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

An approach using Sorting:

• Sort the array in increasing order.
• Take the product of the first K elements of the array
• Return the result.

Below is the implementation of the above approach:

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)
{
    sort(arr, arr + n);

    long long result = 1;

    for (int i = 0; i < k; i++) {
        result = ((long long)arr[i] * result);
    }

    return result;
}

// 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;
}

// This code is contributed by hkdass001

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.

Output

Minimum product is 9348

Time Complexity: O(n*log(n))
Auxiliary Space: O(1)

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

Flowchart:

Flowchart

Implementation:

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

Javascript

<script>

// Javascript program to find minimum product of
// k elements in an array

function minProduct(arr, n, k) {
    let pq = new Array();
    for (let i = 0; i < n; i++)
        pq.push(arr[i]);

    let count = 0, ans = 1;

    // One by one extract items
    while (pq.length != 0 && count < k) {
        pq.sort((a, b) => a - b);
        ans = ans * pq[0];
        pq.shift(0);
        count++;
    }

    return ans;
}

// Driver Code

let arr = [198, 76, 544, 123, 154, 675];
let k = 2;
let n = arr.length;
document.write("Minimum product is " + minProduct(arr, n, k));


// This code is contributed by Saurabh Jaiswal
</script>

Output

Minimum product is 9348

Time Complexity: O(n * log n), 
Auxiliary Space: O(n) for priority queue

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

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