[algorithm] Difference between Divide and Conquer Algo and Dynamic Programming

I assume you have already read Wikipedia and other academic resources on this, so I won't recycle any of that information. I must also caveat that I am not a computer science expert by any means, but I'll share my two cents on my understanding of these topics...

Dynamic Programming

Breaks the problem down into discrete subproblems. The recursive algorithm for the Fibonacci sequence is an example of Dynamic Programming, because it solves for fib(n) by first solving for fib(n-1). In order to solve the original problem, it solves a different problem.

Divide and Conquer

These algorithms typically solve similar pieces of the problem, and then put them together at the end. Mergesort is a classic example of divide and conquer. The main difference between this example and the Fibonacci example is that in a mergesort, the division can (theoretically) be arbitrary, and no matter how you slice it up, you are still merging and sorting. The same amount of work has to be done to mergesort the array, no matter how you divide it up. Solving for fib(52) requires more steps than solving for fib(2).