Memoization and dynamic programming come together in top down DP algorithms. These are also referred to as recursion with memoization. The recursive function often looks something like:
f(arguments) {
results = memoTable[arguments]
if(results) // use results
else
results = // expensive recursive call to f
memoTable[arguments] = results
}
As far as I have understood, this is just regular memoization. I mean, often in functional languages one just turns a regular function into a memoized version by calling memoize(function). Sometimes that works to create a function that does what your code does, and sometimes it does not. When it does not I think that's a shortcoming of the language/implementation.
