Lecture 6: Top-down design is a recursive heuristic for solving problems by writing functions: start with a big-picture view of the problem; break it into a few big sub-problems; figure out how to integrate the solutions to each sub-problem; and then repeat for each part. The big-picture view: resources (mostly arguments), requirements (mostly return values), the steps which transform the one into the other. Breaking into parts: try not to use more than 5 sub-problems, each one a well-defined and nearly-independent calculation; this leads to code which is easy to understand and to modify. Synthesis: assume that a function can be written for each sub-problem; write code which integrates their outputs. Recursive step: repeat for each sub-problem, until you hit something which can be solved using the built-in functions alone. Top-down design forces you to think not just about the problem, but also about the method of solution, i.e., it forces you to think algorithmically; this is why it deserves to be part of your education in the liberal arts. Exemplification: how we could write the lm function for linear regression, if it did not exist and it were necessary to invent it.
Additional optional reading: Herbert Simon, The Sciences of the Artificial.
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