Unlike linear data structures (Array, Linked List, Queues, Stacks, etc) which have only one logical way to traverse them, trees can be traversed in different ways.
A Tree Data Structure can be traversed in following ways:
- Depth First Search or DFS
- Inorder Traversal
- Preorder Traversal
- Postorder Traversal
- Level Order Traversal or Breadth First Search or BFS
- Boundary Traversal
- Diagonal Traversal
In the case of binary search trees (BST), Inorder traversal gives nodes in non-decreasing order. To get nodes of BST in non-increasing order, a variation of Inorder traversal where Inorder traversal is reversed can be used.
Preorder traversal is used to create a copy of the tree. Preorder traversal is also used to get prefix expressions on an expression tree.
Postorder traversal is used to delete the tree. Postorder traversal is also useful to get the postfix expression of an expression tree.
https://www.bigocheatsheet.com/ https://neetcode.io/courses/lessons/big-o-notation
Below are the Big O performance of common functions of different Java Collections.
| List | Add | Remove | Get | Contains | Next | Data Structure |
|---|---|---|---|---|---|---|
| ArrayList | O(1) | O(n) | O(1) | O(n) | O(1) | Array |
| LinkedList | O(1) | O(1) | O(n) | O(n) | O(1) | Linked List |
| CopyOnWriteArrayList | O(n) | O(n) | O(1) | O(n) | O(1) | Array |
| Set | Add | Remove | Contains | Next | Size | Data Structure |
|---|---|---|---|---|---|---|
| HashSet | O(1) | O(1) | O(1) | O(h/n) | O(1) | Hash Table |
| LinkedHashSet | O(1) | O(1) | O(1) | O(1) | O(1) | Hash Table + Linked List |
| EnumSet | O(1) | O(1) | O(1) | O(1) | O(1) | Bit Vector |
| TreeSet | O(log n) | O(log n) | O(log n) | O(log n) | O(1) | Red-black tree |
| CopyOnWriteArraySet | O(n) | O(n) | O(n) | O(1) | O(1) | Array |
| ConcurrentSkipListSet | O(log n) | O(log n) | O(log n) | O(1) | O(n) | Skip List |
| Queue | Offer | Peak | Poll | Remove | Size | Data Structure |
|---|---|---|---|---|---|---|
| PriorityQueue | O(log n) | O(1) | O(log n) | O(n) | O(1) | Priority Heap |
| LinkedList | O(1) | O(1) | O(1) | O(1) | O(1) | Array |
| ArrayDequeue | O(1) | O(1) | O(1) | O(n) | O(1) | Linked List |
| ConcurrentLinkedQueue | O(1) | O(1) | O(1) | O(n) | O(n) | Linked List |
| ArrayBlockingQueue | O(1) | O(1) | O(1) | O(n) | O(1) | Array |
| PriorirityBlockingQueue | O(log n) | O(1) | O(log n) | O(n) | O(1) | Priority Heap |
| SynchronousQueue | O(1) | O(1) | O(1) | O(n) | O(1) | None! |
| DelayQueue | O(log n) | O(1) | O(log n) | O(n) | O(1) | Priority Heap |
| LinkedBlockingQueue | O(1) | O(1) | O(1) | O(n) | O(1) | Linked List |
| Map | Get | ContainsKey | Next | Data Structure |
|---|---|---|---|---|
| HashMap | O(1) | O(1) | O(h / n) | Hash Table |
| LinkedHashMap | O(1) | O(1) | O(1) | Hash Table + Linked List |
| IdentityHashMap | O(1) | O(1) | O(h / n) | Array |
| WeakHashMap | O(1) | O(1) | O(h / n) | Hash Table |
| EnumMap | O(1) | O(1) | O(1) | Array |
| TreeMap | O(log n) | O(log n) | O(log n) | Red-black tree |
| ConcurrentHashMap | O(1) | O(1) | O(h / n) | Hash Tables |
| ConcurrentSkipListMap | O(log n) | O(log n) | O(1) | Skip List |
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