Python Program for Minimum product subset of an array

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.

Python3

# Python3 program to find maximum
# product of a subset.

# def to find maximum
# product of a subset


def 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
    max_neg = float('-inf')
    min_pos = float('inf')
    count_neg = 0
    count_zero = 0
    prod = 1
    for i in range(0, n):

        # If number is 0, we don't
        # multiply it with product.
        if (a[i] == 0):
            count_zero = count_zero + 1
            continue

        # Count negatives and keep
        # track of maximum valued
        # negative.
        if (a[i] < 0):
            count_neg = count_neg + 1
            max_neg = max(max_neg, a[i])

        # Track minimum positive
        # number of array
        if (a[i] > 0):
            min_pos = min(min_pos, a[i])

        prod = prod * a[i]

    # If there are all zeros
    # or no negative number
    # present
    if (count_zero == n or (count_neg == 0
                            and count_zero > 0)):
        return 0

    # If there are all positive
    if (count_neg == 0):
        return min_pos

    # If there are even number of
    # negative numbers and count_neg
    # not 0
    if ((count_neg & 1) == 0 and
            count_neg != 0):

        # Otherwise result is product of
        # all non-zeros divided by
        # maximum valued negative.
        prod = int(prod / max_neg)

    return prod


# Driver code
a = [-1, -1, -2, 4, 3]
n = len(a)
print(minProductSubset(a, n))
# This code is contributed by
# Manish Shaw (manishshaw1)

Output:

-24

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

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