Introduction

Average of Levels means:

  • calculating average value
  • for every tree level

Goal:

  • process one level at a time
  • compute average of nodes

Example:

        3      /   \
     9     20
          /  \
         15   7

Output:
3
14.5
11

Explanation:

Level 1:3

Average:
3

Level 2:
9 20

Average:
14.5

Level 3:
15 7

Average:
11

This problem is one of the most important applications of

BFS Traversal

Constraints

1 <= Number of Nodes <= 10^5

Approach : Queue Based BFS Solution

Explanations:

Explanation:

The idea is:

  • traverse tree level by level
  • calculate sum for every level
  • divide by number of nodes

Steps:

  1. Push root into queue.
  2. Process one level.
  3. Calculate level sum.
  4. Count level nodes.
  5. Compute average.
  6. Repeat for all levels.

This approach:

  • uses queue
  • follows BFS traversal
  • processes levels independently

Dry Run

Level 1:3

Sum:
3


Average:

3


Level 2:
9 20

Sum:
29

Average:
14.5

Level 3:
15 7

Sum:
22

Average:
11

Practice :

Complexity Analysis :

Time Complexity:- O(n)
Explanation :
Every tree node is visited once.

Space Complexity:- O(n)
Explanation :
Queue stores tree nodes level wise.

Why This Problem is Important

This problem builds the foundation for:

  • BFS traversal
  • Queue processing
  • Level-wise traversal
  • Tree aggregation problems
  • Binary tree processing

Real-World Applications

Average of levels concepts are used in:

  • Analytics systems
  • Hierarchical data processing
  • BFS simulations
  • Monitoring systems
  • Statistical tree analysis

Common Beginner Mistakes

  • Incorrect level sum calculation
  • Forgetting level separation
  • Wrong queue handling
  • Division errors
  • Queue underflow issues

Interview Tip

Interviewers often expect:

  • BFS understanding
  • queue explanation
  • level processing logic
  • aggregation clarity

Always explain:

  • queue operations
  • level-by-level traversal
  • average calculation flow

Related Questions

  • Level Order Traversal
  • Zigzag Traversal
  • Right Side View
  • DFS Traversal
  • Binary Tree Height

Final Takeaway

The Average of Levels problem is one of the most important beginner BFS tree problems.

It teaches:

  • BFS traversal
  • queue processing
  • level aggregation
  • binary tree exploration

Understanding this problem builds a strong foundation for:

  •  advanced tree problems
  • graph traversal
  • interview-level algorithms.