this one might be a bit off the topic here

I am looking for a good generic algorithms that does two sequence comparison
I will have sequence A which contain n items (think them as doubles)
and sequence B which contain m items

I need to comparsion item1 in A to all items in B, and do the same for all items in B
therefore, there should be n*m comparison.

there might not be any quicker way to do this, but if you know, please let me know, thanks.

I guess it depends on what you're doing, and what comparison you need to make. For example, if you need to compare every item in A with every item in B to find out whether the item in B is less than, equal to, or greater than an A item, you could sort B first, and reduce the number of comparisons (either to n log m by doing a sort of binary search, or just simply iterating through B until you find a value that is larger - all subsequent items in B would be larger).

How much this would speed things up depends on the data and the speed of the sort.

If it is a magnitude comparison as stated above, you can simplify by sorting each first. Unless you can relate the elements of A to others in A and likewise with B, I think you are stuck with an m*n algorithm.

If you keep it 2 lists; sort first, then have 2 positional references; one for the position on A and one for B. Then you can compare and increment the appropriate position accordingly, and base your analysis on a comparison of the current list positions.

If they are the same type, you can use an associative structure that has one member as the list value and the name/pointer/etc. of the list as another value:

A: 1 2 3 4 5
B: 6 7 8 9 0
-->
<1, A> <2, A> ...
<6, B> <7, B> ...

Then combine the lists and sort by list value, then extract your info based on the distribution of A and B elements. The bottom line is m*n is basically the least efficient algorithm you can have because the sets do not intersect, but if you can somehow combine/internally relate the 2 lists you can end up with something like log(m+n) complexity with something like a merge sort (very fast and 'stable'; like elements retain relational order.)

Sorry it is so vague, but I don't know what you are comparing, or even what language you intend to use. I generally write my algorithms in C++, then when I get them working I extract the substance of the algorithm and make it into something generic.
ta0kira