What are the time complexities of various data structures?

Solution 1:

Arrays

• Set, Check element at a particular index: O(1)
• Searching: O(n) if array is unsorted and O(log n) if array is sorted and something like a binary search is used,
• As pointed out by Aivean, there is no Delete operation available on Arrays. We can symbolically delete an element by setting it to some specific value, e.g. -1, 0, etc. depending on our requirements
• Similarly, Insert for arrays is basically Set as mentioned in the beginning

ArrayList:

• Add: Amortized O(1)
• Remove: O(n)
• Contains: O(n)
• Size: O(1)

Linked List:

• Inserting: O(1), if done at the head, O(n) if anywhere else since we have to reach that position by traveseing the linkedlist linearly.
• Deleting: O(1), if done at the head, O(n) if anywhere else since we have to reach that position by traveseing the linkedlist linearly.
• Searching: O(n)

Doubly-Linked List:

• Inserting: O(1), if done at the head or tail, O(n) if anywhere else since we have to reach that position by traveseing the linkedlist linearly.
• Deleting: O(1), if done at the head or tail, O(n) if anywhere else since we have to reach that position by traveseing the linkedlist linearly.
• Searching: O(n)

Stack:

• Push: O(1)
• Pop: O(1)
• Top: O(1)
• Search (Something like lookup, as a special operation): O(n) (I guess so)

Queue/Deque/Circular Queue:

• Insert: O(1)
• Remove: O(1)
• Size: O(1)

Binary Search Tree:

• Insert, delete and search: Average case: O(log n), Worst Case: O(n)

Red-Black Tree:

• Insert, delete and search: Average case: O(log n), Worst Case: O(log n)

Heap/PriorityQueue (min/max):

• Find Min/Find Max: O(1)
• Insert: O(log n)
• Delete Min/Delete Max: O(log n)
• Extract Min/Extract Max: O(log n)
• Lookup, Delete (if at all provided): O(n), we will have to scan all the elements as they are not ordered like BST

HashMap/Hashtable/HashSet:

• Insert/Delete: O(1) amortized
• Re-size/hash: O(n)
• Contains: O(1)