segtri

This crate provides a simple implementation of a segment tree with lazy propagation. It supports efficient updates and queries over ranges of data.

Features

• Customizable Data Type and Query Method: Any type T can be used as the data in the segment tree, as long as:

  • It implements [Clone].
  • Its reference implements Add<Output = T> and Mul<usize, Output = T>.

  To customize queries, you can redefine how the data are summed and multiplied.

  The multiplication trait is used to efficiently compute the "sum" of repeated data and is assumed to be faster than "adding" multiple components individually.

• Customizable Update Operations: Any type Op can be used as an update operation, provided it implements [ModifyOp<T>].

• Lazy Node Creation: Nodes in the segment tree are created lazily. This ensures the tree remains small when built with [SegTree::new] and when updates are applied to large ranges.

Performance

The segment tree achieves O(log(n)) for updates and queries, provided:

• Customized update operations are O(1).
• Data type addition [Add::add] is O(1).
• Data type multiplication [Mul::mul] is O(log(k)), where k is the multiplier.

Example

use segtri::{SegTree, ModifyOp};

struct Add(usize);
impl ModifyOp<usize> for Add {
    fn nop() -> Self {
        Add(0)
    }

    fn combine(&mut self, another_op: &Self) {
        self.0 += another_op.0
    }

    fn apply(&self, orig_seg_data: &mut usize, seg_len: usize) {
        *orig_seg_data += seg_len * self.0
    }
}

// Segment tree of length 10 with initial point value 1
let mut seg = SegTree::new(10, 1);
// Query the sum of segment 2..4
assert_eq!(seg.query(&(2..4)), 2);
// Add 2 to the segment 0..10
seg.modify(&(0..10), &Add(2));
// Query the value at point 1
assert_eq!(seg.query_point(1), 3);
// Add 2 to point 0
seg.modify_point(0, &Add(2));
assert_eq!(seg.query(&(0..2)), 5 + 3);

For more examples please see examples directory.