Segment Tree

Implements a basic sum segment tree in Rust

Features

• Thread safe
• Safe for any system bit-width
• query - Query the sum of a range
• parallel_query - Query the sum of a range in parallel using system threads
• update - Update a value at a specific index
• batch_update - Update multiple values at specific indices

State

Overall, the code is organized and safe.

This code would need some cleanup for any production use

• For large vectors, the recursive nature of the tree could cause a stack overflow
• Support different operations other than sum
• Results as Result<T, E> rather than Result<T, &'static str>
• from_iter - Create a segment tree from an iterator
• from_slice - Create a segment tree from a slice
• from_vec - Create a segment tree from a vector
• from_vec_with_default - Create a segment tree from a vector with a default value

Tree Description

A segment tree is a data structure designed to efficiently perform range queries and updates on an array of values. It is particularly useful when you need to perform multiple range operations on a static array.

Properties

• Height: O(log n) where n is the number of elements
• Space complexity: O(n)
• Query time complexity: O(log n)
• Update time complexity: O(log n)

Common Use Cases

• Range sum queries
• Range minimum/maximum queries
• Range GCD queries
• Finding the smallest number greater than a given value in a given range

Structure

The segment tree is structured as a binary tree where:

• Each leaf node represents a single element from the input array
• Each internal node represents a merger of its children (in this implementation, the sum)
• The root node represents the entire range

Example

For an array [1, 2, 3, 4], the segment tree might look like:

                10 (sum of 0-3)
               /              \
          3 (sum of 0-1)    7 (sum of 2-3)
          /        \        /        \
         1         2      3          4

Operations

1. Query: Find the sum of elements from index i to j
2. Update: Modify the value at a given index and update affected ranges

Implementation Details

This implementation uses:

• A vector to store the tree nodes
• Each node contains the sum of its range and range boundaries
• Leaf indices are stored separately for efficient updates

Note: This implementation specifically handles range sum queries, but the concept can be extended to other range operations (min, max, GCD, etc.) by modifying the merge operation between nodes.