rev4: A very eloquent comment by user Sammaron has noted that, perhaps, this answer previously confused top-down and bottom-up. While originally this answer (rev3) and other answers said that “bottom-up is memoization” (“assume the subproblems”), it may be the inverse (that is, “top-down” may be “assume the subproblems” and “bottom-up” may be “compose the subproblems”). Previously, I have read on memoization being a different kind of dynamic programming as opposed to a subtype of dynamic programming. I was quoting that viewpoint despite not subscribing to it. I have rewritten this answer to be agnostic of the terminology until proper references can be found in the literature. I have also converted this answer to a community wiki. Please prefer academic sources. List of references: {Web: 1,2} {Literature: 5}
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