Check with local libraries. Sometimes they have programming books for loaning.
I made the mistake of buying the Head First Java book, which I assume is similar to your C++ book, in that it tries to teach you through a jokey style that doesn't really work. Also the exercises are pretty poor.
Ideally, if you can afford them or find them at a library, I would get both.
My advice when using Accelerated C++ is to make sure you read each line/paragraph/chapter and take everything in. You can very easily miss something of importance if you skim or are distracted whilst reading.
As I said, it is very dense but full of good techniques.
I'm excited! I'm ready to continue to tackle Project Euler. I've solved the first 3 problems.