Introduction to Computation and Programming Using Python by John V. Guttag

Author:John V. Guttag
Language: eng
Format: epub, pdf
Publisher: The MIT Press

Notice that we are computing the same values over and over again. For example, fib gets called with 3 three times, and each of these calls provokes four additional calls of fib. It doesn’t require a genius to think that it might be a good idea to record the value returned by the first call, and then look it up rather than compute it each time it is needed. This is called memoization, and is the key idea behind dynamic programming.

Figure 13.2 contains an implementation of Fibonacci based on this idea. The function fastFib has a parameter, memo, that it uses to keep track of the numbers it has already evaluated. The parameter has a default value, the empty dictionary, so that clients of fastFib don’t have to worry about supplying an initial value for memo. When fastFib is called with an n > 1, it attempts to look up n in memo. If it is not there (because this is the first time fastFib has been called with that value), an exception is raised. When this happens, fastFib uses the normal Fibonacci recurrence, and then stores the result in memo.

Figure 13.2 Implementing Fibonacci using a memo

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