maximum possible difference of two subsets of an array

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]; The array may contain repetitive elements but the highest frequency of any element must not exceed two. Note: The subsets cannot any common element. Note: We may have a large answer, so we have to calculate the answer with mod 10^9 +7. 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. Note, this is the maximum difference possible. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. It is not necessary to include all the elements in the two subsets. So we have to put at least one element in both of them. 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 make use of First and third party cookies to improve our user experience. Contribute to AlexanderAzharjan/geeksforgeeks-zh development by creating an account on GitHub. Lets now understand what we have to do using an example . 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. Asking for help, clarification, or responding to other answers. Example 3: Given an array of n-integers. By using our site, you consent to our Cookies Policy. While building up the subsets, take care that no subset should contain repetitive elements. 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. Each element of the array should belong to exactly one of the subset. 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. 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. Contribute to apachecn/geeksforgeeks-dsal-zh development by creating an account on GitHub. 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. While building up the subsets, take care that no subset should contain repetitive elements. 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. The subarrays are: (1), (2), (3), (4), (1,2), (2,3), (3,4), (1,2,3), (2,3,4), and (1,2,3,4) Suppose max (s) represents the maximum value in any subset 's' whereas min (s) represents the minimum value in the set 's'. The output of the program should be the maximum possible sum. The size of both of these subsets is 3 which is the maximum possible. Approach: The given problem can be solved with the help of the Greedy Approach using the Sliding Window Technique. 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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. So, if the input is like A = [1, 3, 4], then the output will be 9. rev2023.1.17.43168. 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. We use cookies to provide and improve our services. and is attributed to GeeksforGeeks.org, k largest(or smallest) elements in an array | added Min Heap method, Kth Smallest/Largest Element in Unsorted Array | Set 1. getline() Function and Character Array in C++, Write a program to reverse an array or string, Largest Sum Contiguous Subarray (Kadane's Algorithm). We will pick each element from the array starting from the left. 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A Computer Science portal for geeks. In this problem both the subsets A and B must be non-empty. 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. What's the term for TV series / movies that focus on a family as well as their individual lives? 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[]. How do I merge two dictionaries in a single expression? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. A Computer Science portal for geeks. Wall shelves, hooks, other wall-mounted things, without drilling? Explanation Here the highest 4 numbers are 22,16,14,13 and the sum is 65. The above problem can be better understood using the example below: A Computer Science portal for geeks. 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. So the required minimum number of partitions is always 1 or 2. Affordable solution to train a team and make them project ready. (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. How were Acorn Archimedes used outside education? A subset can contain repeating elements. Now if this difference is maximum then return it. I wrote following logic in python. This work is licensed under Creative Common Attribution-ShareAlike 4.0 International What is the origin and basis of stare decisis? I have an array with N elements. 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. 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. Same element should not appear in both the subsets. Affordable solution to train a team and make them project ready. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing. 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. Now you can take M elements from either from start or from the end. Find centralized, trusted content and collaborate around the technologies you use most. We have to find the sum of max (s)-min (s) for all possible subsets. Lowest 3 numbers are 1,2,3 and sum is 6. Suppose, we have an integer array. 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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. 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. Examples: Input: arr [] = {1, 3, 2, 4, 5} Output: 13 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. Making statements based on opinion; back them up with references or personal experience. Note that another optimal solution is to partition nums into the two subsequences [1] and [2,3]. 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. C++ code to find Maximum possible difference of two subsets of an array, Java code to find Maximum possible difference of two subsets of an array, Find postorder traversal of BST from preorder traversal. Agree This article is contributed by Shivam Pradhan (anuj_charm). 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. Store the positive elements and their count in one map. 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. The idea is to first sort the array, then find sum of first m elements and sum of last m elements. How to check if two given sets are disjoint? We are going to store it in the map (making it a positive number) with its number of occurrences. So the highest or maximum difference is 65-45 which is 20. We can solve this problem by following the same logic. https://www.geeksforgeeks.org/maximum-possible-difference-two-subsets-array/, n , 2 , . Note sort(arr[],int) is assumed to return the sorted array. The difference in subset = 21 - 9 = 12. :book: [] GeeksForGeeks . 2. 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. Keep adding up all the negative elements that have frequency 1 and storing it in. This article is attributed to GeeksforGeeks.org 0 1 tags: (say count of integers is n, if n is even, each set must have n/2 elements and if n is odd, one set has (n-1)/2 elements and other has (n+1)/2 elements) is there DP approach for this problem. Let us say that the elements of arr[] in non-decreasing order are {a1,a2,, an}. Avoiding alpha gaming when not alpha gaming gets PCs into trouble. 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++. Site Maintenance- Friday, January 20, 2023 02:00 UTC (Thursday Jan 19 9PM Were bringing advertisements for technology courses to Stack Overflow. Check our Website: https://www.takeuforward.org/In case you are thinking to buy courses, please check below: Link to get 20% additional Discount at Coding Ni. Maximum possible difference of two subsets of an array in C++ C++ Server Side Programming Programming In this tutorial, we will be discussing a program to find maximum possible difference of two subsets of an array For this we will be provided with an array containing one or two instances of few random integers. The task is to find the greatest difference between the sum of m elements in an array. Store the negative element and its count in another map. Input : arr [] = 1 2 3 4 5 m = 4 Output : 4 The maximum four elements are 2, 3, 4 and 5. Maximum possible difference of two subsets of an array Given an array of n-integers. An array can contain repeating elements, but the highest frequency of an element should not be greater than 2. The only difference is that we need to iterate the elements of arr[] in non-increasing order. 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. Return the minimum possible absolute difference. 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. Then we are going to store it in the map with its number of occurrences. In general, for an array of size n, there are n* (n+1)/2 non-empty subarrays. 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. Not the answer you're looking for? How to automatically classify a sentence or text based on its context? Then we will find the sum of first m and last m elements as these will be least m and highest m numbers of arr[] . Example 1: Input: nums = [3,9,7,3] Output: 2 Explanation: One optimal partition is: [3,9] and [7,3]. k largest(or smallest) elements in an array | added Min Heap method, This article is attributed to GeeksforGeeks.org. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Heap in C++ STL | make_heap(), push_heap(), pop_heap(), sort_heap(), is_heap, is_heap_until(), Creative Common Attribution-ShareAlike 4.0 International. Suppose max (s) represents the maximum value in any subset 's' whereas min (s) represents the minimum value in the set 's'. Given an array of n-integers. We can optimize the above solution using more efficient approaches discussed in below post. An array can contain positive and negative elements both, so we have to handle that thing too. Note, this is the maximum difference possible. 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. I have to divide the array into two subset such that one subset has exactly M elements and the other subset has the rest. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. What does "you better" mean in this context of conversation? We are going to use two Maps. 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. See your article appearing on the GeeksforGeeks main page and help other Geeks. Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. 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). Program for array left rotation by d positions. This work is licensed under Creative Common Attribution-ShareAlike 4.0 International To partition nums, put each element of nums into one of the two arrays. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Thanks for contributing an answer to Stack Overflow! Hashing provides an efficient way to solve this question. 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. Why is sending so few tanks Ukraine considered significant? Just return the biggest of the two. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. When was the term directory replaced by folder? Subsets containing element a1: These subsets can be obtained by taking any subset of {a2,a3,, an} and then adding a1 into it. So, we can easily ignore them. The minimum four elements are 1, 2, 3 and 4. For example, Consider the array [1, 2, 3, 4], There are 10 non-empty sub-arrays. A Computer Science portal for geeks. Keep adding up all the positive elements that have frequency 1 and storing it in. i.e 1,2,3,4,6 is given array we can have max two equal sum as 6+2 = 4+3+1. What is the difference between __str__ and __repr__? The two subarrays are { 6, -3, 5 }, { -9, 3, 4, -1, -8 } whose sum of elements are 8 and -11, respectively. Subset-sum is the sum of all the elements in that subset. How could one outsmart a tracking implant? 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. 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. So, we can easily ignore them. The task here is to find the maximum distance between any two same elements of the array.

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