What does this mean?:
double dp[(1<<12)];

I've only used that symbol for stream i/o. It looks like he declared an array of doubles but the 1<<12 I have never seen before.

What if someone says:
#define REP(i,n) for((i)=0;(i)<(int)(n);(i)++)

It looks to me like that replaces all
REP(x,y)
in your code with
for(x=0;x<(int)(y);x++)

But then what is this?:
REP(i,(1<<n)) REP(j,probs.size())
{
//blah blah blah
}

probs is a vector<int>
i and j are integers
n isn't anything. There is no n declared anywhere. I guess it has something to do with the #define above but I don't get it and I don't understand his use of '<<'.

<< is the binary "left shift" operator. 1<<12 is 2^12 or 4096

So then
REP(i,(1<<n)) REP(j,probs.size())
means
Right?

Why would someone use 1<<n instead of 2^12? Is that common in the professional world?

very fast!

There is no ^ for "to the power of" in C or C++. In fact ^ is bitwise XOR so perhaps my previous post wasn't completely robust.

As for the macro, I think that re-writing the for loop as a macro is pretty bad coding. In theory you could use the preprocessor to make C look like any nonsense language but it doesn't make it any more readable. The fact that you need to ask this is testament to that.

I wouldn't like to say for certain that your interpretation is correct but it looks right to me.

Was Vrajgh's answer enough?
x<<y is x shifted left y places, which assuming no overflow is (x times (2 to the y power))

If that is true then the code you found and quoted is wrong. The n in REP(i,(1<<n)) must refer to some n already declared at that time. It is safely distinct from the n in
#define REP(i,n) for((i)=0;(i)<(int)(n);(i)++)

Because x^y meaning x to the y power exists in other programming languages but not in C nor in C++.

1<<n has significant advantages over pow(2,n) so good professional programmers will use 1<<n rather than pow(2,n) and anyone programming in C or C++ should learn to recognize and understand that usage.

Oh right, there's no ^ operator for exponents.

Oh yeah and I translated 1<<n to 4096 in my last example. Oops. What the hell is n? Hold on. (I wish I could copy and paste this guy's code but the stupid java applet won't let me.)

Hey you're right, there is an n. n is an int, passed to the function, sorry.

Yeah I understood the left shift thing. But what if you want to do a quick power of 3,5,6,7,9,etc... In that case do you have to use the pow() function?

I think the guy used all those annoying macros because it's a timed competition. I think he copies that garble into every competition. He has a ton of #include's that he didn't need either.