Inorder traversal gives sorted order in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is inorder traversal in a binary search tree?

Inorder traversal visits nodes in this order: left child, current node, then right child. This order helps visit nodes in ascending order for a binary search tree.

beginner

Why does inorder traversal give sorted order in a binary search tree?

Because in a binary search tree, all left children are smaller and all right children are larger than the current node. Visiting left, node, then right visits values from smallest to largest.

beginner

What is the sequence of node visits in inorder traversal?

The sequence is: first visit the left subtree, then the current node, and finally the right subtree.

intermediate

Does inorder traversal give sorted order for all binary trees?

No. It only gives sorted order if the tree is a binary search tree, where left nodes are smaller and right nodes are larger than the current node.

beginner

How can inorder traversal be used in real life?

It can be used to list items in order, like sorting names or numbers stored in a binary search tree quickly and efficiently.

What order does inorder traversal follow?

A Left, Node, Right

B Node, Left, Right

C Right, Node, Left

D Node, Right, Left

Inorder traversal visits the left subtree first, then the current node, and finally the right subtree.

In which type of tree does inorder traversal produce sorted values?

A Complete Binary Tree

B Binary Search Tree

C Full Binary Tree

D Any Binary Tree

Only in a binary search tree does inorder traversal produce sorted values because of the tree's ordering property.

If a tree is not a binary search tree, what will inorder traversal produce?

A Reverse sorted order

B Sorted order

C Random order

D Preorder sequence

Without the binary search tree property, inorder traversal does not guarantee sorted order.

Which traversal visits the current node before its children?

A Preorder

B Level order

C Postorder

D Inorder

Preorder traversal visits the current node first, then left and right children.

What is the main benefit of inorder traversal in binary search trees?

A It finds the maximum value

B It counts the number of nodes

C It finds the minimum value

D It lists all values in sorted order

Inorder traversal lists all values in ascending sorted order in a binary search tree.

Explain why inorder traversal of a binary search tree results in sorted order.

Think about how the tree is structured and the order nodes are visited.

Describe a real-life scenario where inorder traversal could be useful.

Consider how sorted lists help in everyday tasks.

Practice

1. What is the main result of performing an inorder traversal on a binary search tree (BST)?

easy

A. It visits nodes randomly.

B. It visits nodes in descending sorted order.

C. It visits only leaf nodes.

D. It visits nodes in ascending sorted order.

Solution

1. Step 1: Understand inorder traversal definition

   Inorder traversal visits the left child, then the node itself, then the right child.

2. Step 2: Apply inorder traversal to BST property

   Since BST nodes have smaller values on the left and larger on the right, inorder traversal visits nodes in ascending order.

3. Final Answer:

   It visits nodes in ascending sorted order. -> Option D

4. Quick Check:

   Inorder traversal = ascending order [OK]

Hint: Inorder on BST always gives sorted ascending list [OK]

Common Mistakes:

• Confusing inorder with preorder or postorder
• Thinking traversal visits nodes randomly
• Assuming it visits nodes in descending order

2. Which of the following is the correct sequence of steps in an inorder traversal of a binary tree?

easy

A. Visit left child, then node, then right child

B. Visit node, then left child, then right child

C. Visit right child, then node, then left child

D. Visit left child, then right child, then node

Solution

1. Step 1: Recall inorder traversal order

   Inorder traversal means visiting the left subtree first, then the node, then the right subtree.

2. Step 2: Match the correct sequence

   Visit left child, then node, then right child matches this order exactly: left child, node, right child.

3. Final Answer:

   Visit left child, then node, then right child -> Option A

4. Quick Check:

   Inorder = left, node, right [OK]

Hint: Inorder = left subtree, node, right subtree [OK]

Common Mistakes:

• Mixing up preorder and inorder sequences
• Visiting node before left child
• Visiting right child before node

3. Given the BST below, what is the output of an inorder traversal?

      10
     /  \
    5    15
   / \     \
  3   7     20

medium

A. [20, 15, 10, 7, 5, 3]

B. [10, 5, 3, 7, 15, 20]

C. [3, 5, 7, 10, 15, 20]

D. [5, 3, 7, 10, 15, 20]

Solution

1. Step 1: Perform inorder traversal on the BST

   Visit left subtree (3, 5, 7), then root (10), then right subtree (15, 20).

2. Step 2: Write nodes in visited order

   The order is 3, 5, 7, 10, 15, 20.

3. Final Answer:

   [3, 5, 7, 10, 15, 20] -> Option C

4. Quick Check:

   Inorder traversal output = sorted ascending list [OK]

Hint: Inorder traversal of BST = sorted ascending values [OK]

Common Mistakes:

• Listing nodes in preorder or postorder instead
• Confusing left and right subtree order
• Forgetting to include all nodes

4. A student wrote this inorder traversal code but it does not print nodes in sorted order for a BST. What is the mistake?

def inorder(node):
    if node:
        inorder(node.right)
        print(node.value)
        inorder(node.left)

medium

A. The function visits right child before left child, reversing order.

B. The function misses printing the node value.

C. The function does not check if node is None.

D. The function should print before visiting children.

Solution

1. Step 1: Analyze the traversal order in code

   The code visits right child first, then node, then left child, which is reverse of inorder.

2. Step 2: Understand effect on BST traversal

   This reversed order prints nodes in descending order, not ascending sorted order.

3. Final Answer:

   The function visits right child before left child, reversing order. -> Option A

4. Quick Check:

   Inorder must visit left before right [OK]

Hint: Inorder visits left child before right child [OK]

Common Mistakes:

• Swapping left and right subtree calls
• Printing node value in wrong place
• Not checking for null node

5. You have a binary tree that is not a BST. You perform an inorder traversal and get the sequence [4, 2, 5, 1, 6]. Which of the following is true?

hard

A. The tree is a BST because inorder traversal is sorted.

B. The tree is not a BST because inorder traversal is not sorted.

C. Inorder traversal always gives sorted order regardless of tree type.

D. The tree must be balanced to get this sequence.

Solution

1. Step 1: Check if inorder traversal sequence is sorted

   The sequence [4, 2, 5, 1, 6] is not in ascending order.

2. Step 2: Understand BST property and inorder traversal

   In a BST, inorder traversal always produces a sorted ascending sequence. Since this is not sorted, the tree is not a BST.

3. Final Answer:

   The tree is not a BST because inorder traversal is not sorted. -> Option B

4. Quick Check:

   Inorder sorted = BST; not sorted = not BST [OK]

Hint: Inorder sorted? Yes BST; No not BST [OK]

Common Mistakes:

• Assuming inorder always sorts any tree
• Confusing balanced tree with BST
• Ignoring order of traversal output