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//! Interval tree, a data structure for efficiently storing and searching intervals.
//!
//! This implementation is based on the sorted array version as described/given in
//! https://github.com/lh3/cgranges / https://github.com/lh3/cgranges/blob/master/cpp/IITree.h
//!
//! It uses the same conventions as `crate::data_structures::interval_tree::IntervalTree`.
//! Note that if you do not use the `ArrayBackedIntervalTree::from_iter` constructor, you have to call `index(&mut self)`
//! first before `find()`-ing overlaps.
//!
//! # Example
//! ```
//! use bio::data_structures::interval_tree::ArrayBackedIntervalTree;
//! use bio::utils::Interval;
//! use std::iter::FromIterator;
//!
//! let mut tree = ArrayBackedIntervalTree::new();
//! tree.insert(12..34, 0);
//! tree.insert(0..23, 1);
//! tree.insert(34..56, 2);
//! // since we did at least one manual insert, we have to index the tree
//! tree.index();
//! let i1 = &tree.find(22..25)[0];
//! assert_eq!(i1.interval().start, 0);
//! assert_eq!(i1.interval().end, 23);
//! assert_eq!(i1.data(), &1u32);
//!
//! let tree =
//! ArrayBackedIntervalTree::from_iter(vec![(12..34, 0), (0..23, 1), (34..56, 2)].into_iter());
//! // no call to `index` needed here, since that happens in `from_iter` already
//! let i2 = &tree.find(22..25)[1];
//! assert_eq!(i2.interval().start, 12);
//! assert_eq!(i2.interval().end, 34);
//! assert_eq!(i2.data(), &0u32);
//! ```
use crate::utils::Interval;
use std::cmp::min;
use std::iter::FromIterator;
/// A `find` query on the interval tree does not directly return references to the intervals in the
/// tree but wraps the fields `interval` and `data` in an `Entry`.
#[derive(Clone, Eq, PartialEq, Hash, Debug, Serialize, Deserialize)]
struct InternalEntry<N: Ord + Clone + Copy, D> {
data: D,
interval: Interval<N>,
max: N,
}
/// A `find` query on the interval tree does not directly return references to the nodes in the tree, but
/// wraps the fields `interval` and `data` in an `Entry`.
#[derive(Copy, Clone, Eq, PartialEq, Hash, Debug, Serialize)]
pub struct Entry<'a, N: Ord + Clone, D> {
data: &'a D,
interval: &'a Interval<N>,
}
impl<'a, N: Ord + Clone + 'a, D: 'a> Entry<'a, N, D> {
/// Get a reference to the data for this entry
pub fn data(&self) -> &'a D {
self.data
}
/// Get a reference to the interval for this entry
pub fn interval(&self) -> &'a Interval<N> {
self.interval
}
}
impl<N: Ord + Clone + Copy, D> Default for ArrayBackedIntervalTree<N, D> {
fn default() -> Self {
ArrayBackedIntervalTree {
entries: vec![],
max_level: 0,
indexed: false,
}
}
}
#[derive(Clone, Eq, PartialEq, Hash, Debug, Serialize, Deserialize)]
pub struct ArrayBackedIntervalTree<N: Ord + Clone + Copy, D> {
entries: Vec<InternalEntry<N, D>>,
max_level: usize,
indexed: bool,
}
impl<N, D, V> FromIterator<(V, D)> for ArrayBackedIntervalTree<N, D>
where
V: Into<Interval<N>>,
N: Ord + Clone + Copy,
D: Clone,
{
fn from_iter<T: IntoIterator<Item = (V, D)>>(iter: T) -> Self {
let mut tree = Self::new();
iter.into_iter()
.for_each(|(interval, data)| tree.insert(interval, data));
tree.index();
tree
}
}
impl<N: Ord + Clone + Copy, D: Clone> ArrayBackedIntervalTree<N, D> {
pub fn new() -> Self {
Default::default()
}
pub fn insert<I: Into<Interval<N>>>(&mut self, interval: I, data: D) {
let interval = interval.into();
let max = interval.end;
self.entries.push(InternalEntry {
interval,
data,
max,
});
self.indexed = false;
}
pub fn index(&mut self) {
if !self.indexed {
self.entries.sort_by_key(|e| e.interval.start);
self.index_core();
self.indexed = true;
}
}
fn index_core(&mut self) {
let a = &mut self.entries;
if a.is_empty() {
return;
}
let n = a.len();
let mut last_i = 0;
let mut last_value = a[0].max;
(0..n).step_by(2).for_each(|i| {
last_i = i;
a[i].max = a[i].interval.end;
last_value = a[i].max;
});
let mut k = 1;
while (1 << k) <= n {
// process internal nodes in the bottom-up order
let x = 1 << (k - 1);
let i0 = (x << 1) - 1; // i0 is the first node
let step = x << 2;
for i in (i0..n).step_by(step) {
// traverse all nodes at level k
let end_left = a[i - x].max; // max value of the left child
let end_right = if i + x < n { a[i + x].max } else { last_value }; // max value of the right child
let end = max3(a[i].interval.end, end_left, end_right);
a[i].max = end;
}
last_i = if (last_i >> k & 1) > 0 {
last_i - x
} else {
last_i + x
};
if last_i < n && a[last_i].max > last_value {
last_value = a[last_i].max
}
k += 1;
}
self.max_level = k - 1;
}
/// Find overlapping intervals in the index.
/// Returns a vector of entries, consisting of the interval and its associated data.
///
/// # Arguments
///
/// * `interval` - The interval for which overlaps are to be found in the index. Can also be a `Range`.
///
/// # Panics
///
/// Panics if this `IITree` instance has not been indexed yet.
pub fn find<I: Into<Interval<N>>>(&self, interval: I) -> Vec<Entry<N, D>> {
let mut buf = Vec::with_capacity(512);
self.find_into(interval, &mut buf);
buf
}
/// Find overlapping intervals in the index
///
/// # Arguments
///
/// * `interval` - The interval for which overlaps are to be found in the index. Can also be a `Range`.
/// * `results` - A reusable buffer vector for storing the results.
///
/// # Panics
///
/// Panics if this `IITree` instance has not been indexed yet.
pub fn find_into<'b, 'a: 'b, I: Into<Interval<N>>>(
&'a self,
interval: I,
results: &'b mut Vec<Entry<'a, N, D>>,
) {
if !self.indexed {
panic!("This IITree has not been indexed yet. Call `index()` first.")
}
let interval = interval.into();
let (start, end) = (interval.start, interval.end);
let n = self.entries.len() as usize;
let a = &self.entries;
results.clear();
let mut stack = [StackCell::empty(); 64];
// push the root; this is a top down traversal
stack[0].k = self.max_level;
stack[0].x = (1 << self.max_level) - 1;
stack[0].w = false;
let mut t = 1;
while t > 0 {
t -= 1;
let StackCell { k, x, w } = stack[t];
if k <= 3 {
// we are in a small subtree; traverse every node in this subtree
let i0 = x >> k << k;
let i1 = min(i0 + (1 << (k + 1)) - 1, n);
for (i, node) in a.iter().enumerate().take(i1).skip(i0) {
if node.interval.start >= end {
break;
}
if start < node.interval.end {
// if overlap, append to `results`
results.push(Entry {
interval: &self.entries[i].interval,
data: &self.entries[i].data,
});
}
}
} else if !w {
// if left child not processed
let y = x - (1 << (k - 1)); // the left child of x; NB: y may be out of range (i.e. y>=n)
stack[t].k = k;
stack[t].x = x;
stack[t].w = true; // re-add node x, but mark the left child having been processed
t += 1;
if y >= n || a[y].max > start {
// push the left child if y is out of range or may overlap with the query
stack[t].k = k - 1;
stack[t].x = y;
stack[t].w = false;
t += 1;
}
} else if x < n && a[x].interval.start < end {
// need to push the right child
if start < a[x].interval.end {
results.push(Entry {
interval: &self.entries[x].interval,
data: &self.entries[x].data,
});
}
stack[t].k = k - 1;
stack[t].x = x + (1 << (k - 1));
stack[t].w = false;
t += 1;
}
}
}
}
fn max3<T: Ord>(a: T, b: T, c: T) -> T {
a.max(b.max(c))
}
#[derive(Clone, Copy)]
struct StackCell {
// node
x: usize,
// level
k: usize,
// false if left child hasn't been processed
w: bool,
}
impl StackCell {
fn empty() -> Self {
Self {
x: 0,
k: 0,
w: false,
}
}
}
#[cfg(test)]
mod tests {
use proptest::prelude::*;
use super::*;
#[test]
fn test_example() {
let mut tree = ArrayBackedIntervalTree::new();
tree.insert(12..34, 0);
tree.insert(0..23, 1);
tree.insert(34..56, 2);
tree.index();
let overlap = tree.find(22..25);
let e1 = Entry {
interval: &(0..23).into(),
data: &1,
};
let e2 = Entry {
interval: &(12..34).into(),
data: &0,
};
let expected = vec![e1, e2];
assert_eq!(overlap, expected);
}
/// Regression test: catch a scenario where the `max` value of an entry
/// wasn't extended to take into account all of the leaf nodes it contained
/// when indexing
#[test]
fn test_disjoint_two_element_search() {
let mut tree = ArrayBackedIntervalTree::new();
tree.insert(12..34, 0);
tree.insert(40..56, 1);
tree.index();
let overlap = tree.find(40..41);
let e1 = Entry {
interval: &(40..56).into(),
data: &1,
};
let expected = vec![e1];
assert_eq!(overlap, expected);
}
proptest! {
/// Given a query interval in the format `(start, len)` and a sequence
/// of intervals `(start, len)` to index, assert that
/// `ArrayBackedIntervalTree::find` returns all the intervals which
/// overlap the query.
#[test]
fn find_arbitrary(
query in (0u32..1001, 0u32..1001),
intervals in prop::collection::vec((0u32..1000, 0u32..1000), 0..1000)
) {
let tree = ArrayBackedIntervalTree::from_iter(
intervals
.into_iter()
.enumerate()
.map(|(i, (start, len))| (start..start + len, i)),
);
let (start, len) = query;
let end = start + len;
let expected: Vec<_> = tree
.entries
.iter()
.filter_map(|internal| {
if internal.interval.start < end && start < internal.interval.end {
Some(Entry {
interval: &internal.interval,
data: &internal.data,
})
} else {
None
}
})
.collect();
prop_assert_eq!(
tree.find(start..end),
expected,
"{:?} in {:?}",
start..end,
tree.entries
);
}
}
}