Python – Minimum Product Pair in List

Sometimes, we need to find the specific problem of getting the pair that yields the minimum product, this can be solved by sorting and getting the first and second elements of the list. But in some case, we don’t with to change the ordering of list and perform some operation in the similar list without using extra space. Let’s discuss certain ways in which this can be performed.
Note: All elements in the list are positive integer.

Method #1 : Using list comprehension + min() + combination() + lambda This particular task can be performed using the combination of above functions in which we use list comprehension to bind all the functionalities and min function to get the minimum product, combination function finds all product internally and lambda function is used to compute the product. 

The original list : [3, 4, 1, 7, 9, 1]
The minimum product pair is : (1, 1)

Time Complexity: O(n*n), where n is the number of elements in the list “test_list”.
Auxiliary Space: O(n), where n is the number of elements in the list “test_list”.

Method #2 : Using list comprehension + nsmallest() + combination() + lambda This method has potential of not only finding a single minimum but also k minimum product pairs if required and uses nsmallest function instead of min function to achieve this functionality. 

The original list : [3, 4, 1, 7, 9, 8]
The minimum product pair is : [(3, 1), (4, 1)]

Time Complexity: O(n*n), where n is the number of elements in the list “test_list”.
Auxiliary Space: O(n), where n is the number of elements in the list “test_list”.