Maximum difference between two subsets of m elements Last Updated : 04 Mar, 2025 Summarize Comments Improve Suggest changes Share Like Article Like Report 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.Examples: Input : arr[] = 1 2 3 4 5 m = 4Output : 4The maximum four elements are 2, 3, 4 and 5. The minimum four elements are 1, 2, 3 and 4. The difference between two sums is (2 + 3 + 4 + 5) - (1 + 2 + 3 + 4) = 4 Input : arr[] = 5 8 11 40 15 m = 2Output : 42The difference is (40 + 15) - (5 + 8). [Naive Solution] - Using Sorting - O(n Log n) Time and O(1) SpaceThe idea is to first sort the array, then find sum of first m elements and sum of last m elements. Finally return difference between two sums. C++ #include <bits/stdc++.h> using namespace std; // utility function int findDiff(vector<int>& arr, int m) { int max = 0, min = 0; // sort array sort(arr.begin(), arr.end()); // Traverse m elements from both ends int n = arr.size(); for (int i = 0; i < m; i++) { min += arr[i]; max += arr[n - 1 - i]; } return (max - min); } // Driver code int main() { vector<int> arr = { 1, 2, 3, 4, 5 }; int m = 4; cout << findDiff(arr, m); return 0; } Java import java.util.Arrays; public class Main { // utility function public static int findDiff(int[] arr, int m) { int max = 0, min = 0; // sort array Arrays.sort(arr); // Traverse m elements from both ends int n = arr.length; for (int i = 0;i < m; i++) { min += arr[i]; max += arr[n - 1 - i]; } return (max - min); } // Driver code public static void main(String[] args) { int[] arr = {1, 2, 3, 4, 5}; int m = 4; System.out.println(findDiff(arr, m)); } } Python def find_diff(arr, m): max_sum = 0 min_sum = 0 # sort array arr.sort() # Traverse m elements from both ends n = len(arr) for i in range(m): min_sum += arr[i] max_sum += arr[n - 1 - i] return max_sum - min_sum # Driver code arr = [1, 2, 3, 4, 5] m = 4 print(find_diff(arr, m)) C# using System; using System.Collections.Generic; using System.Linq; class Program { // utility function static int FindDiff(List<int> arr, int m) { int max = 0, min = 0; // sort array arr.Sort(); // Traverse m elements from both ends int n = arr.Count; for (int i = 0; i < m; i++) { min += arr[i]; max += arr[n - 1 - i]; } return max - min; } // Driver code static void Main() { List<int> arr = new List<int> { 1, 2, 3, 4, 5 }; int m = 4; Console.WriteLine(FindDiff(arr, m)); } } JavaScript function findDiff(arr, m) { let max = 0, min = 0; // sort array arr.sort((a, b) => a - b); // Traverse m elements from both ends let n = arr.length; for (let i = 0; i < m; i++) { min += arr[i]; max += arr[n - 1 - i]; } return max - min; } // Driver code let arr = [1, 2, 3, 4, 5]; let m = 4; console.log(findDiff(arr, m)); Output4[Naive Solution] - Using Heap - O(n Log m) Time and O(m) SpaceThe idea is based on the solution discussed in k largest elements in an arrayCreate a Min Heap to Store m largest. We first push first m elements. For remaining n-m elements, we compare every element with the heap top. If Heap top is smaller, we insert the new element in the min heapIn the same way, create a Max Heap to Store m smallest.Find the sums of elements in both the heaps and return the difference of two sums. C++ #include <iostream> #include <queue> #include <vector> using namespace std; int findDiff(vector<int>& arr, int m) { // Min heap to store the 'm' largest elements priority_queue<int, vector<int>, greater<int>> mnH; // Max heap to store the 'm' smallest elements priority_queue<int> mxH; // Maintain 'm' smallest elements in mxH for (int x : arr) { mxH.push(x); if (mxH.size() > m) mxH.pop(); } // Maintain 'm' largest elements in mnH for (int x : arr) { mnH.push(x); if (mnH.size() > m) mnH.pop(); } // Compute sum of 'm' smallest and 'm' largest int minSum = 0, maxSum = 0; while (!mxH.empty()) minSum += mxH.top(), mxH.pop(); while (!mnH.empty()) maxSum += mnH.top(), mnH.pop(); return maxSum - minSum; } int main() { vector<int> arr = {1, 2, 3, 4, 5}; int m = 4; cout << findDiff(arr, m) << endl; return 0; } Java import java.util.*; class GfG { static int findDiff(int[] arr, int m) { // Min heap to store the 'm' largest elements PriorityQueue<Integer> mnH = new PriorityQueue<>(); // Max heap to store the 'm' smallest elements PriorityQueue<Integer> mxH = new PriorityQueue<>(Collections.reverseOrder()); // Maintain 'm' smallest elements in mxH for (int x : arr) { mxH.add(x); if (mxH.size() > m) mxH.poll(); } // Maintain 'm' largest elements in mnH for (int x : arr) { mnH.add(x); if (mnH.size() > m) mnH.poll(); } // Compute sum of 'm' smallest and 'm' largest int minSum = 0, maxSum = 0; while (!mxH.isEmpty()) minSum += mxH.poll(); while (!mnH.isEmpty()) maxSum += mnH.poll(); return maxSum - minSum; } public static void main(String[] args) { int[] arr = {1, 2, 3, 4, 5}; int m = 4; System.out.println(findDiff(arr, m)); } } Python # Function to find the difference between the sum of m largest and m smallest elements import heapq def find_diff(arr, m): # Min heap to store the 'm' largest elements mnH = [] # Max heap to store the 'm' smallest elements mxH = [] # Maintain 'm' smallest elements in mxH for x in arr: heapq.heappush(mxH, -x) if len(mxH) > m: heapq.heappop(mxH) # Maintain 'm' largest elements in mnH for x in arr: heapq.heappush(mnH, x) if len(mnH) > m: heapq.heappop(mnH) # Compute sum of 'm' smallest and 'm' largest min_sum = -sum(mxH) max_sum = sum(mnH) return max_sum - min_sum arr = [1, 2, 3, 4, 5] m = 4 print(find_diff(arr, m)) Output4 Time Complexity: O(n * log m), this solution can work in O(m + (n-m) Log m) as build heap take linear time. Comment More infoAdvertise with us Next Article Maximum difference between two subsets of m elements T TheGameOf256 Follow Improve Article Tags : Misc Searching Heap DSA Arrays +1 More Practice Tags : ArraysHeapMiscSearching Similar Reads Heap Data Structure A Heap is a complete binary tree data structure that satisfies the heap property: for every node, the value of its children is greater than or equal to its own value. Heaps are usually used to implement priority queues, where the smallest (or largest) element is always at the root of the tree.Basics 2 min read Introduction to Heap - Data Structure and Algorithm Tutorials A Heap is a special tree-based data structure with the following properties:It is a complete binary tree (all levels are fully filled except possibly the last, which is filled from left to right).It satisfies either the max-heap property (every parent node is greater than or equal to its children) o 15+ min read Binary Heap A Binary Heap is a complete binary tree that stores data efficiently, allowing quick access to the maximum or minimum element, depending on the type of heap. It can either be a Min Heap or a Max Heap. In a Min Heap, the key at the root must be the smallest among all the keys in the heap, and this pr 13 min read Advantages and Disadvantages of Heap Advantages of Heap Data StructureTime Efficient: Heaps have an average time complexity of O(log n) for inserting and deleting elements, making them efficient for large datasets. We can convert any array to a heap in O(n) time. The most important thing is, we can get the min or max in O(1) timeSpace 2 min read Time Complexity of building a heap Consider the following algorithm for building a Heap of an input array A. A quick look over the above implementation suggests that the running time is O(n * lg(n)) since each call to Heapify costs O(lg(n)) and Build-Heap makes O(n) such calls. This upper bound, though correct, is not asymptotically 2 min read Applications of Heap Data Structure Heap Data Structure is generally taught with Heapsort. Heapsort algorithm has limited uses because Quicksort is better in practice. Nevertheless, the Heap data structure itself is enormously used. Priority Queues: Heaps are commonly used to implement priority queues, where elements with higher prior 2 min read Comparison between Heap and Tree What is Heap? A Heap is a special Tree-based data structure in which the tree is a complete binary tree. Types of Heap Data Structure: Generally, Heaps can be of two types: Max-Heap: In a Max-Heap the key present at the root node must be greatest among the keys present at all of its children. The sa 3 min read When building a Heap, is the structure of Heap unique? What is Heap? A heap is a tree based data structure where the tree is a complete binary tree that maintains the property that either the children of a node are less than itself (max heap) or the children are greater than the node (min heap). Properties of Heap: Structural Property: This property sta 4 min read Some other type of HeapBinomial HeapThe main application of Binary Heap is to implement a priority queue. Binomial Heap is an extension of Binary Heap that provides faster union or merge operation with other operations provided by Binary Heap. A Binomial Heap is a collection of Binomial Trees What is a Binomial Tree? A Binomial Tree o 15 min read Fibonacci Heap | Set 1 (Introduction)INTRODUCTION:A Fibonacci heap is a data structure used for implementing priority queues. It is a type of heap data structure, but with several improvements over the traditional binary heap and binomial heap data structures.The key advantage of a Fibonacci heap over other heap data structures is its 5 min read Leftist Tree / Leftist HeapINTRODUCTION:A leftist tree, also known as a leftist heap, is a type of binary heap data structure used for implementing priority queues. Like other heap data structures, it is a complete binary tree, meaning that all levels are fully filled except possibly the last level, which is filled from left 15+ min read K-ary HeapPrerequisite - Binary Heap K-ary heaps are a generalization of binary heap(K=2) in which each node have K children instead of 2. Just like binary heap, it follows two properties: Nearly complete binary tree, with all levels having maximum number of nodes except the last, which is filled in left to r 15 min read Easy problems on HeapCheck if a given Binary Tree is a HeapGiven a binary tree, check if it has heap property or not, Binary tree needs to fulfil the following two conditions for being a heap: It should be a complete tree (i.e. Every level of the tree, except possibly the last, is completely filled, and all nodes are as far left as possible.).Every node’s v 15+ min read How to check if a given array represents a Binary Heap?Given an array, how to check if the given array represents a Binary Max-Heap.Examples: Input: arr[] = {90, 15, 10, 7, 12, 2} Output: True The given array represents below tree 90 / \ 15 10 / \ / 7 12 2 The tree follows max-heap property as every node is greater than all of its descendants. Input: ar 11 min read Iterative HeapSortHeapSort is a comparison-based sorting technique where we first build Max Heap and then swap the root element with the last element (size times) and maintains the heap property each time to finally make it sorted. Examples: Input : 10 20 15 17 9 21 Output : 9 10 15 17 20 21 Input: 12 11 13 5 6 7 15 11 min read Find k largest elements in an arrayGiven an array arr[] and an integer k, the task is to find k largest elements in the given array. Elements in the output array should be in decreasing order.Examples:Input: [1, 23, 12, 9, 30, 2, 50], k = 3Output: [50, 30, 23]Input: [11, 5, 12, 9, 44, 17, 2], k = 2Output: [44, 17]Table of Content[Nai 15+ min read K’th Smallest Element in Unsorted ArrayGiven an array arr[] of N distinct elements and a number K, where K is smaller than the size of the array. Find the K'th smallest element in the given array. Examples:Input: arr[] = {7, 10, 4, 3, 20, 15}, K = 3 Output: 7Input: arr[] = {7, 10, 4, 3, 20, 15}, K = 4 Output: 10 Table of Content[Naive Ap 15 min read Height of a complete binary tree (or Heap) with N nodesConsider a Binary Heap of size N. We need to find the height of it. Examples: Input : N = 6 Output : 2 () / \ () () / \ / () () () Input : N = 9 Output : 3 () / \ () () / \ / \ () () () () / \ () ()Recommended PracticeHeight of HeapTry It! Let the size of the heap be N and the height be h. If we tak 3 min read Heap Sort for decreasing order using min heapGiven an array of elements, sort the array in decreasing order using min heap. Examples: Input : arr[] = {5, 3, 10, 1}Output : arr[] = {10, 5, 3, 1}Input : arr[] = {1, 50, 100, 25}Output : arr[] = {100, 50, 25, 1}Prerequisite: Heap sort using min heap.Using Min Heap Implementation - O(n Log n) Time 11 min read Like