线性时间算法计算笛卡尔积

Question

I was asked in an interview to come up with a solution with linear time for cartesian product. I did the iterative manner O(mn) and a recursive solution also which is also O(mn). But I could not reduce the complexity further. Does anyone have ideas on how this complexity can be improved? Also can anyone suggest an efficient recursive approach?

Answer 1

There are mn results; the minimum work you have to do is write each result to the output. So you cannot do better than O(mn) .

Answer 2

The question that comes to my mind reading this is, "Linear with respect to what?" Remember that in mathematics, all variables must be defined to have meaning. Big-O notation is no exception. Simply saying an algorithm is O(n) is meaningless if n is not defined.

Assuming the question was meaningful, and not a mistake, my guess is that they wanted you to ask for clarification. Another possibility is that they wanted to see how you would respond when presented with an impossible situation.