(i) Design an efficient algorithm (pseudocode or a succinct verbal...

Pseudocode:

1. Create an empty HashMap
2. Traverse array elments and do following for every element arr[i].
â–ª If arr[i] is 0 and M is also 0, return true, else ignore arr[i].
â–ª If M % arr[i] is 0 and M/arr[i] exists in table, return true.
â–ª Insert arr[i] into the hash table.
3. Return false

Detailed Explanation:

1. You create a function which takes the array and the product M as input.
2. You iterate through the elements of the array.
For each element,
if the element is 0 and the product you are looking for is also 0 then return TRUE.
else, continue;