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What is the average time complexity of counting sort?

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What is the average time complexity of counting sort?

(a) O(n)

(b) O(n+k) k=range of input

(c) O(n^2)

(d) O(n log n)

This question was posed to me in an online interview.

Origin of the question is Sorting in section Sorting of Data Structures & Algorithms II

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The correct choice is (b) O(n+k) k=range of input

To explain: Time complexity of counting sort is O(n+k) as counting the occurrence of each element in the input range takes k time and then finding the correct index value of each element in the sorted array takes n time.

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