# Minimum product of k integers in an array of positive Integers

Given an array of n positive integers. We are required to write a program to print the minimum product of k integers of the given array.**Examples:**

Input : 198 76 544 123 154 675 k = 2 Output : 9348 We get minimum product after multiplying 76 and 123. Input : 11 8 5 7 5 100 k = 4 Output : 1400

The idea is simple, we find the smallest k elements and print multiplication of them. In below implementation, we have used simple Heap based approach where we insert array elements into a min heap and then find product of top k elements.

## C++

`// CPP program to find minimum product of` `// k elements in an array` `#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `minProduct(` `int` `arr[], ` `int` `n, ` `int` `k)` `{` ` ` `priority_queue<` `int` `, vector<` `int` `>, greater<` `int` `> > pq;` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `pq.push(arr[i]);` ` ` `int` `count = 0, ans = 1;` ` ` `// One by one extract items from max heap` ` ` `while` `(pq.empty() == ` `false` `&& count < k) {` ` ` `ans = ans * pq.top();` ` ` `pq.pop();` ` ` `count++;` ` ` `}` ` ` `return` `ans;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `arr[] = {198, 76, 544, 123, 154, 675};` ` ` `int` `k = 2;` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` `cout << ` `"Minimum product is "` ` ` `<< minProduct(arr, n, k);` ` ` `return` `0;` `}` |

## Java

`// Java program to find minimum product of` `// k elements in an array` `import` `java.util.PriorityQueue;` `class` `GFG` `{` ` ` `public` `static` `int` `minProduct(` `int` `[] arr, ` `int` `n, ` `int` `k)` ` ` `{` ` ` `PriorityQueue<Integer> pq = ` `new` `PriorityQueue<>();` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++)` ` ` `pq.add(arr[i]);` ` ` ` ` `int` `count = ` `0` `, ans = ` `1` `;` ` ` `// One by one extract items` ` ` `while` `(pq.isEmpty() == ` `false` `&& count < k)` ` ` `{` ` ` `ans = ans * pq.element();` ` ` `pq.remove();` ` ` `count++;` ` ` `}` ` ` ` ` `return` `ans;` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `arr[] = {` `198` `, ` `76` `, ` `544` `, ` `123` `, ` `154` `, ` `675` `};` ` ` `int` `k = ` `2` `;` ` ` `int` `n = arr.length;` ` ` `System.out.print(` `"Minimum product is "` `+` ` ` `minProduct(arr, n, k));` ` ` `}` `}` `// This code is contributed by sanjeev2552` |

## Python3

`# Python3 program to find minimum` `# product of k elements in an array` `import` `math` `import` `heapq` `def` `minProduct(arr, n, k):` ` ` `heapq.heapify(arr)` ` ` `count ` `=` `0` ` ` `ans ` `=` `1` ` ` `# One by one extract` ` ` `# items from min heap` ` ` `while` `( arr ) ` `and` `count < k:` ` ` `x ` `=` `heapq.heappop(arr)` ` ` `ans ` `=` `ans ` `*` `x` ` ` `count ` `=` `count ` `+` `1` ` ` ` ` `return` `ans;` `# Driver method` `arr ` `=` `[` `198` `, ` `76` `, ` `544` `, ` `123` `, ` `154` `, ` `675` `]` `k ` `=` `2` `n ` `=` `len` `(arr)` `print` `(` `"Minimum product is"` `,` ` ` `minProduct(arr, n, k))` |

## C#

`// C# program to find minimum product of` `// k elements in an array` `using` `System;` `using` `System.Collections.Generic;` `public` `class` `GFG` `{` ` ` `public` `static` `int` `minProduct(` `int` `[] arr, ` `int` `n, ` `int` `k)` ` ` `{` ` ` `List<` `int` `> pq = ` `new` `List<` `int` `>();` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `pq.Add(arr[i]);` ` ` `int` `count = 0, ans = 1;` ` ` `// One by one extract items` ` ` `while` `(pq.Count!=0 && count < k)` ` ` `{` ` ` `pq.Sort();` ` ` `ans = ans * pq[0];` ` ` `pq.RemoveAt(0);` ` ` `count++;` ` ` `}` ` ` `return` `ans;` ` ` `}` ` ` `// 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 Rajput-Ji` |

**Output:**

Minimum product is 9348

**Time Complexity :** O(n * log n)

Note that the above problem can be solved in O(n) time using methods discussed here and here.

This article is contributed by **Gitanjali Sharma**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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