How to Use
- Initialize: Enter size and click "Initialize"
- Update: Enter index and value, click "Update"
- Query: Enter index and click "Query Sum"
- Range Query: Enter left and right indices
- Reset: Click to clear the tree
Binary Indexed Tree Concept
Binary Indexed Tree (Fenwick Tree) is a data structure that efficiently supports prefix sum queries and updates in O(log n) time.
Key Properties:
- Efficient prefix sum calculation
- O(log n) update and query operations
- Space efficient: O(n) space
- Uses binary representation for indexing
BIT stands for Binary Indexed Tree, also known as Fenwick Tree after Peter Fenwick who invented it in 1994.
Query Sum calculates the prefix sum from index 1 to a given index, efficiently traversing parent nodes in the BIT structure.
Range Query finds the sum of elements between two indices using the formula: sum(left, right) = prefixSum(right) - prefixSum(left-1).
Binary Indexed Tree Setup
Binary Indexed Tree Operations
Tree Visualization
Initialize the Binary Indexed Tree to see visualization
(Array indices start from 1 for BIT implementation)
Operation Steps
Purpose & Applications
- Competitive programming
- Range sum queries
- Frequency counting
- Inversion counting
- 2D range queries
Time & Space Complexity
| Operation | Time Complexity | Space Complexity |
|---|---|---|
| Initialize | O(n log n) | O(n) |
| Update | O(log n) | O(1) |
| Query Sum | O(log n) | O(1) |
| Range Query | O(log n) | O(1) |
Strengths & Limitations
Strengths:
- Fast prefix sum queries
- Efficient updates
- Space efficient
- Simple implementation
Limitations:
- Only works with associative operations
- 1-indexed implementation