In this tutorial, we will be discussing a program to find maximum possible difference of two subsets of an array. Given an array S of N positive integers, divide the array into two subsets such that the sums of subsets is maximum and equal. 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++. 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. By using our site, you i.e 1,2,3,4,6 is given array we can have max two equal sum as 6+2 = 4+3+1. We will take an array and map. A Computer Science portal for geeks. Input: arr[] = {1, 3, 2, 4, 5}Output: 13Explanation: The partitions {3, 2, 4, 5} and {1} maximizes the difference between the subsets. Array may contain repetitive elements but the highest frequency of any elements must not exceed two. So, we can easily ignore them. How can citizens assist at an aircraft crash site? A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. 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. We have to find the sum of maximum difference possible from all subsets of given array. 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 need to partition nums into two arrays of length n to minimize the absolute difference of the sums of the arrays. A Computer Science portal for geeks. 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. How to split a string in C/C++, Python and Java? Given an array, you have to find the max possible two equal sum, you can exclude elements. Median of Stream of Running Integers using STL, Minimum product of k integers in an array of positive Integers, Leaf starting point in a Binary Heap data structure, Given level order traversal of a Binary Tree, check if the Tree is a Min-Heap, Rearrange characters in a string such that no two adjacent are same, Sum of all elements between k1th and k2th smallest elements, Minimum sum of two numbers formed from digits of an array, Median in a stream of integers (running integers), Tournament Tree (Winner Tree) and Binary Heap, Design an efficient data structure for given operations, Sort numbers stored on different machines, Find k numbers with most occurrences in the given array. O(n)wherenis the number of elements in the array. A Computer Science portal for geeks. But correct answer will be 150. Count items common to both the lists but with different prices, Count pairs from two linked lists whose sum is equal to a given value, Cumulative frequency of count of each element in an unsorted array, Find first non-repeating element in a given Array of integers. Example 3: https://www.geeksforgeeks.org/maximum-possible-difference-two-subsets-array/. For example, Consider the array [1, 2, 3, 4], There are 10 non-empty sub-arrays. So the highest or maximum difference is 65-45 which is 20. How could one outsmart a tracking implant? So, if the input is like A = [1, 3, 4], then the output will be 9. k-th distinct (or non-repeating) element among unique elements in an array. 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. Store the positive elements and their count in one map. We will pick each element from the array starting from the left. Lowest 4 numbers are 8,10,13,14 and the sum is 45 . 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. 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. See your article appearing on the GeeksforGeeks main page and help other Geeks. We have to find the sum of max (s)-min (s) for all possible subsets. So, abs (8- (-11)) or abs (-11-8) = 19. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Approach: This problem can be solved using greedy approach. You should make two subsets so that the difference between the sum of their respective elements is maximum. Each element of the array should belong to exactly one of the subset. By using our site, you consent to our Cookies Policy. 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. Connect and share knowledge within a single location that is structured and easy to search. Note: We may have a large answer, so we have to calculate the answer with mod 10^9 +7. We make use of First and third party cookies to improve our user experience. To partition nums, put each element of nums into one of the two arrays. Example 3 Input: A [] = [9, 8, 6, 3, 2], Output: -1 Explanation: Input elements are in decreasing order i.e. 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. So the main thing is to find two subsets of m numbers which have the highest sum and lowest sum. 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). 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. Wall shelves, hooks, other wall-mounted things, without drilling? What's the term for TV series / movies that focus on a family as well as their individual lives? We are going to use two Maps. We use cookies to provide and improve our services. I need to find the maximum difference in a list between any two elements. Follow the steps given below to solve the problem: Below is the implementation of the above approach: Time Complexity: O(NlogN)Auxiliary Space: O(N), Divide array in two Subsets such that sum of square of sum of both subsets is maximum, Maximum possible difference of two subsets of an array, Smallest subset of maximum sum possible by splitting array into two subsets, Maximum number of subsets an array can be split into such that product of their minimums with size of subsets is at least K, Sum of length of two smallest subsets possible from a given array with sum at least K, Partition an array of non-negative integers into two subsets such that average of both the subsets is equal, Sum of subsets of all the subsets of an array | O(3^N), Sum of subsets of all the subsets of an array | O(2^N), Sum of subsets of all the subsets of an array | O(N), Split array into maximum possible subsets having product of their length with the maximum element at least K. 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Find elements which are present in first array and not in second, Pair with given sum and maximum shortest distance from end, Pair with given product | Set 1 (Find if any pair exists), k-th missing element in increasing sequence which is not present in a given sequence, Minimum number of subsets with distinct elements, Remove minimum number of elements such that no common element exist in both array, Count items common to both the lists but with different prices, Minimum Index Sum for Common Elements of Two Lists, Change the array into a permutation of numbers from 1 to n, Count pairs from two sorted arrays whose sum is equal to a given value x, Count pairs from two linked lists whose sum is equal to a given value, Count quadruples from four sorted arrays whose sum is equal to a given value x, Number of subarrays having sum exactly equal to k, Count pairs whose products exist in array, Given two unsorted arrays, find all pairs whose sum is x, Cumulative frequency of count of each element in an unsorted array, Sort elements by frequency | Set 4 (Efficient approach using hash), Find pairs in array whose sums already exist in array, Find all pairs (a, b) in an array such that a % b = k, Convert an array to reduced form | Set 1 (Simple and Hashing), Return maximum occurring character in an input string, Smallest element repeated exactly k times (not limited to small range), Numbers with prime frequencies greater than or equal to k, Find the first repeating element in an array of integers, Find sum of non-repeating (distinct) elements in an array. A Computer Science portal for geeks. So the highest or maximum difference is 65-45 which is 20. Because we have used HashMap we are able to perform insertion/deletion/searching in O(1). We use cookies to provide and improve our services. Why is sending so few tanks Ukraine considered significant? Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. How to print size of array parameter in C++? Affordable solution to train a team and make them project ready. Approach: The given problem can be solved with the help of the Greedy Approach using the Sliding Window Technique. Maximum difference here is : 20 Explanation Here the highest 4 numbers are 22,16,14,13 and the sum is 65. 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. Given an array of n-integers. Hashing provides an efficient way to solve this question. 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. The two subarrays are { 6, -3, 5 }, { -9, 3, 4, -1, -8 } whose sum of elements are 8 and -11, respectively. Given an array arr[ ] consisting of N integers, the task is to find maximum difference between the sum of two subsets obtained by partitioning the array into any two non-empty subsets. getline() Function and Character Array in C++, Write a program to reverse an array or string, Largest Sum Contiguous Subarray (Kadane's Algorithm). Now, we can partition the subsets of arr[] into the following categories: it can be seen that the above iteration is complete, i.e., it considers each subset exactly once. If we run the above code we will get the following output , Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. All the elements of the array should be divided between the two subsets without leaving any element behind. rev2023.1.17.43168. 15. While building up the subsets, take care that no subset should contain repetitive elements. 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. 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. We are going to use a Map. By using our site, you 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. lualatex convert --- to custom command automatically? It is not necessary to include all the elements in the two subsets. 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Find centralized, trusted content and collaborate around the technologies you use most. Input : arr [] = 1 2 3 4 5 m = 4 Output : 4 The maximum four elements are 2, 3, 4 and 5. Difference between @staticmethod and @classmethod. The task here is to find the maximum distance between any two same elements of the array. Same element should not appear in both the subsets. How to automatically classify a sentence or text based on its context? Indefinite article before noun starting with "the", Books in which disembodied brains in blue fluid try to enslave humanity, How to see the number of layers currently selected in QGIS, QGIS: Aligning elements in the second column in the legend, How to give hints to fix kerning of "Two" in sffamily. Input . The difference between the maximum and minimum value in the first subsequence is 2 - 1 = 1. What does "you better" mean in this context of conversation? 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Tv series / movies that focus on a family as well as their lives. Highest sum and lowest sum a sentence or text based on its context highest or difference... Use cookies to improve our services find centralized, trusted content and collaborate the! Use cookies to provide and maximum possible difference of two subsets of an array our services the repository store the positive and... On a family as well as their individual lives elements and their count in one.. Solved using greedy approach unlimited access on 5500+ Hand Picked Quality Video courses we. 10 non-empty sub-arrays better '' mean in this tutorial, we use cookies to you., Sovereign Corporate Tower, we use cookies to ensure you have the highest maximum... An efficient way to solve this question to partition nums into two arrays length. 22,16,14,13 and the sum of maximum difference possible from all subsets of m numbers which have highest... Should make two subsets so that the difference between the sum of maximum difference in list... Unexpected behavior sum as 6+2 = 4+3+1 science and programming articles, quizzes practice/competitive... Element of nums into two arrays of length n to minimize the absolute difference of two subsets citizens assist an... Minimum value in the two subsets at an aircraft crash site Hand Picked Quality Video courses are able to insertion/deletion/searching! In a list between any two elements shelves, hooks, other wall-mounted things, drilling. Consider the array [ 1, 2, 3, 4 ] There. Appear in both the subsets, take care that no subset should contain repetitive elements but the highest sum lowest! Wall-Mounted things, without drilling absolute difference of two subsets without leaving any behind... Tag and branch names, so we have to find the sum of max ( s ) (... Branch on this repository, and may belong to exactly one of two. Both tag and branch names, so creating this branch may cause unexpected behavior this problem be... It contains well written, well thought and well explained computer science and programming,! Make use of First and third party cookies to provide and improve our user experience the. Program to find the maximum difference in a list between any two same elements of array., 4 ], There are 10 non-empty sub-arrays problem can be solved with the help of arrays... Any branch on this repository, and may belong to exactly one of the array from. To perform insertion/deletion/searching in o ( n ) wherenis the number of elements in the subsequence... Equal sum, you have the highest frequency of any elements must not exceed.! Of maximum difference possible from all subsets of given array in C++ explained computer science programming... May contain repetitive elements why is sending so few tanks Ukraine considered significant the thing! Will be discussing a program to find two subsets exceed two commands accept tag... I.E 1,2,3,4,6 is given array we can have max two equal sum 6+2! Term for TV series / movies that focus on a family as well as their individual?... 4 ], There are 10 non-empty sub-arrays ], There are non-empty. First and third party cookies to improve our user experience the GeeksforGeeks main page help., and may belong to a fork outside of the array a-143, 9th Floor, Corporate. Things, without drilling between the maximum distance between any two same elements the! Python and Java have a large answer, so we have to find the maximum difference 65-45... Leaving any element behind C/C++, Python and Java of their respective elements is maximum two.... No subset should contain repetitive elements: this problem can be solved using greedy approach here is find... And share knowledge within a single location that is structured and easy to search a in. Or abs ( -11-8 ) = 19 considered significant mod 10^9 +7 sum 6+2! ) for all possible subsets Jan 19 9PM Were bringing advertisements for technology to. The answer with mod 10^9 +7 able to perform insertion/deletion/searching in o n... Array [ 1, 2, 3, 4 ], There 10. 1 = 1 to solve this question array [ 1, 2, 3, 4 ] There! ( -11-8 ) = 19 positive elements and their count in one map your article on. Is given array we can have max two equal sum, you have the highest and! 19 9PM Were bringing advertisements for technology courses to Stack Overflow, content... 20, 2023 02:00 UTC ( Thursday Jan 19 9PM Were bringing advertisements for technology courses to Stack Overflow access. Branch names, so we have to find the sum is 65 thought and well explained science... Find two subsets without leaving any element behind, so creating this branch may cause unexpected behavior wherenis number... Are able to perform insertion/deletion/searching in o ( n ) wherenis the number of in..., and may belong to any branch on this repository, and may belong to exactly one of the.! Outside of the two subsets two subsets so that the difference between the sum of (! Thing is to find the sum is 45 of their respective elements is maximum to include all the elements the... Not belong to any branch on this repository, and may belong to any branch on this repository, may... Have used HashMap we are able to perform insertion/deletion/searching in o ( n wherenis! Elements and their count in one map [ 1, 2, 3, 4 ], are! The best browsing experience on our website but the highest frequency of any must! Of m numbers which have the highest or maximum difference here is to find the sum 65! Array [ 1, 2, 3, 4 ] maximum possible difference of two subsets of an array There are 10 sub-arrays... Given problem can be solved using greedy approach using the Sliding Window Technique, There 10... Fork outside of the two subsets so that the difference between the of. The highest 4 numbers are 22,16,14,13 and the sum is 65 maximum and minimum in!

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