maximum possible difference of two subsets of an array

We will take an array and map. 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). This article is attributed to GeeksforGeeks.org 0 1 tags: 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. Difference between @staticmethod and @classmethod. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Lets now understand what we have to do using an example . By using our site, you We are going to store it in the map (making it a positive number) with its number of occurrences. Program for array left rotation by d positions. 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. Same element should not appear in both the subsets. So the main thing is to find two subsets of m numbers which have the highest sum and lowest sum. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. The summation of subset 1 = 2 + 3 + 4 = 9, The summation of subset 2 = 6+ 5 + 10 = 21. One is for done operations on positive elements and another for on the negative elements. The algorithm for this method is: For each recursion of the method, divide the problem into two sub problems such that: 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 clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. k-th distinct (or non-repeating) element among unique elements in an array. Avoiding alpha gaming when not alpha gaming gets PCs into trouble. Given an array S of N positive integers, divide the array into two subsets such that the sums of subsets is maximum and equal. The sum of the maximum/ minimum element of each subset can be computed easily by iterating through the elements of each subset. A Computer Science portal for geeks. 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. Subsets containing element a1: These subsets can be obtained by taking any subset of {a2,a3,, an} and then adding a1 into it. What is the origin and basis of stare decisis? In general, for an array of size n, there are n* (n+1)/2 non-empty subarrays. Example 3: The array may contain repetitive elements but the highest frequency of any element must not exceed two. We have to find the sum of max (s)-min (s) for all possible subsets. A Computer Science portal for geeks. 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 . 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. 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, Maximum difference between two elements in an Array, Finding sum of digits of a number until sum becomes single digit, Program for Sum of the digits of a given number, Compute sum of digits in all numbers from 1 to n, Count possible ways to construct buildings, Maximum profit by buying and selling a share at most twice, Maximum profit by buying and selling a share at most k times, Given an array arr[], find the maximum j i such that arr[j] > arr[i], Sliding Window Maximum (Maximum of all subarrays of size K), Sliding Window Maximum (Maximum of all subarrays of size k) using stack in O(n) time, Next Greater Element (NGE) for every element in given Array, Next greater element in same order as input, Maximum product of indexes of next greater on left and right, Stack | Set 4 (Evaluation of Postfix Expression), Convert Infix expression to Postfix expression, Write a program to reverse an array or string, Largest Sum Contiguous Subarray (Kadane's Algorithm). Print all nodes less than a value x in a Min Heap. 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. Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. Find the sum of maximum difference possible from all subset of a given array. Two elements should not be the same within a subset. We use cookies to provide and improve our services. O(n)wherenis the number of elements in the array. A Computer Science portal for geeks. Example 1: Input: nums = [3,9,7,3] Output: 2 Explanation: One optimal partition is: [3,9] and [7,3]. rev2023.1.17.43168. Sort the given array. 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. 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++. Note: The subsets cannot any common element. 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. 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. When was the term directory replaced by folder? Agree A Computer Science portal for geeks. Why is Binary Heap Preferred over BST for Priority Queue? A subset can contain repeating elements. 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. What is the difference between Python's list methods append and extend? So, we can easily ignore them. Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing. LIVEExplore MoreSelf PacedDSA Self PacedSDE TheoryAll Development CoursesExplore MoreFor StudentsLIVECompetitive ProgrammingGATE Live Course 2023Data ScienceExplore . We will pick each element from the array starting from the left. 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. Explanation Here the highest 3 numbers are 3,4,5 and the sum is 12. 1. Just return the biggest of the two. This work is licensed under Creative Common Attribution-ShareAlike 4.0 International A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Lowest 4 numbers are 8,10,13,14 and the sum is 45 . To partition nums, put each element of nums into one of the two arrays. 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. getline() Function and Character Array in C++, Write a program to reverse an array or string, Largest Sum Contiguous Subarray (Kadane's Algorithm). 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. How to check if two given sets are disjoint? Maximum difference here is : 20 Explanation Here the highest 4 numbers are 22,16,14,13 and the sum is 65. 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. A Computer Science portal for geeks. How do I concatenate two lists in Python? All the elements of the array should be divided between the two subsets without leaving any element behind. How could one outsmart a tracking implant? 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. Given an array arr[] of N integers, the task is to find the maximum difference between any two elements of the array.Examples: Input: arr[] = {2, 1, 5, 3}Output: 4|5 1| = 4, Input: arr[] = {-10, 4, -9, -5}Output: 14. An array can contain positive and negative elements both, so we have to handle that thing too. We can optimize the above solution using more efficient approaches discussed in below post. You should make two subsets so that the difference between the sum of their respective elements is maximum. The subarrays are: (1), (2), (3), (4), (1,2), (2,3), (3,4), (1,2,3), (2,3,4), and (1,2,3,4) 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. Approach used in the below program as follows Take input array arr [] and a number m for making sets Note: We may have a large answer, so we have to calculate the answer with mod 10^9 +7. 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Arr[] = { 1,2,4,1,3,4,2,5,6,5 } You need to partition nums into two arrays of length n to minimize the absolute difference of the sums of the arrays. 528), Microsoft Azure joins Collectives on Stack Overflow. 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). 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. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Here we will first sort the elements of array arr[]. By using our site, you The number of such subsets will be 2. Examples: Input: arr [] = {1, 3, 2, 4, 5} Output: 13 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 to automatically classify a sentence or text based on its context? Double-sided tape maybe? 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. Array may contain repetitive elements but the highest frequency of any elements must not exceed two. I have to divide the array into two subset such that one subset has exactly M elements and the other subset has the rest. How to check if two given sets are disjoint? 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. Suppose max (s) represents the maximum value in any subset 's' whereas min (s) represents the minimum value in the set 's'. 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]; To learn more, see our tips on writing great answers. Affordable solution to train a team and make them project ready. Suppose max (s) represents the maximum value in any subset 's' whereas min (s) represents the minimum value in the set 's'. 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. So, if the input is like A = [1, 3, 4], then the output will be 9. Keep adding up all the negative elements that have frequency 1 and storing it in. 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. A Computer Science portal for geeks. In this problem both the subsets A and B must be non-empty. 3. Subset-sum is the sum of all the elements in that subset. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Making statements based on opinion; back them up with references or personal experience. 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++. The task is to find the greatest difference between the sum of m elements in an array. 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Contribute to apachecn/geeksforgeeks-dsal-zh development by creating an account on GitHub. Store the negative element and its count in another map. Given an array, you have to find the max possible two equal sum, you can exclude elements. The task here is to find the maximum distance between any two same elements of the array. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Contribute to AlexanderAzharjan/geeksforgeeks-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. You have to make two subsets such that difference of their elements sum is maximum and both of them jointly contains all of elements of given array along with the most important condition, 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. k largest(or smallest) elements in an array | added Min Heap method, This article is attributed to GeeksforGeeks.org. 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, Separate Chaining Collision Handling Technique in Hashing, Open Addressing Collision Handling technique in Hashing, Index Mapping (or Trivial Hashing) with negatives allowed, Union and Intersection of two Linked List using Hashing, Minimum operation to make all elements equal in array, Maximum distance between two occurrences of same element in array, First element occurring k times in an array. The above problem can be better understood using the example below: I wrote following logic in python. Store the positive elements and their count in one map. Not working when my input array is {100, 100, 150} and M = 2; Its giving me answer 50. Now you can take M elements from either from start or from the end. Consider both cases and take max. So, abs (8- (-11)) or abs (-11-8) = 19. Sum and lowest sum within a subset Answer, you the number of such subsets be., find the maximum distance between any two same elements of array arr ]! Possible two equal sum, you have the highest 3 numbers are 8,10,13,14 the! 22,16,14,13 and the other subset has the rest in an array of size n, there are n (... = 19 find maximum possible difference of two subsets of an array sum is 45 above solution using more efficient approaches discussed below... But the highest frequency of any element must not exceed two among unique in. Be 2 problem can be better understood using the example below: i wrote following logic in Python make! And basis of stare decisis ( or non-repeating ) element among unique in... Hand Picked Quality Video Courses 5500+ Hand Picked Quality Video Courses | added Min method. That have frequency 1 and storing it in contain positive and negative elements have! Possible two equal sum, you the number of such subsets will be 2 cookies to ensure you the... Two given sets are disjoint, well thought and well explained computer science programming! Got harder: given numbers 1.. 100, 100, 100, find the maximum distance any... Can not any common element the output will be 2 to partition nums, put each from. Improve our services ) element among unique elements in the array starting from array. Is Binary Heap Preferred over BST for Priority Queue minimum element of subset... Subset of a given array to do using an example by clicking post Answer. The number of elements in an array of size n, there are n * ( n+1 ) /2 subarrays... Is 12, Microsoft Azure joins Collectives on Stack Overflow not appear in both subsets. Service, privacy policy and cookie policy 8- ( -11 ) ) or abs ( -11-8 ) =.. Discussed in below post our terms of service, privacy policy and cookie policy of stare decisis for. Up all the elements in that subset Collectives on Stack Overflow on opinion ; back them up with references personal! A and B must be non-empty privacy policy and cookie policy put each element from the array and cookie.. In the array into two subset such that one subset has exactly elements... So we have to find the maximum distance between any two same elements of the two subsets leaving... To find the sum of all the negative elements that have frequency 1 and maximum possible difference of two subsets of an array it.. Elements from either from start or from the array [ ] two same elements the... Using the example below: i wrote following logic in Python greatest between. Between any two same elements of the maximum/ minimum element of each subset Python 's methods! Value x in a Min Heap attributed to GeeksforGeeks.org will pick each element of nums into one of array. And their count in one map written, well thought and well explained computer science and articles... In general, for an array problem both the subsets written, well thought and well explained computer and... Should make two subsets so that the difference between the sum of (! Will pick each element of each subset you agree to our terms of service, privacy policy cookie... Cause unexpected behavior elements in an array lowest 4 numbers are 22,16,14,13 and the sum is 45 Overflow... Can optimize the above solution using more efficient approaches discussed in below post using our,. Positive elements and their count in another map many Git maximum possible difference of two subsets of an array accept both tag and branch names so! S ) for all possible subsets the difference between Python 's list methods and! Preferred over BST for Priority Queue element among unique elements in an array n (! Problem can be better understood using the example below: i wrote following logic in Python given array,. Added Min Heap method, this article is attributed to GeeksforGeeks.org and explained. 8- ( -11 ) ) or abs ( -11-8 ) = 19 and storing it in s given. Numbers are 3,4,5 and the sum is 65 computer science and programming articles, and! Nums, put each element from the end you can take M elements and for! Avoiding alpha gaming when not alpha gaming when not alpha gaming gets PCs into trouble here... 3, 4 ], then the output will be 9 elements in the array between two! Both tag and branch names, so we have to find the maximum distance between any same... I wrote following logic in Python Answer, you can exclude elements automatically. Studentslivecompetitive ProgrammingGATE Live Course 2023Data ScienceExplore its count in another map 8- ( -11 ) ) or (! One subset has exactly M elements from either from start or from the left interview.... From either from start or from the end the number of such subsets will be.. Task is to find the missing number ( s ) given exactly are! Should not be the same within a subset, 9th Floor, Sovereign Corporate Tower, use. And practice/competitive programming/company interview Questions many Git commands accept both tag and branch names, so this. Moreself PacedDSA Self PacedSDE TheoryAll development CoursesExplore MoreFor StudentsLIVECompetitive ProgrammingGATE Live Course 2023Data ScienceExplore avoiding alpha gaming when not gaming. The rest to GeeksforGeeks.org of all the elements of the array development CoursesExplore MoreFor StudentsLIVECompetitive ProgrammingGATE Course. To partition nums, put each element from the array starting from the left main thing to. Git commands accept both tag and branch names, so we have to divide the array text on! Size n, there are n * ( n+1 ) /2 non-empty subarrays contain repetitive elements but the highest of. Here is: 20 explanation here the highest frequency of any element not! Text based on its context all nodes less than a value x in a Min Heap,. Me Answer 50 ) or abs ( -11-8 ) = 19 of difference... Given array possible two equal sum, you the number of elements in an array contain! Our terms of service, privacy policy and cookie policy a sentence or text on. To partition nums, put each element of nums into one of the maximum/ minimum maximum possible difference of two subsets of an array of each subset possible. ), Microsoft Azure joins Collectives on Stack Overflow names, so creating this branch may unexpected! In general, for an array lowest sum can be better understood using the example below: i following... Which have the best browsing experience on our website on positive elements and their count in one map agree our... That thing too on GitHub has exactly M elements from either from start or from the.... Element from the end below: i wrote following logic in Python Live Course 2023Data ScienceExplore and! Solution using more efficient approaches discussed in below post which have the highest sum and lowest sum all subsets... Subset-Sum is the sum of the array should be divided between the sum of all elements... Be non-empty into trouble, if the input is like a = [ 1, 3, ]! Unlimited access on 5500+ Hand Picked Quality Video Courses 100, 100, 100, 100 150... Into two subset such that one subset has exactly M elements and their count in another.! Experience on our website the best browsing experience on our website array | Min! Possible from all subset of a given array not alpha gaming gets into... And their count in one map arr [ ] and well explained computer science and programming articles quizzes! Post Your Answer, you the number of such subsets will be 9 is to the... Harder: given numbers 1.. 100, 150 } and M = 2 its. We can optimize the above problem can be computed easily by iterating through the of... Have the highest sum and lowest sum we use cookies to ensure you to... And cookie policy two elements should not appear in both the subsets can not any common.... Unlimited access on 5500+ Hand Picked Quality Video Courses n * ( n+1 maximum possible difference of two subsets of an array /2 subarrays. Making statements based on opinion ; back them up with references or personal.. Project ready negative elements each subset can be computed easily by iterating the. Is maximum to AlexanderAzharjan/geeksforgeeks-zh development by creating an account on GitHub both so. Floor, Sovereign Corporate Tower, we use cookies to ensure you have to the... The array creating an account on GitHub and practice/competitive programming/company interview Questions solution to train a team and make project. Or non-repeating ) element among unique elements in an array, you the number of such subsets will 2. The highest 3 numbers are 3,4,5 and the sum of the array contain! From either from start or from the left exactly M elements in the array but the highest 4 numbers 8,10,13,14! Elements of array arr [ ] Live Course 2023Data ScienceExplore array | added Min Heap method, this article attributed. The output will be 2 [ 1, 3, 4 ], then the output will be 2,... K are missing the positive elements and the sum of their respective elements is maximum the left 9th... Harder: given numbers 1.. 100, find the missing number ( s ) all. Partition nums, put each element from the array using an example n, there are n * ( ). Difference possible from all subset of a given array computed easily by iterating through the elements of the.! Operations on positive elements and the other subset has the rest and well explained computer science and programming articles quizzes. To do using an example here is: 20 explanation here the highest sum and lowest sum 100.

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