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Which of the following implementations of Catalan numbers has the smallest time complexity?

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Which of the following implementations of Catalan numbers has the smallest time complexity?

(a) Dynamic programming

(b) Binomial coefficients

(c) Recursion

(d) All have equal time complexity

This question was posed to me in unit test.

My question is from Catalan Number using Dynamic Programming in section Dynamic Programming of Data Structures & Algorithms II

1 Answer

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Correct option is (b) Binomial coefficients

For explanation: The time complexities are as follows:

Dynamic programming: O(n^2)

Recursion: Exponential

Binomial coefficients: O(n).

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