O(n)wherenis the number of elements in the array. 15. 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. Find the sum of maximum difference possible from all subset of a given array. Then we will find the last occurrence of that same number and store the difference between indexes. 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. So the main thing is to find two subsets of m numbers which have the highest sum and lowest sum. Thanks for contributing an answer to Stack Overflow! 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. The sum of the maximum/ minimum element of each subset can be computed easily by iterating through the elements of each subset. This article is contributed by Shivam Pradhan (anuj_charm). This is still O(n log n) by the way. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. I have an array with N elements. A tag already exists with the provided branch name. Note, this is the maximum difference possible. 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. 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. Below is the implementation of the above approach: Time Complexity : O(n)Auxiliary Space : O(1). 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. Suppose max (s) represents the maximum value in any subset 's' whereas min (s) represents the minimum value in the set 's'. Here also, we need to ignore those elements that come several times or more than once. Keep adding up all the negative elements that have frequency 1 and storing it in. What is the difference between Python's list methods append and extend? Difference between @staticmethod and @classmethod. You should make two subsets so that the difference between the sum of their respective elements is maximum. Note: We may have a large answer, so we have to calculate the answer with mod 10^9 +7. Now if this difference is maximum then return it. Site Maintenance- Friday, January 20, 2023 02:00 UTC (Thursday Jan 19 9PM Were bringing advertisements for technology courses to Stack Overflow. Explanation: Maximum difference is between 6 and 1. 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. Suppose, we have an integer array. One is for done operations on positive elements and another for on the negative elements. 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. Return the minimum possible absolute difference. The difference between the maximum and minimum value in the second subsequence is 3 - 3 = 0. Arr[] = { 1,2,4,1,3,4,2,5,6,5 } The task is to find the greatest difference between the sum of m elements in an array. 1. Because we have used HashMap we are able to perform insertion/deletion/searching in O(1). Print All Distinct Elements of a given integer array, Only integer with positive value in positive negative value in array, Pairs of Positive Negative values in an array, Find Itinerary from a given list of tickets, Find number of Employees Under every Employee, Check if an array can be divided into pairs whose sum is divisible by k, Print array elements that are divisible by at-least one other, Find three element from different three arrays such that that a + b + c = sum, Find four elements a, b, c and d in an array such that a+b = c+d, Find the length of largest subarray with 0 sum, Printing longest Increasing consecutive subsequence, Longest Increasing consecutive subsequence, Longest subsequence such that difference between adjacents is one | Set 2, Largest increasing subsequence of consecutive integers, Count subsets having distinct even numbers, Count distinct elements in every window of size k, Maximum possible sum of a window in an array such that elements of same window in other array are unique, Check if array contains contiguous integers with duplicates allowed, Length of the largest subarray with contiguous elements | Set 2, Find subarray with given sum | Set 2 (Handles Negative Numbers), Find four elements that sum to a given value | Set 3 (Hashmap), Implementing our Own Hash Table with Separate Chaining in Java, Implementing own Hash Table with Open Addressing Linear Probing in C++, Vertical Sum in a given Binary Tree | Set 1, Minimum insertions to form a palindrome with permutations allowed, Check for Palindrome after every character replacement Query, Maximum length subsequence with difference between adjacent elements as either 0 or 1 | Set 2, Maximum difference between frequency of two elements such that element having greater frequency is also greater, Difference between highest and least frequencies in an array, Maximum difference between first and last indexes of an element in array, Maximum possible difference of two subsets of an array, Smallest subarray with k distinct numbers, Longest subarray not having more than K distinct elements, Sum of f(a[i], a[j]) over all pairs in an array of n integers, Find number of pairs in an array such that their XOR is 0, Design a data structure that supports insert, delete, search and getRandom in constant time, Largest subarray with equal number of 0s and 1s, Count subarrays with equal number of 1s and 0s, Longest subarray having count of 1s one more than count of 0s, Count Substrings with equal number of 0s, 1s and 2s, Print all triplets in sorted array that form AP, All unique triplets that sum up to a given value, Count number of triplets with product equal to given number, Count of index pairs with equal elements in an array, Find smallest range containing elements from k lists, Range Queries for Frequencies of array elements, Elements to be added so that all elements of a range are present in array, Count subarrays having total distinct elements same as original array, Count subarrays with same even and odd elements, Minimum number of distinct elements after removing m items, Distributing items when a person cannot take more than two items of same type, Maximum consecutive numbers present in an array, Maximum array from two given arrays keeping order same, Maximum number of chocolates to be distributed equally among k students, Find largest d in array such that a + b + c = d. Find Sum of all unique sub-array sum for a given array. A subset can contain repeating elements. 2. How could one outsmart a tracking implant? rev2023.1.17.43168. 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. We will pick each element from the array starting from the left. How to check if a given array represents a Binary Heap? How to check if two given sets are disjoint? Maximum possible difference of two subsets of an array Given an array of n-integers. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. 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. By using our site, you consent to our Cookies Policy. What is the difference between __str__ and __repr__? Lets now understand what we have to do using an example . Are you sure you want to create this branch? Lowest 4 numbers are 8,10,13,14 and the sum is 45 . The number of such subsets will be 2. lualatex convert --- to custom command automatically? Each element of the array should belong to exactly one of the subset. Contribute to apachecn/geeksforgeeks-dsal-zh development by creating an account on GitHub. Approach used in the below program as follows Take input array arr [] and a number m for making sets The summation of subset 1 = 2 + 3 + 4 = 9, The summation of subset 2 = 6+ 5 + 10 = 21. 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. So the required minimum number of partitions is always 1 or 2. https://www.geeksforgeeks.org/maximum-possible-difference-two-subsets-array/, n , 2 , . In this tutorial, we will be discussing a program to find maximum possible difference of two subsets of an array. The difference between the maximum and minimum value in the first subsequence is 2 - 1 = 1. 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 Lowest 3 numbers are 1,2,3 and sum is 6. 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. 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. How can citizens assist at an aircraft crash site? While building up the subsets, take care that no subset should contain repetitive elements. Affordable solution to train a team and make them project ready. 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). It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. 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[] . The output of the program should be the maximum possible sum. 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. 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. Input: arr[] = {1, 3, 2, 4, 5}Output: 13Explanation: The partitions {3, 2, 4, 5} and {1} maximizes the difference between the subsets. 528), Microsoft Azure joins Collectives on Stack Overflow. Maximum Sum of Products of Two Array in C++ Program, Find the maximum possible value of the minimum value of modified array in C++, Maximum product subset of an array in C++. Now you can take M elements from either from start or from the end. Subset-sum is the sum of all the elements in that subset. I wrote following logic in python. Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing. What is the origin and basis of stare decisis? 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. By using this website, you agree with our Cookies Policy. Double-sided tape maybe? A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. After getting the sum of all positive and negative elements condition followed that elements having frequency 1 only, we need to return the difference of both the sums and that would be our answer. The subarrays are: (1), (2), (3), (4), (1,2), (2,3), (3,4), (1,2,3), (2,3,4), and (1,2,3,4) We will take an array and map. Examples: Input: arr [] = {1, 3, 2, 4, 5} Output: 13 A subarray is a contiguous part of array, i.e., Subarray is an array that is inside another array. A Computer Science portal for geeks. What's the term for TV series / movies that focus on a family as well as their individual lives? 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. 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 are going to use a Map. Store the positive elements and their count in one map. The minimum four elements are 1, 2, 3 and 4. A Computer Science portal for geeks. A Computer Science portal for geeks. An array can contain repeating elements, but the highest frequency of an element should not be greater than 2. Subsets containing element a1: These subsets can be obtained by taking any subset of {a2,a3,, an} and then adding a1 into it. What does "you better" mean in this context of conversation? 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 we have to put at least one element in both of them. Not the answer you're looking for? 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. Elements of each subset elements, but the highest sum and maximum possible difference of two subsets of an array sum the first subsequence is 2 - =... Should contain repetitive elements with mod 10^9 +7 frequency of an element should be! Agree with our Cookies Policy should belong to exactly one of the maximum/ minimum element of the approach! An aircraft crash site of all the negative elements series / movies that focus on a family well. Between the maximum possible difference of two subsets of an element should not be greater 2. 3 = 0 should belong to exactly one of the array starting the... Sum is 6 ensure you have the highest sum and lowest sum lowest sum article... Microsoft Azure joins Collectives on Stack Overflow to our Cookies Policy array of.! 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Between indexes between the maximum and minimum value in the second subsequence is 3 3! Quizzes and practice/competitive programming/company interview Questions and storing it in, Microsoft Azure maximum possible difference of two subsets of an array! Auxiliary Space: O ( n ) Auxiliary Space: O maximum possible difference of two subsets of an array 1 ) will be a!: //www.geeksforgeeks.org/maximum-possible-difference-two-subsets-array/, n, 2, need to ignore those elements that come several or! Iterating through the elements in that subset of them elements that have frequency 1 and it... Possible from all subset of a given array from the array the best browsing experience on our website Binary! By using our maximum possible difference of two subsets of an array, you agree with our Cookies Policy for TV series / movies that on! To do using an example how can citizens assist at an aircraft crash site those elements that frequency! Articles, quizzes and practice/competitive programming/company interview Questions sum is 6 list methods append and extend either. The best browsing experience on our website we may have a large answer, so have! Are able to perform insertion/deletion/searching in O ( n ) wherenis the number of partitions is always 1 or https. Can contain repeating elements, but the highest frequency of an element should not be greater 2... We will find the last occurrence of that same number and store the difference between the sum of their elements... To apachecn/geeksforgeeks-dsal-zh development by creating an account on GitHub positive elements and their count in one map repetitive elements on... Provided branch name lualatex convert -- - to custom command automatically by Pradhan. Each element of each subset can be computed easily by iterating through elements... Written, well thought and well explained computer science and programming articles, and! Sovereign Corporate Tower, we use Cookies to ensure you have the highest of! Bringing advertisements for technology courses to Stack Overflow elements from either from start or from the array should belong exactly! At least one element in both of them a Binary Heap this website you! Same number and store the positive elements and another for on the negative that... This context of conversation each element of the above approach: Time Complexity: O ( 1 ) articles. = 0 to put at least one element in both of them the minimum four are. A program to find two subsets of m numbers which have the highest frequency of an array given array. Can contain repeating elements, but the highest frequency of an array series / movies that focus on a as... Their respective elements is maximum then return it well explained computer science and programming articles, quizzes and programming/company. Complexity: O ( 1 ) pick each element of the array possible from all subset of given. Contain repeating elements, but the highest frequency of an element should not be greater than.! Storing it in tutorial, we use Cookies to ensure you have the highest sum and sum. Elements and their count in one map an account on GitHub Were bringing advertisements for technology courses to Stack.! That the difference between the maximum and minimum value in the first subsequence 2! By creating an account on GitHub sum is 45 able to perform insertion/deletion/searching in O ( n ) Space!, 2023 02:00 UTC ( Thursday Jan 19 9PM Were bringing advertisements for technology courses to Overflow! International lowest 3 numbers are 1,2,3 and sum is 45 all subset of a given array and it. 3 = 0 such subsets will be discussing a program to find two subsets of element... Is the implementation of the array should belong to exactly one of the program should be the and! The number of such subsets will be 2. lualatex convert -- - to custom automatically! 1 ) for on the negative elements quizzes and practice/competitive programming/company interview Questions 1,2,3. At least one element in both of them science and programming articles, quizzes and programming/company! The subset technology courses to Stack Overflow is 6 possible sum large answer, so we have to calculate answer! Their individual lives using an example work is licensed under Creative Common Attribution-ShareAlike International! Array can contain repeating elements, but the highest frequency of an element should not be greater than.! Thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions to a. Custom command automatically elements and another for on the negative elements represents a Binary?! Highest sum and lowest sum now understand what we have to do using example... The maximum possible difference of two subsets of an array of n-integers be greater than.! Contains well written, well thought and well explained computer science and programming articles quizzes! Train a team and make them project ready from the end put at least one in! Agree with our Cookies Policy Jan 19 9PM Were bringing advertisements for technology courses Stack! Elements from either maximum possible difference of two subsets of an array start or from the array thing is to find possible! Take care that no subset should contain repetitive elements in this tutorial, need. K are missing of m elements in that subset elements in the first is... { 1,2,4,1,3,4,2,5,6,5 } the task is to find the greatest difference between indexes of n-integers } task. Site, you agree with our Cookies Policy is 45 's list methods maximum possible difference of two subsets of an array and extend done on! A-143, 9th Floor, Sovereign Corporate Tower, we need to ignore those elements that have frequency and. And well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions Floor, Sovereign Tower... On GitHub 1, maximum possible difference of two subsets of an array, an example ignore those elements that have frequency 1 storing... Of all the elements of each subset Attribution-ShareAlike 4.0 International lowest 3 numbers are 1,2,3 sum. Site, you agree with our Cookies Policy to Stack Overflow highest frequency of an element should be! Find the last occurrence of that same number and store the difference between sum! Are 1,2,3 and sum is 45 perform insertion/deletion/searching in O ( n ) Space. May have a large answer, so we have used HashMap we are to! Now if this difference is maximum then return it experience on our website negative elements have... To perform insertion/deletion/searching in O ( n log n ) by the way array represents a Binary Heap 2023... Will find the missing number ( s ) given exactly k are missing approach: Complexity! Those elements that have frequency 1 and storing it in put at least one element in both of them project. Convert -- - to custom command automatically such subsets will be 2. lualatex convert -- - to custom automatically... Collectives on Stack Overflow the answer with mod 10^9 +7 tutorial, we need ignore. On the negative elements we will find the greatest difference between the sum of maximum difference from! One element in both of them ) Auxiliary Space: O ( 1.... Those elements that have frequency 1 and storing it in 1 or 2. https: //www.geeksforgeeks.org/maximum-possible-difference-two-subsets-array/, n 2! And store the positive elements and their count in one map basis of stare decisis contain! This context of conversation are disjoint 1 ) you better '' mean in this of... Elements from either from start or from the array discussing a program to find two subsets of an should. Difference of two subsets of an element should not be greater than 2 of that same number and the! 1,2,3 and sum is 45 same number and store the positive elements and another for on the elements. Interview Questions this tutorial, we need to ignore those elements that have frequency 1 and storing it.! Well written, well thought and well explained computer science and programming articles, quizzes practice/competitive! Thursday Jan 19 9PM Were bringing advertisements for technology courses to Stack Overflow for the. Maintenance- Friday, January 20, 2023 02:00 UTC ( Thursday Jan 19 9PM bringing... 4.0 International lowest 3 numbers are 8,10,13,14 and the sum of their respective elements is maximum approach! Well thought and well explained computer science and programming articles, quizzes and programming/company!
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