How to encode shortest brainf_ck strings

This is an interesting one.

I have written a short program in objective-c to encode a string into a brainf_ck string, this is what it looks like:

NSString *input; // set this to your input string NSMutableString *output = [[NSMutableString alloc] init]; int currentPosition = 0; for (int i = 0; i<[input length]; i++) { int charPos = [input characterAtIndex:i]; int amountToGo = charPos-currentPosition; if (amountToGo > 0) { for (int b = 0; b<amountToGo; b++) { [output appendString:@"+"]; } } else { int posVal = abs(amountToGo); for (int b = 0; b<posVal; b++) { [output appendString:@"-"]; } } currentPosition += amountToGo; [output appendString:@"."]; } NSLog(@"%@", output); [output release]; 

Now I could ask you to optimize that code.

Or, I could ask you to optimize the bf code it produces?

EXAMPLE: Output of 'Hello World!' from my code (365 chars)

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++.+++++++++++++++++++++++++++++.+++++++..+++.-------------------------------------------------------------------------------.+++++++++++++++++++++++++++++++++++++++++++++++++++++++.++++++++++++++++++++++++.+++.------.--------.-------------------------------------------------------------------.

EXAMPLE 2: Now, looking at that code, I could probably shorten it by putting reset to zeros in, for a start... (290 chars - 75 improvement)

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++.+++++++++++++++++++++++++++++.+++++++..+++.[-]++++++++++++++++++++++++++++++++.+++++++++++++++++++++++++++++++++++++++++++++++++++++++.++++++++++++++++++++++++.+++.------.--------.[-]+++++++++++++++++++++++++++++++++.

But this takes it a step further... output of 'Hello World!' from some sample code I found on the internet: (111 chars, 179 on last, 254 on original!)

++++++++++[>+++++++>++++++++++>+++>+<<<<-]>++.>+.+++++++..+++.>++.<<+++++++++++++++.>.+++.------.--------.>+.>.

Now, I don't know how that loop works, but it does. My question is this:

1. Explain how the loop in the last example works.
2. Write some code that can turn any string into highly optimized brainf_ck, like the last example.