Combining lists

Question

How can I combine

list1={{x1,y1},{x2,y2},{x3,y3}} 

and

list2={{x4,y4},{x5,y5}} 

to

list={{x1,y1},{x2,y2},{x3,y3},{x4,y4},{x5,y5}}

?

Answer 1

You need Join :

list = Join[list1, list2]

sometimes you would choose :

listU = Union[list1, list2]

The latter doesn't include duplicates, as the first approach could, if some of elements in list1 and list2 were common.

Edit

It should be emphasized that since for small lists different approaches (pointed out in the other answers) are elegant and quite satisfactory, however for big lists Join is much superior. We compare their efficiency in a few different cases :

1. lA1 = RandomReal[1, {500000, 2}];
   lA2 = RandomReal[1, {500000, 2}];
   
   Join[lA1, lA2]; // AbsoluteTiming // First
   ## & @@@ {lA1, lA2}; // AbsoluteTiming // First
   {lA1, lA2}~Flatten~1; // AbsoluteTiming // First
   

   0.0210000
   0.8090000
   0.4620000
   

2. lB1 = RandomReal[1, {2500000, 2}];
   lB2 = RandomReal[1, {1500000, 2}];
   
   Join[lB1, lB2]; // AbsoluteTiming // First
   ## & @@@ {lB1, lB2}; // AbsoluteTiming // First
   {lB1, lB2}~Flatten~1; // AbsoluteTiming // First
   

   0.0820000
   3.1500000
   1.9000000
   

3. lC1 = RandomReal[1, {300000, 2}];
   lC2 = RandomReal[1, {900000, 2}];
   
   Join[lC1, lC2]; // AbsoluteTiming // First
   ## & @@@ {lC1, lC2}; // AbsoluteTiming // First
   {lC1, lC2}~Flatten~1; // AbsoluteTiming // First
   

   0.0220000
   0.9320000
   0.6640000
   

We can see that Join is roughly about 20-30 times faster than {list1, list2}~Flatten~1; and the latter is about 1.5-2 times faster than ## & @@@.

Answer 2

Since there's always more than one way to do things in Mathematica, here's another alternative:

{list1, list2} ~Flatten~ 1

The above uses infix notation, which might be a little hard to grok at first, but can make the code very readable for functions that take 2 arguments and have descriptive names.

For comparison, here is the same expression written in 3 other forms:

Flatten[{list1, list2}, 1]           (* Matchfix *)
Flatten[#, 1] &@{list1, list2}       (*  Prefix  *)
{list1, list2} // Flatten[#, 1] &    (* Postfix  *)

Answer 3

And another:

## & @@@ {list1, list2}