Big O notation is really important for checking how well different data structures work, especially when we think about time and space.

Here are some common data structures and how they perform:

1. Arrays:

   • Accessing an item: $O(1)$ (Very fast)
   • Searching for an item: $O(n)$ (Slower, depends on size)
   • Adding or removing an item at the end: $O(1)$ (Very fast);
     • In the middle: $O(n)$ (Slower, depends on size)

2. Linked Lists:

   • Accessing an item: $O(n)$ (Slower, depends on size)
   • Searching for an item: $O(n)$ (Slower, depends on size)
   • Adding or removing an item: $O(1)$ (If you know where it is)

3. Stacks/Queues:

   • All actions like adding or removing items: $O(1)$ (Very fast)

4. Hash Tables:

   • Accessing or searching for an item: $O(1)$ on average (Very fast);
     • $O(n)$ in the worst case (Slower)
   • Adding or removing an item: $O(1)$ on average (Very fast);
     • $O(n)$ in the worst case (Slower)

5. Binary Search Trees (BST):

   • Accessing, searching, adding, or removing an item: $O(h)$ (h is the height of the tree, could be $O(n)$ in the worst case)

Knowing about these complexities helps developers pick the best data structure for their needs. It’s all about finding the right balance between efficiency and how well it works.