Exponential Complexity

A word of caution is in order about recursive programs like the one we use here to generate Fibonacci numbers. Each level of recursion in function fibonacci has a doubling effect on the number of function calls; i.e., the number of recursive calls that are required to calculate the nth Fibonacci number is on the order of 2n. This rapidly gets out of hand. Calculating only the 20th Fibonacci number would require on the order of 220 or about a million calls, calculating the 30th Fibonacci number would require on the order of 230 or about a billion calls, and so on. Computer scientists refer to this as exponential complexity. Problems of this nature humble even the world’s most powerful computers!

Performance Tip 6.8

Avoid ...

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