From charlesreid1

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Note: you can find a much more detailed walkthrough of a nearly identical class at Priority Queues/Sorted#Implementation.

Insert Method

The unsorted priority queue makes adding very fast - add operations are O(1), because items are just added to the end of the list, in no particular order.

Removing the minimum item is an O(N) operation, since the entire array must be traversed to find the minimum element. Note that finding the minimum also requires examining every item in the list.