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Consider the brute force implementation in which we find all the possible ways of multiplying the given set of n matrices. What is the time complexity of this implementation?

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Consider the brute force implementation in which we find all the possible ways of multiplying the given set of n matrices. What is the time complexity of this implementation?

(a) O(n!)

(b) O(n^3)

(c) O(n^2)

(d) Exponential

This question was posed to me in unit test.

This interesting question is from Matrix-chain Multiplication topic in portion Dynamic Programming of Data Structures & Algorithms II

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The correct option is (d) Exponential

Easy explanation - The time complexity of finding all the possible ways of multiplying a set of n matrices is given by (n-1)^th Catalan number which is exponential.

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