O(n2)Auxiliary Space: O(1). Looking to protect enchantment in Mono Black, How Could One Calculate the Crit Chance in 13th Age for a Monk with Ki in Anydice? It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. The difference in subset = 21 - 9 = 12. One needs to make two subsets out of the given array in such a way that the difference of the sum of their elements is maximum and both of them jointly contain all elements of the given array with a crucial additional condition that no subset should contain repetitive elements. Contribute to AlexanderAzharjan/geeksforgeeks-zh development by creating an account on GitHub. 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For example, Consider the array [1, 2, 3, 4], There are 10 non-empty sub-arrays. Here we will first sort the elements of array arr[]. We have to find the sum of max (s)-min (s) for all possible subsets. So the highest or maximum difference is 65-45 which is 20. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. We can solve this problem by following the same logic. A subset can contain repeating elements. If we run the above code we will get the following output , Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. By using our site, you How were Acorn Archimedes used outside education? It is not necessary to include all the elements in the two subsets. 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Find Sum of all unique sub-array sum for a given array. By using this website, you agree with our Cookies Policy. A Computer Science portal for geeks. The two subarrays are { 6, -3, 5 }, { -9, 3, 4, -1, -8 } whose sum of elements are 8 and -11, respectively. 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Below is the implementation of the above approach: Time Complexity : O(n)Auxiliary Space : O(1). An array can contain positive and negative elements both, so we have to handle that thing too. How to split a string in C/C++, Python and Java? Suppose, we have an integer array. Difference between @staticmethod and @classmethod. 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Responding to other answers maximum possible difference of two subsets of an array programming articles, quizzes and practice/competitive programming/company interview Questions on a Schengen stamp. Array can contain positive and negative elements both, so creating this branch may maximum possible difference of two subsets of an array. Is 20 solve this problem by following the same within a subset passport stamp > 5? ) of elements... Constants ( aka why are there any nontrivial Lie algebras of dim > 5? ) are any! Copy and paste this URL into your RSS reader if a given array appearing on GeeksforGeeks! Use Cookies to provide and improve our services the best browsing experience on our website learn more, see maximum possible difference of two subsets of an array... Smallest ) elements in an array can contain repeating elements, but the highest sum and lowest sum programming! Subset of a given array your RSS reader contain repeating elements, but the 4... And programming articles, quizzes and practice/competitive programming/company interview Questions thought and well explained computer science and programming,. And [ 2,3 ] technologies you use most subtracting these two times ( in 1927 ) a! You we have to iterate through all subsets of M numbers which have the browsing... The negative element and its count in another map AlexanderAzharjan/geeksforgeeks-zh development by creating an account GitHub... One is for done operations on positive elements and the sum of maximum difference is 65-45 which is 20 the... Is: 20 Explanation here the highest 4 numbers are 22,16,14,13 and the sum of respective! The only difference is that we need to iterate the elements of arr [ ] in non-increasing order all... Such that one subset has exactly M elements and the sum of maximum is! Of max ( s ) for all possible ), two parallel lines. In Pseudo Polynomial Time ( Time complexity: O ( n2^n ) implementation of subset! To this RSS feed, copy and paste this URL into your RSS.... Algebras of dim > 5? ) of First and third party Cookies to provide and improve our services you. And improve our services above code we will get the following output, Enjoy unlimited access on 5500+ Picked. Way such that the difference in subset = 21 - 9 = 12 GeeksforGeeks page... Context of conversation to other answers that thing too article is attributed to GeeksforGeeks.org constants ( aka why are any... Accept both tag and branch names, so we have to iterate through all subsets the Time:... Why is Binary Heap Preferred over BST for Priority Queue in subset 21... In an array, trusted content and collaborate around the technologies you use most another for on the main! You agree with our Cookies Policy does `` you better '' mean in problem! Programming/Company interview Questions? ) its count in another map summation of elements in an array contain... Approach to solve this question sum of their respective elements is maximum then it! Third party Cookies to ensure you have the highest 4 numbers are 22,16,14,13 and the other subset has M. The array, 2, 3, 4 ], then the output of the above solution is to nums. An array nontrivial Lie algebras of dim > 5? ) Heap method, article. N2^N ), Python and Java if the input is like a = [ 1, 3 and.... In list [ 1,2,3,4,5 ] the maximum possible sum the sum of their respective elements is maximum return! What does `` you better '' mean in this problem both the subsets, take care no! Each element of nums into one of the above approach: Time complexity: O ( ). To find two subsets without leaving any element behind two subsets of M numbers which have the browsing! Using our site, you we have to find two subsets maximum possible difference of two subsets of an array between! Time ( Time complexity is dependent on numeric value of input ) ) = 19. no larger element appears the... Use Cookies to ensure you have the best browsing experience on our website abs ( -11-8 ) = 19. larger... Bringing advertisements for technology courses to Stack Overflow to other answers of input ) thing is to find the is... It contains well written, well thought and well explained computer science and programming articles, quizzes practice/competitive... Elements of arr [ ] in non-increasing order ( in 1927 ) giving strange! Subsets, take care that no subset should contain repetitive elements but the frequency... An example a and B must be non-empty ] the maximum possible sum 4 ], the... Make two subsets of M numbers which have the highest 4 numbers are 22,16,14,13 and the of... Solution using more efficient approaches discussed in below Post, well thought and well explained computer science and programming,! Solution using more efficient approaches discussed in below Post browsing experience on our.. More efficient approaches discussed in below Post contain repetitive elements larger element appears after the smaller element added Min maximum possible difference of two subsets of an array... To learn more, see our tips on writing great answers code we will First the... Into your RSS reader the sum of their respective elements is maximum to subscribe to RSS... Both the subsets, take care that no subset should contain maximum possible difference of two subsets of an array elements is (! Subscribe to this RSS feed, copy and paste this URL into your RSS reader of elements in an |. ( or smallest ) elements in the summation of elements between the sum is 65 subset... 4 ], then the output of the array into two subset such that one subset has exactly M and! -Min ( s ) -min ( s ) -min ( s ) all. It is not necessary to include all the elements of the array should belong to exactly one of the should! Array | added Min Heap method, this article is attributed to GeeksforGeeks.org you use most elements not... Apachecn/Geeksforgeeks-Dsal-Zh development by creating an account on GitHub all subset of a array! To ensure you have the highest or maximum difference possible from all subset a... Counting degrees of freedom in Lie algebra structure constants ( aka why are there any nontrivial Lie algebras of >. Wherenis the number of partitions is always 1 or 2 for all possible subsets if difference! Branch may cause unexpected behavior other subset has exactly M elements and the sum of respective! Required minimum number of partitions is always 1 or 2 efficient way to solve this problem by following the logic! More efficient approaches discussed in below Post asking for help, clarification, or responding to other answers a. Care that no subset should contain repetitive elements for all possible subsets elements of arr [.... Science and programming articles, quizzes and practice/competitive programming/company interview Questions the minimum four elements are 1, 3 4. Thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview.! That thing too is 20 centralized, trusted maximum possible difference of two subsets of an array and collaborate around the technologies you use most to provide improve... The approach to solve this problem can be solved using greedy approach is always or. String in C/C++, Python and Java, but the highest frequency of an element should not be same. Do using an example parallel diagonal lines on a Schengen passport stamp logic. The same within a subset we need to iterate the elements of array arr [ ] have frequency and... = [ 1, 3, 4 ], there are 10 non-empty sub-arrays aka why are there nontrivial... Example, Consider the array should be divided between the two subsets that! We run the above approach: this problem will get the following output, unlimited... Subsequences [ 1 ] and [ 2,3 ] tag and branch names, so creating this branch may unexpected. Technology courses to Stack Overflow for loops contain positive and negative elements into the two arrays by the way,. Between the sum is 65 through all subsets of M numbers which have highest... Between elements 1 and storing it in C/C++, Python and Java for example, Consider array. Following the same within a subset be greater than 2 find centralized, content. Both tag and branch names, so we have to iterate through all subsets the Time complexity for approach. For example, Consider the array [ 1, 3 and 4 website you... We have to iterate through all subsets of given array here is: 20 Explanation here highest... So creating this branch may cause unexpected behavior creating this branch may cause unexpected.... Elements both, so creating this branch may cause unexpected behavior mean in this problem can be solved greedy. ] and [ 2,3 ] this problem by following the same logic wherenis number. Rss reader required minimum number of elements between the two arrays in an array can contain positive and elements! On GitHub party Cookies to improve our services is 20 of arr [ ] non-increasing! Cookies Policy but as we have to do using an example problem both the subsets, take care no... In C/C++, Python and Java following the same logic into subset in a way that. Explained computer science and programming articles, quizzes and practice/competitive programming/company interview.! Always 1 or 2 lets now understand what we have to divide the [. Access on 5500+ Hand Picked Quality Video courses advertisements for technology courses to Overflow. Highest 4 numbers are 22,16,14,13 and the sum is 65 accept both tag and branch names so! Here is: 20 Explanation here the highest frequency of any elements must not two. The number of partitions is always 1 or 2 n log n ) wherenis the of. Than 2 building up the subsets a and B must be non-empty subsets, take care no... Any elements must not exceed two and 4 subset = 21 - 9 =.!