Tree traversals (inorder, preorder, postorder) in Data Structures Theory - Step-by-Step Execution

Concept Flow - Tree traversals (inorder, preorder, postorder)

Start at Root

↓

Preorder

↓

Visit Root

↓

Left

↓

Right

↓

End

Traversal starts at the root node and visits nodes in different orders depending on the method: preorder visits root first, inorder visits root between left and right, postorder visits root last.

Execution Sample

Data Structures Theory

def preorder(node):
    if node:
        print(node.val)
        preorder(node.left)
        preorder(node.right)

This code prints nodes in preorder: root, then left subtree, then right subtree.

Analysis Table

Step	Operation	Node Visited	Action	Traversal Output So Far
1	Visit Root	A	Print A	A
2	Traverse Left	B	Print B	A, B
3	Traverse Left	D	Print D	A, B, D
4	Left Child None	None	Return	A, B, D
5	Right Child None	None	Return	A, B, D
6	Traverse Right	E	Print E	A, B, D, E
7	Left Child None	None	Return	A, B, D, E
8	Right Child None	None	Return	A, B, D, E
9	Traverse Right	C	Print C	A, B, D, E, C
10	Traverse Left	F	Print F	A, B, D, E, C, F
11	Left Child None	None	Return	A, B, D, E, C, F
12	Right Child None	None	Return	A, B, D, E, C, F
13	Traverse Right	G	Print G	A, B, D, E, C, F, G
14	Left Child None	None	Return	A, B, D, E, C, F, G
15	Right Child None	None	Return	A, B, D, E, C, F, G
16	End	None	Traversal Complete	A, B, D, E, C, F, G

💡 All nodes visited, traversal complete

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 6	After Step 9	After Step 13	Final
Current Node	A	A	B	D	E	C	G	None
Traversal Output	[]	[A]	[A, B]	[A, B, D]	[A, B, D, E]	[A, B, D, E, C]	[A, B, D, E, C, F, G]	[A, B, D, E, C, F, G]

Key Insights - 3 Insights

Why do we print the node value before traversing children in preorder?

In preorder traversal, the root node is visited first before its children, as shown in execution_table steps 1, 2, and 3 where the node is printed before recursive calls.

Why do we return immediately when a child node is None?

When a child is None, it means there is no node to visit, so the function returns without action, as seen in steps 4, 5, 7, etc., preventing errors and ending that path.

How does the traversal output build up over time?

The output list grows step-by-step as nodes are visited and printed, tracked clearly in the 'Traversal Output So Far' column of the execution_table.

Visual Quiz - 3 Questions

Look at the execution_table at step 3. Which node is visited and printed?

A Node E

B Node B

C Node D

D Node A

💡 Hint

Check the 'Node Visited' and 'Action' columns at step 3 in the execution_table.

At which step does the traversal move to the right child of node B?

A Step 6

B Step 5

C Step 9

D Step 10

💡 Hint

Look for the step where 'Traverse Right' visits node E after handling node D's children (steps 4 and 5) in the execution_table.

If we changed the traversal to inorder, when would node A be printed?

A Before visiting left subtree

B Between visiting left and right subtree

C After visiting right subtree

D Node A would not be printed

💡 Hint

Recall inorder visits left subtree first, then root, then right subtree as described in concept_flow.

Concept Snapshot

Tree Traversals:
- Preorder: Visit root, left subtree, right subtree
- Inorder: Visit left subtree, root, right subtree
- Postorder: Visit left subtree, right subtree, root
Used to process or print all nodes in a tree in different orders.

Full Transcript

Tree traversals are ways to visit all nodes in a tree. Preorder visits the root node first, then left and right children. Inorder visits left child first, then root, then right child. Postorder visits children first, then root last. The example code shows preorder traversal printing nodes as it visits them. The execution table traces each step visiting nodes A, B, D, E, C, F, G in preorder. Variables track current node and output list growing. Key moments explain why nodes print before children in preorder and why None children cause returns. The quiz tests understanding of node visits and order differences. This helps understand how trees are processed in different orders for tasks like searching or printing.