Minimum product of k integers in an array of positive Integers Last Updated : 05 May, 2025 Comments Improve Suggest changes Like Article Like Report Try it on GfG Practice Given an array arr[] containing n positive integers and an integer k. Your task is to find the minimum possible product of k elements of the given array.Examples: Input: arr[] = [198, 76, 544, 123, 154, 675], k = 2Output: 9348Explanation: We will choose two smallest numbers from the given array to get the minimum product. The two smallest numbers are 76 and 123, and their product is 9348.Input: arr[] = [5, 4, 1, 2, 3], k = 3Output: 6Explanation: We will choose three smallest numbers from the given array to get the minimum product. The three smallest numbers are 1, 2, and 3, and their product is 6.[Naive Approach] - Using Sorting - O(n * log n) Time and O(1) SpaceTo get the minimum product of k elements, we are required to choose the k smallest elements. We sort the given array in ascending order, and find the product of first k elements of the sorted array. C++ #include <bits/stdc++.h> using namespace std; int minProduct(vector<int> &arr, int k) { // sort the array sort(arr.begin(), arr.end()); // to store the result int res = 1; // find product of first k elements for(int i = 0; i < k; i++) { res *= arr[i]; } return res; } int main() { vector<int> arr = { 198, 76, 544, 123, 154, 675 }; int k = 2; cout << minProduct(arr, k); return 0; } Java import java.util.Arrays; public class Main { public static int minProduct(int[] arr, int n, int k) { Arrays.sort(arr); long result = 1; for (int i = 0; i < k; i++) { result = (arr[i] * result); } return (int)result; } public static void main(String[] args) { int[] arr = { 198, 76, 544, 123, 154, 675 }; int k = 2; int n = arr.length; System.out.println("Minimum product is " + minProduct(arr, n, k)); } } // This code is contributed by adityamaharshi21. Python # Python program to find minimum product of # k elements in an array def minProduct(arr, n, k): arr.sort() result = 1 for i in range(k): result = (arr[i] * result) return result # Driver code arr = [198, 76, 544, 123, 154, 675] k = 2 n = len(arr) print("Minimum product is", minProduct(arr, n, k)) # This code is contributed by aadityamaharshi21. C# // C# program to find minimum product of // k elements in an array using System; using System.Collections.Generic; public class GFG { public static long minProduct(int[] arr, int n, int k) { Array.Sort(arr); long result = 1; for(int i = 0; i<k; i++){ result = ((long)arr[i] * result); } return result; } // Driver Code public static void Main(String[] args) { int []arr = {198, 76, 544, 123, 154, 675}; int k = 2; int n = arr.Length; Console.Write("Minimum product is " + minProduct(arr, n, k)); } } // This code is contributed by Yash Agarwal(yashagarwal2852002) JavaScript // JavaScript program to find minimum product of // k elements in an array function minProduct(arr, n, k) { arr.sort((a, b) => a - b); let result = 1; for (let i = 0; i < k; i++) { result = (arr[i] * result); } return result; } // Driver code let arr = [198, 76, 544, 123, 154, 675]; let k = 2; let n = arr.length; console.log(`Minimum product is ${minProduct(arr, n, k)}`); // This code is contributed by adityamaharshi21. Output9348[Expected Approach] - Using Max Heap - O(n * log k) Time and O(k) SpaceThe idea is to use max heap (priority queue) to find the k smallest elements of the given array.1) Create a max heap and push first k array elements into it.2) For remaining n-k elements, compare each element with the heap top, if smaller, then remove root of the heap and insert into the heap. If greater than ignore.3) Finally compute product of the heap elements. C++ #include <iostream> #include <vector> #include <queue> using namespace std; int minProduct(vector<int>& arr, int k) { // Step 1: Create a max heap with first k elements priority_queue<int> maxHeap; for (int i = 0; i < k; ++i) { maxHeap.push(arr[i]); } // Step 2: Process remaining elements for (int i = k; i < arr.size(); ++i) { if (arr[i] < maxHeap.top()) { maxHeap.pop(); maxHeap.push(arr[i]); } } // Step 3: Multiply elements in heap int product = 1; while (!maxHeap.empty()) { product *= maxHeap.top(); maxHeap.pop(); } return product; } int main() { vector<int> arr1 = {198, 76, 544, 123, 154, 675}; cout << minProduct(arr1, 2) << endl; // Output: 9348 vector<int> arr2 = {5, 4, 1, 2, 3}; cout << minProduct(arr2, 3) << endl; // Output: 6 return 0; } Java import java.util.PriorityQueue; import java.util.Arrays; public class Main { public static int minProduct(int[] arr, int k) { // Step 1: Create a max heap with first k elements PriorityQueue<Integer> maxHeap = new PriorityQueue<>(Collections.reverseOrder()); for (int i = 0; i < k; ++i) { maxHeap.add(arr[i]); } // Step 2: Process remaining elements for (int i = k; i < arr.length; ++i) { if (arr[i] < maxHeap.peek()) { maxHeap.poll(); maxHeap.add(arr[i]); } } // Step 3: Multiply elements in heap int product = 1; while (!maxHeap.isEmpty()) { product *= maxHeap.poll(); } return product; } public static void main(String[] args) { int[] arr1 = {198, 76, 544, 123, 154, 675}; System.out.println(minProduct(arr1, 2)); // Output: 9348 int[] arr2 = {5, 4, 1, 2, 3}; System.out.println(minProduct(arr2, 3)); // Output: 6 } } Python import heapq def min_product(arr, k): # Step 1: Create a max heap with first k elements max_heap = [-x for x in arr[:k]] heapq.heapify(max_heap) # Step 2: Process remaining elements for i in arr[k:]: if -i > max_heap[0]: heapq.heappop(max_heap) heapq.heappush(max_heap, -i) # Step 3: Multiply elements in heap product = 1 while max_heap: product *= -heapq.heappop(max_heap) return product arr1 = [198, 76, 544, 123, 154, 675] print(min_product(arr1, 2)) # Output: 9348 arr2 = [5, 4, 1, 2, 3] print(min_product(arr2, 3)) # Output: 6 C# using System; using System.Collections.Generic; class Program { public static int MinProduct(int[] arr, int k) { // Step 1: Create a max heap with first k elements SortedSet<int> maxHeap = new SortedSet<int>(Comparer<int>.Create((a, b) => b.CompareTo(a))); for (int i = 0; i < k; ++i) { maxHeap.Add(arr[i]); } // Step 2: Process remaining elements for (int i = k; i < arr.Length; ++i) { if (arr[i] < maxHeap.Max) { maxHeap.Remove(maxHeap.Max); maxHeap.Add(arr[i]); } } // Step 3: Multiply elements in heap int product = 1; foreach (var num in maxHeap) { product *= num; } return product; } static void Main() { int[] arr1 = {198, 76, 544, 123, 154, 675}; Console.WriteLine(MinProduct(arr1, 2)); // Output: 9348 int[] arr2 = {5, 4, 1, 2, 3}; Console.WriteLine(MinProduct(arr2, 3)); // Output: 6 } } JavaScript function minProduct(arr, k) { // Step 1: Create a max heap with first k elements const maxHeap = []; for (let i = 0; i < k; ++i) { maxHeap.push(arr[i]); } maxHeap.sort((a, b) => b - a); // Step 2: Process remaining elements for (let i = k; i < arr.length; ++i) { if (arr[i] < maxHeap[0]) { maxHeap.shift(); maxHeap.push(arr[i]); maxHeap.sort((a, b) => b - a); } } // Step 3: Multiply elements in heap let product = 1; for (const num of maxHeap) { product *= num; } return product; } const arr1 = [198, 76, 544, 123, 154, 675]; console.log(minProduct(arr1, 2)); // Output: 9348 const arr2 = [5, 4, 1, 2, 3]; console.log(minProduct(arr2, 3)); // Output: 6 Output9348 Comment More infoAdvertise with us Next Article Minimum product of k integers in an array of positive Integers G Gitanjali Improve Article Tags : Misc Sorting Heap DSA Arrays Order-Statistics +2 More Practice Tags : ArraysHeapMiscSorting 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. 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