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What is running time of Dijkstra’s algorithm using Binary min- heap method?

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What is running time of Dijkstra’s algorithm using Binary min- heap method?

(a) O(V)

(b) O(VlogV)

(c) O(E)

(d) O(ElogV)

The question was posed to me during an internship interview.

My question is taken from Shortest Path topic in portion Shortest Path of Data Structures & Algorithms II

1 Answer

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Correct choice is (d) O(ElogV)

Explanation: Time required to build a binary min heap is O(V). Each decrease key operation takes O(logV) and there are still at most E such operations. Hence total running time is O(ElogV).

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