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Segment Tree for Range Queries

Certification: Advanced Level Accuracy: 100% Submissions: 2 Points: 15

Write a Python class SegmentTree that implements a segment tree data structure for efficient range queries. The segment tree should support the following operations:

  1. Build a segment tree from an array
  2. Update a single element in the segment tree
  3. Query for the sum of elements in a given range
Example 1
     
  • Input: arr = [1, 3, 5, 7, 9, 11], query(1, 3)
    •  
  • Output: 15
    •  
  • Explanation: 
       
    • Step 1: Build segment tree for array [1, 3, 5, 7, 9, 11].
      •  
    • Step 2: Query for sum from index 1 to 3.
      •  
    • Step 3: Elements at indices 1, 2, 3 are 3, 5, and 7 respectively.
      •  
    • Step 4: Return 3 + 5 + 7 = 15.
      •  
     
    •
Example 2
     
  • Input: arr = [1, 3, 5, 7, 9, 11], update(1, 10), query(1, 3)
    •  
  • Output: 22
    •  
  • Explanation: 
       
    • Step 1: Build segment tree for array [1, 3, 5, 7, 9, 11].
      •  
    • Step 2: Update index 1 to value 10 → array becomes [1, 10, 5, 7, 9, 11].
      •  
    • Step 3: Query for sum from index 1 to 3.
      •  
    • Step 4: Return 10 + 5 + 7 = 22.
      •  
     
    •
Constraints
     
  • 1 ≤ arr.length ≤ 105
    •  
  • -104 ≤ arr[i] ≤ 104
    •  
  • 0 ≤ left ≤ right < arr.length
    •  
  • Time Complexity: Build - O(n), Query - O(log n), Update - O(log n)
    •  
  • Space Complexity: O(n)
    •
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Hint
Solution

Solution Hints

    
  
  • Design a recursive function to build the segment tree
    • 
  
  • For query operations, check if the current range completely overlaps with the query range
    • 
  
  • For update operations, recursively update all affected nodes
    • 
  
  • Store the segment tree in an array of size 4*n
    • 
  
  • Handle edge cases like empty arrays or invalid ranges
    •

Steps to solve by this approach:

 Step 1: Create a segment tree class with methods for building, querying, and updating.
 Step 2: Build the segment tree recursively, where each node stores the sum of elements in its range.
 Step 3: For query operations, recursively find the sum of elements in the specified range.
 Step 4: For update operations, recursively update the value and recalculate sums for affected nodes.
 Step 5: Use helper functions to handle recursion for both query and update operations.

Submitted Code :