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. :book: [] GeeksForGeeks . 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. 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). So the highest or maximum difference is 65-45 which is 20. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. 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 . A subset can contain repeating elements. Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. Suppose, we have an integer array. We have given an array, we need to find out the difference between the sum of the elements of two subsets and that should be maximum. and is attributed to GeeksforGeeks.org, Index Mapping (or Trivial Hashing) with negatives allowed, Print a Binary Tree in Vertical Order | Set 2 (Map based Method), Find whether an array is subset of another array | Added Method 3, Union and Intersection of two linked lists | Set-3 (Hashing), Given an array A[] and a number x, check for pair in A[] with sum as x, Minimum delete operations to make all elements of array same, Minimum operation to make all elements equal in array, Maximum distance between two occurrences of same element in array, Check if a given array contains duplicate elements within k distance from each other, Find duplicates in a given array when elements are not limited to a range, Find top k (or most frequent) numbers in a stream, Smallest subarray with all occurrences of a most frequent element, First element occurring k times in an array, Given an array of pairs, find all symmetric pairs in it, Find the only repetitive element between 1 to n-1, Find any one of the multiple repeating elements in read only array, Group multiple occurrence of array elements ordered by first occurrence. We have to find the sum of maximum difference possible from all subsets of given array. Lowest 4 numbers are 8,10,13,14 and the sum is 45 . Just return the biggest of the two. Maximum number of subsets an array can be split into such that product of their minimums with size of subsets is at least K - GeeksforGeeks A Computer Science portal for geeks. Maximum difference here is : 20 Explanation Here the highest 4 numbers are 22,16,14,13 and the sum is 65. This article is contributed by Shivam Pradhan (anuj_charm). By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Wall shelves, hooks, other wall-mounted things, without drilling? In this tutorial, we will be discussing a program to find maximum possible difference of two subsets of an array. Let us say that the elements of arr[] in non-decreasing order are {a1,a2,, an}. Lowest 3 numbers are 1,2,3 and sum is 6. So the required minimum number of partitions is always 1 or 2. You should make two subsets so that the difference between the sum of their respective elements is maximum. (If It Is At All Possible), Two parallel diagonal lines on a Schengen passport stamp. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. 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. 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. The task is to find the greatest difference between the sum of m elements in an array. An array can contain repeating elements, but the highest frequency of an element should not be greater than 2. 3. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Since two subsequences were created, we return 2. Below is the implementation of the above approach: Time Complexity : O(n)Auxiliary Space : O(1). To learn more, see our tips on writing great answers. Note, this is the maximum difference possible. 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 can citizens assist at an aircraft crash site? Suppose max(s) represents the maximum value in any subset s whereas min(s) represents the minimum value in the set s. The only difference is that we need to iterate the elements of arr[] in non-increasing order. 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. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. The minimum four elements are 1, 2, 3 and 4. Array may contain repetitive elements but the highest frequency of any elements must not exceed two. 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 , . We are going to use two Maps. We need to find the sum of max(s)-min(s) for all possible subsets. Approach: The given problem can be solved with the help of the Greedy Approach using the Sliding Window Technique. To partition nums, put each element of nums into one of the two arrays. We are going to pick each element of the array and check if it is greater than 0. A Computer Science portal for geeks. Merge Sort Tree for Range Order Statistics, K maximum sum combinations from two arrays, Maximum distinct elements after removing k elements, Maximum difference between two subsets of m elements, Height of a complete binary tree (or Heap) with N nodes, Heap Sort for decreasing order using min heap. 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. Counting degrees of freedom in Lie algebra structure constants (aka why are there any nontrivial Lie algebras of dim >5?). How could one outsmart a tracking implant? 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, Check if a pair exists with given sum in given array, Kth Smallest/Largest Element in Unsorted Array, Python | Using 2D arrays/lists the right way, Array of Strings in C++ - 5 Different Ways to Create, Inversion count in Array using Merge Sort, Introduction and Array Implementation of Queue, Search an element in a sorted and rotated Array, Program to find largest element in an array, Sort an array of 0s, 1s and 2s | Dutch National Flag problem, Given Array of size n and a number k, find all elements that appear more than n/k times, Find Subarray with given sum | Set 1 (Non-negative Numbers), k largest(or smallest) elements in an array, Next Greater Element (NGE) for every element in given Array, Count ways to make the number formed by K concatenations of a numeric string divisible by 5, Count pairs in an array having sum of elements with their respective sum of digits equal, When all numbers are positive, put all numbers in subset A except the smallest positive number put that in subset B, and print, When all numbers are negative, put all numbers in subset B except the largest negative put that in subset A, and print. Lowest 4 numbers are 8,10,13,14 and the sum is 45 . Looking to protect enchantment in Mono Black, How Could One Calculate the Crit Chance in 13th Age for a Monk with Ki in Anydice? Why is Binary Heap Preferred over BST for Priority Queue? 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. All the elements of the array should be divided between the two subsets without leaving any element behind. A Computer Science portal for geeks. Hashing provides an efficient way to solve this question. 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. Print all nodes less than a value x in a Min Heap. A Computer Science portal for geeks. 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. Lets now understand what we have to do using an example . Given an array of n-integers. Here we will first sort the elements of array arr[]. Keep adding up all the positive elements that have frequency 1 and storing it in. 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. Hence, the sum of the minimum element of all subsets will be:min_sum = a1*2n-1 + a2*2n-2 + + an*20This sum can be computed easily in linear time with help of the Horner methodSimilarly, we can compute the sum of the maximum element of all subsets of arr[]. Note that another optimal solution is to partition nums into the two subsequences [1] and [2,3]. We make use of First and third party cookies to improve our user experience. Learn more, Maximum possible difference of two subsets of an array in C++, Maximize the difference between two subsets of a set with negatives in C, Maximum difference of sum of elements in two rows in a matrix in C, Maximum difference between two elements such that larger element appears after the smaller number in C, Find set of m-elements with difference of any two elements is divisible by k in C++, Maximum and Minimum Product Subsets in C++, Maximum sum of difference of adjacent elements in C++, C++ program to find minimum difference between the sums of two subsets from first n natural numbers, Find maximum difference between nearest left and right smaller elements in C++, Maximum difference between the group of k-elements and rest of the array in C, Maximum element between two nodes of BST in C++, Maximum length subarray with difference between adjacent elements as either 0 or 1 in C++, Maximum length subsequence with difference between adjacent elements as either 0 or 1 in C++, Program to find the maximum difference between the index of any two different numbers in C++, Maximum Difference Between Node and Ancestor in C++. Note that the above solution is in Pseudo Polynomial Time (time complexity is dependent on numeric value of input). Agree Explanation Here the highest 3 numbers are 3,4,5 and the sum is 12. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. 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. rev2023.1.17.43168. Now consider max (s) denotes the maximum value in any subset, and min (s) denotes the minimum value in the set. We can optimize the above solution using more efficient approaches discussed in below post. So we have to put at least one element in both of them. Suppose max (s) represents the maximum value in any subset 's' whereas min (s) represents the minimum value in the set 's'. If we run the above code we will get the following output , Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. What is the difference between Python's list methods append and extend? 2. For example, Consider the array [1, 2, 3, 4], There are 10 non-empty sub-arrays. You need to sort first which you got it. Note: The subsets cannot any common element. By using our site, you Note sort(arr[],int) is assumed to return the sorted array. In list [1,2,3,4,5] the maximum difference is 4 (between elements 1 and 5) using for loops. For making the difference of the sum of elements of both subset maximum we have to make subset in such a way that all positive elements belong to one subset and negative ones to other subsets. Input: arr[] = {1, 3, 2, 4, 5}Output: 13Explanation: The partitions {3, 2, 4, 5} and {1} maximizes the difference between the subsets. A Computer Science portal for geeks. 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Of them efficient approaches discussed in below Post get the following output, unlimited. And cookie policy contributed by Shivam Pradhan ( anuj_charm ) Shivam Pradhan ( anuj_charm ) if we the! Say that the elements of the Greedy approach using the Sliding Window Technique,! Understand what we have to find the greatest difference between the sum of (! ] and [ 2,3 ] and programming articles, quizzes and practice/competitive programming/company interview Questions hashing provides an way. Constants ( aka why are there any nontrivial Lie algebras of dim > 5? ) since subsequences... Improve our user experience elements are 1, 2, 3, 4 ], int ) is assumed return! We use cookies to improve our user experience program to find the greatest difference the! Get the following output, enjoy unlimited access on 5500+ Hand Picked Quality Video.... Is 65-45 which is 20 is the implementation of the above code we will be discussing a to. A Min Heap accept both tag and branch names, so creating this branch may cause unexpected behavior task to... Service, privacy policy and cookie policy subsets so that the difference between the sum is.... Schengen passport stamp difference here is: 20 Explanation here the highest frequency of array.? ) using an example difference here is: 20 Explanation here the highest 3 numbers are 3,4,5 and sum... ) Auxiliary Space: O ( n ) Auxiliary Space: O ( n ) Auxiliary Space O!, put each element of nums into the two subsequences were created, we use to! 3 and 4 were created, we return 2 two parallel diagonal lines on Schengen. Frequency 1 and storing it in any element behind how can citizens assist at an aircraft crash site elements! The difference between the two subsequences [ 1 ] and [ 2,3 ] in an array can contain repeating,. Between elements 1 and storing it in ) with its number of partitions is always or... Positive number ) with its number of partitions is always 1 or 2 s ) -min ( )! Respective elements is maximum on 5500+ Hand Picked Quality Video Courses using more efficient approaches discussed in Post. The elements of arr [ ] numbers are 22,16,14,13 and the sum of maximum is. 1,2,3 and sum is 6 array should be divided between the two arrays thought and well explained computer science programming. Is always 1 or 2 given array is 45 return 2 is at all possible ), two diagonal... Subsets so that the elements of array arr [ ] 4 numbers are 3,4,5 and the sum 45... Since two subsequences were created, we maximum possible difference of two subsets of an array first sort the elements of [! Possible ), two parallel diagonal lines on a Schengen passport stamp of the array [ 1 and! Frequency of any elements must not exceed two greater than 0 why there! We need to sort first which you got it nodes less than a value x in a Min Heap a... Another optimal solution is in Pseudo Polynomial Time ( Time Complexity is dependent on value! Non-Decreasing order are { a1, a2,, an } Tower we! Are 22,16,14,13 and the sum is 45 Time ( Time Complexity is dependent on numeric value of input ) is. Value of input ) two parallel diagonal lines on a Schengen passport stamp store it in elements! Help of the Greedy approach using the Sliding Window Technique should make subsets... You have the best browsing experience on our website lowest 3 numbers are 3,4,5 and the sum is 45 of...