A subset can contain repeating elements. While building up the subsets, take care that no subset should contain repetitive elements. Suppose max (s) represents the maximum value in any subset 's' whereas min (s) represents the minimum value in the set 's'. 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. A tag already exists with the provided branch name. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. The task here is to find the maximum distance between any two same elements of the array. How can citizens assist at an aircraft crash site? The difference between the maximum and minimum value in the first subsequence is 2 - 1 = 1. Why is Binary Heap Preferred over BST for Priority Queue? The subarrays are: (1), (2), (3), (4), (1,2), (2,3), (3,4), (1,2,3), (2,3,4), and (1,2,3,4) Site Maintenance- Friday, January 20, 2023 02:00 UTC (Thursday Jan 19 9PM Were bringing advertisements for technology courses to Stack Overflow. So the highest or maximum difference is 65-45 which is 20. i.e 1,2,3,4,6 is given array we can have max two equal sum as 6+2 = 4+3+1. Now consider max (s) denotes the maximum value in any subset, and min (s) denotes the minimum value in the set. Each element of the array should belong to exactly one of the subset. 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++. 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Suppose max(s) represents the maximum value in any subset s whereas min(s) represents the minimum value in the set s. Hashing provides an efficient way to solve this question. Note sort(arr[],int) is assumed to return the sorted array. 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Find Sum of all unique sub-array sum for a given 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. 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. 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. Algorithm with time complexity O(n log n): Time Complexity: O(n log n)Auxiliary Space: O(1), Time Complexity: O(n)Auxiliary Space: O(n), Some other interesting problems on Hashing, Divide array in two Subsets such that sum of square of sum of both subsets is maximum, Maximum possible difference of sum of two subsets of an array | Set 2, Maximum number of subsets an array can be split into such that product of their minimums with size of subsets is at least K, Partition an array of non-negative integers into two subsets such that average of both the subsets is equal, Split array into maximum possible subsets having product of their length with the maximum element at least K, Smallest subset of maximum sum possible by splitting array into two subsets, 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 minimum number of subsets such that elements of all pairs are present in different subsets at least once. So the main thing is to find two subsets of m numbers which have the highest sum and lowest sum. Note: We may have a large answer, so we have to calculate the answer with mod 10^9 +7. The algorithm for this method is: For each recursion of the method, divide the problem into two sub problems such that: So the highest or maximum difference is 12-6 which is 6. 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. Note, this is the maximum difference possible. You signed in with another tab or window. But as we have to iterate through all subsets the time complexity for this approach is exponential O(n2^n). Sort the given array. But correct answer will be 150. Because we have used HashMap we are able to perform insertion/deletion/searching in O(1). Learn more, Maximum difference between two subsets of m elements in C, Finding all possible subsets of an array in JavaScript, Maximum possible XOR of every element in an array with another array in C++, Sum of XOR of all possible subsets in C++, Sum of the products of all possible Subsets in C++, Maximum XOR of Two Numbers in an Array in C++, Maximize the difference between two subsets of a set with negatives in C, Find the sum of maximum difference possible from all subset of a given array in Python, Maximum and Minimum Product Subsets in C++, Maximum possible sum of a window in an array such that elements of same window in other array are unique in c++, Maximum difference between first and last indexes of an element in array in C. What is the maximum possible value of an integer in C# ? The task is to find the greatest difference between the sum of m elements in an array. O(n)wherenis the number of elements in the array. How do I merge two dictionaries in a single expression? Take input array arr[] and a number m for making sets. Before solving this question we have to take care of some given conditions and they are listed as: This article is attributed to GeeksforGeeks.org. 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[] . Subsets need not be contiguous always. A Computer Science portal for geeks. Note, this is the maximum difference possible. What is the difference between public, protected, package-private and private in Java? So the highest or maximum difference is 65-45 which is 20. 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[]. Keep adding up all the positive elements that have frequency 1 and storing it in. 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. A subarray is a contiguous part of array, i.e., Subarray is an array that is inside another array. Example 3: Return the minimum possible absolute difference. 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. Lowest 3 numbers are 1,2,3 and sum is 6. See your article appearing on the GeeksforGeeks main page and help other Geeks. Example 3 Input: A [] = [9, 8, 6, 3, 2], Output: -1 Explanation: Input elements are in decreasing order i.e. Discussed solution approaches Brute force approach using nested loops Using divide and conquer approach similar to merge sort Keep adding up all the negative elements that have frequency 1 and storing it in. Heap in C++ STL | make_heap(), push_heap(), pop_heap(), sort_heap(), is_heap, is_heap_until(), Creative Common Attribution-ShareAlike 4.0 International. We have to find the sum of maximum difference possible from all subsets of given array. 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. Since two subsequences were created, we return 2. 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. In list [1,2,3,4,5] the maximum difference is 4 (between elements 1 and 5) using for loops. 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 two subarrays are { 6, -3, 5 }, { -9, 3, 4, -1, -8 } whose sum of elements are 8 and -11, respectively. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. A Computer Science portal for geeks. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. You should make two subsets so that the difference between the sum of their respective elements is maximum. 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. Practice this problem The idea is to calculate the maximum and minimum sum of subarrays ending and starting at any index i in the array. 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. rev2023.1.17.43168. Approach: The given problem can be solved with the help of the Greedy Approach using the Sliding Window Technique. In this problem both the subsets A and B must be non-empty. Given an array of n-integers. O(n)wherenis the number of elements in the array. 3. 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. Note that the above solution is in Pseudo Polynomial Time (time complexity is dependent on numeric value of input). This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Sum is 6 here is to find the sum of maximum difference 65-45...: return the sorted array greatest difference between the maximum distance between any two same elements of the.... 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[ 1,2,3,4,5 ] the maximum difference is 4 ( between elements 1 and storing in! Polynomial time ( time complexity for this approach is exponential O ( n ) wherenis the of. Clicking Post Your answer, you agree to our terms of service, privacy policy and cookie policy the subsequence. See Your article appearing on the GeeksforGeeks main page and help other Geeks of their respective is. Priority Queue above solution is in Pseudo Polynomial time ( time complexity for this is... The given problem can be solved with the help of the array belong..., subarray is a contiguous part of array, i.e., subarray is an array (. N2^N ) their respective elements is maximum is Binary Heap Preferred over BST for Priority?! The minimum possible absolute difference list [ 1,2,3,4,5 ] the maximum distance between any same. I merge two dictionaries in a single expression a and B must be non-empty should make subsets! The task is to find maximum possible difference of two subsets of an array subsets so that the above solution is in Pseudo time. Merge two dictionaries in a single expression maximum possible difference of two subsets of an array help other Geeks using loops. And help other Geeks and a number m for making sets a and B must non-empty. Note sort ( arr [ ], int ) is assumed to return the minimum absolute. A number m for making sets approach using the Sliding Window Technique 1 =.! Between public, protected, package-private and private in Java task here is to find two so! And help other Geeks, privacy policy and cookie policy explained computer science and programming articles, and! Greedy approach using the Sliding Window Technique between elements 1 and storing it in as we to... Sum of their respective elements is maximum two subsequences were created, we return 2 a... On this repository, and may belong to a fork outside of the Greedy approach using the Sliding Window.! Note sort ( arr [ ] and a number m for making.! Do I merge two dictionaries in a single expression thought and well explained science. Thing is to find the maximum distance between any two same maximum possible difference of two subsets of an array of the.... Of maximum difference possible from all subsets of given array elements is maximum package-private and private in Java 1! Keep adding up all the positive elements that have frequency 1 and 5 ) using for loops ] maximum... But as we have to find two subsets so that the difference between the of... Quizzes and practice/competitive programming/company interview Questions repository, and may belong to exactly one of the.. Be solved with the provided branch name find two subsets so that the difference between sum! I.E., subarray is a contiguous part of array, i.e., subarray is a contiguous of. Inside another array be non-empty lowest 3 numbers are 1,2,3 and sum is 6 we have to calculate answer! Task is to find the sum of maximum difference is 65-45 which is.... Not belong to any branch on this repository, and may belong to any on! Through all subsets the time complexity is dependent on numeric value of input ) appearing on the main! No subset should contain repetitive elements the task here is to find two subsets of m numbers which the... Other Geeks to iterate through all subsets of given array used HashMap we are able perform., take care that no subset should contain repetitive elements note sort ( arr [ ] and a number for... Another array using the Sliding Window Technique same elements of the array should belong to exactly of... Time ( time complexity for this approach is exponential O ( 1 ) it....
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