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Javascript Program for Minimum product subset of an array

  • Last Updated : 20 Jan, 2022

Given an array a, we have to find the minimum product possible with the subset of elements present in the array. The minimum product can be a single element also.

Examples: 

Input : a[] = { -1, -1, -2, 4, 3 }
Output : -24
Explanation : Minimum product will be ( -2 * -1 * -1 * 4 * 3 ) = -24

Input : a[] = { -1, 0 }
Output : -1
Explanation : -1(single element) is minimum product possible
 
Input : a[] = { 0, 0, 0 }
Output : 0

A simple solution is to generate all subsets, find the product of every subset and return the minimum product.
A better solution is to use the below facts.  

  1. If there are even number of negative numbers and no zeros, the result is the product of all except the largest valued negative number.
  2. If there are an odd number of negative numbers and no zeros, the result is simply the product of all.
  3. If there are zeros and positive, no negative, the result is 0. The exceptional case is when there is no negative number and all other elements positive then our result should be the first minimum positive number.

Javascript




<script>
  
// Javascript program to find maximum 
// product of a subset.
function minProductSubset(a, n)
{
    if (n == 1)
        return a[0];
  
    // Find count of negative numbers,
    // count of zeros, maximum valued
    // negative number, minimum valued
    // positive number and product of
    // non-zero numbers
    let negmax = Number.MIN_VALUE;
    let posmin = Number.MIN_VALUE;
    let count_neg = 0, count_zero = 0;
    let product = 1;
  
    for(let i = 0; i < n; i++)
    {
          
        // If number is zero, count it
        // but dont multiply
        if (a[i] == 0)
        {
            count_zero++;
            continue;
        }
  
        // Count the negative numbers
        // and find the max negative number
        if (a[i] < 0) 
        {
            count_neg++;
            negmax = Math.max(negmax, a[i]);
        }
  
        // Find the minimum positive number
        if (a[i] > 0 && a[i] < posmin) 
        {
            posmin = a[i];
        }
  
        product *= a[i];
    }
  
    // If there are all zeroes
    // or zero is present but no
    // negative number is present
    if (count_zero == n || (count_neg == 0 && 
        count_zero > 0))
        return 0;
  
    // If there are all positive
    if (count_neg == 0)
        return posmin;
  
    // If there are even number except
    // zero of negative numbers
    if (count_neg % 2 == 0 && count_neg != 0)
    {
  
        // Otherwise result is product of
        // all non-zeros divided by maximum
        // valued negative.
        product = parseInt(product / negmax, 10);
    }
    return product;
}
  
// Driver code
let a = [ -1, -1, -2, 4, 3 ];
let n = 5;
  
document.write(minProductSubset(a, n));
  
// This code is contributed by rameshtravel07
  
</script>
Output: 
-24

 

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

Please refer complete article on Minimum product subset of an array for more details!


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