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My own favorite is an equation parser.

Before attempting to do so I thought it was implemented as a simple seek over the string, maybe a bunch of regex stuff. I guess it can be done that way, at the cost of growing complexity; but the proper solution (with a stack, etc) is so elegant (makeing it easy to add functions, operators, parenthesis, variables, etc) that it really makes one appreciate the value of good, thoughtful engineering.




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