DSA Series Chapter 15 – POSTORDER TRAVERSAL (BINARY TREE)(C Version)

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DSA Series Chapter 15 – POSTORDER TRAVERSAL (BINARY TREE)(C Version)

Focus areas:

  • Clear traversal logic

  • Strong recursion understanding

  • Practical applications (very important for exams)

1. What is Postorder Traversal?

Definition (Exam-Ready)

Postorder traversal is a depth-first traversal technique in which the left subtree is visited first, then the right subtree, and finally the root node.

Traversal Order

Left → Right → Root

2. Binary Tree Diagram Used

            1
          /   \
         2     3
        / \
       4   5

The same tree is used consistently for explanation, dry run, and program output.

3. Step-by-Step Postorder Traversal on Diagram

Traversal rule: Left → Right → Root

  1. Start at root (1)

  2. Move to left subtree of 1 (node 2)

  3. Move to left subtree of 2 (node 4)

    • Left and right are NULL → visit 4

  4. Move to right subtree of 2 (node 5)

    • Left and right are NULL → visit 5

  5. Both subtrees of node 2 processed → visit 2

  6. Move to right subtree of root (node 3)

    • Left and right are NULL → visit 3

  7. Both subtrees of root processed → visit 1

Final Postorder Output

4 5 2 3 1

4. Algorithm (Recursive – Plain English)

  1. If current node is NULL, return

  2. Traverse left subtree recursively

  3. Traverse right subtree recursively

  4. Visit the current node

5. Recursive Algorithm (Pseudo Code)

POSTORDER(node)
{
    if(node != NULL)
    {
        POSTORDER(node->left)
        POSTORDER(node->right)
        visit(node)
    }
}

6. C Program – Postorder Traversal (Recursive)

#include <stdio.h>
#include <stdlib.h>

struct Node {
    int data;
    struct Node *left;
    struct Node *right;
};

struct Node* createNode(int data)
{
    struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
    newNode->data = data;
    newNode->left = NULL;
    newNode->right = NULL;
    return newNode;
}

void postorder(struct Node* root)
{
    if (root != NULL)
    {
        postorder(root->left);
        postorder(root->right);
        printf("%d ", root->data);
    }
}

int main()
{
    struct Node* root = createNode(1);
    root->left = createNode(2);
    root->right = createNode(3);
    root->left->left = createNode(4);
    root->left->right = createNode(5);

    printf("Postorder Traversal: ");
    postorder(root);

    return 0;
}

7. Dry Run of Recursive Calls

postorder(1)
  postorder(2)
    postorder(4)
      print 4
    postorder(5)
      print 5
    print 2
  postorder(3)
    print 3
  print 1

8. Time and Space Complexity

Time Complexity

  • O(n) — each node is visited exactly once

Space Complexity

  • O(h) — recursion stack

    • Skewed tree → O(n)

    • Balanced tree → O(log n)

9. Important Application (Very Important for Exams)

Deleting a Binary Tree

Postorder traversal is used to delete/free a binary tree safely.

Reason:

  • Children nodes are deleted before the parent node

10. Important Applications of Postorder Traversal

  • Deleting or freeing trees

  • Expression tree evaluation (postfix expressions)

  • Bottom-up tree processing

11. Common Exam & Interview Mistakes

  • Printing root before right subtree (becomes inorder)

  • Forgetting NULL base condition

  • Confusing postorder with preorder

12. Practice Questions

  1. Write postorder traversal for a right-skewed tree.

  2. Explain why postorder is preferred for deleting trees.

  3. Predict postorder output for a single-node tree.

  4. Convert recursive postorder traversal to iterative logic.

13. Learning Outcome (Post 3.3)

After this post, a student can:

  • Explain postorder traversal clearly

  • Perform dry runs accurately

  • Write postorder traversal program in C

  • Apply postorder logic in real use cases


ALSO CHECK 

DS(Data Structure) Python&C Edition

DSA Series Chapter 1 Time & Space Complexity ( C Edition)

DSA Series Chapter 2 Arrays  (C Version)


DSA Series Chapter 2 Arrays  (Python Version)

DSA Series Chapter 3 Strings (C Version)


DSA Series Chapter 3 Strings (Python Version)


DSA Series Chapter 4 Linked Lists (Python Version)


DSA Series Chapter 4 Linked Lists (C Version)


DSA Series Chapter 5 Stacks (Python Version)


DSA Series Chapter 5  Stacks  (C Version)




















DSA Series Chapter 13 - Binary Tree traversal, BFS, DFT/DFS, Preorder Traversal In Binary Tree



 

DSA Series Chapter 15 – POSTORDER TRAVERSAL (BINARY TREE)(Python Version)


DSA Series Chapter 15 – POSTORDER TRAVERSAL (BINARY TREE)(C Version)








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Advanced Sorting Algorithms: Merge Sort Internals — Merge Tree, Cache Behavior & Real Cost Analysis


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