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//! # Slighly over-engineered Fenwick Tree implmentation.
//!
//! Allows efficient prefix sum calculation.
//!
//! Created for training purposes to test:
//!
//! 1. rust typesystem, default trait implmentation, enums as a way for polymorphism
//! 2. memory management and consumption of value
//! 3. cargo tools, docs, tests, clippy and benchmarks, build and publish.
//!
//! Code is free to do whatever you feel like.
//!
//! Provides abstraction for Fenwick tree data structure and 2 implmentations:
//! - [`prelude::FixedSizeFenwickTree`]
//! - [`prelude::GrowingFenwickTree`]
//!
//! Key space for a tree lies within [`usize`] range. Tree support any value that
//! implements [`FenwickTreeValue`] trait. [`FenwickTreeValue`] is automatically
//! implmented for all primitive numeric types that support [`std::ops::AddAssign`],
//! [`std::ops::Sub`], [`core::cmp::PartialEq`] and [`Copy`] traits.
//!
//! ## Installation
//!
//! ```bash
//! cargo install fenwick-bit-tree
//! ```
//!
//! ## Test
//!
//! ```bash
//! cargo test
//! ```
//!
//! ## Benchmarks
//!
//! ```bash
//! cargo bench --features benchmarks
//! ```
//!
//! ## Basic usage:
//!
//! ```rust
//! use fenwick_bit_tree::prelude::*;
//!
//! // Create the tree with capacity for 32 aggregated [`i32`] data points.
//! // One can use whole usize range to store datapoints for unicode timestamps
//! let mut tree = FixedSizeFenwickTree::<i32>::new(32);
//!
//! // Add values
//!
//! tree.update(0, 1);
//! tree.update(0, 4); // Will aggregate value at index 0 so it would be 5
//! tree.update(10, 10);
//! tree.update(20, 10);
//! tree.update(30, 10);
//!
//! // Now you can query data.
//! // NOTE: FixedSizeFenwickTree will raise error when query goes out of bounds.
//! // GrowingFenwickTree will automatically truncate the range to the rightmost index.
//!
//! assert_eq!(tree.query(4).unwrap(), 5);
//! assert_eq!(tree.query(15).unwrap(), 15);
//! assert_eq!(tree.query(31).unwrap(), 35);
//!
//! // Also allows making range queries
//!
//! let val = tree.range_query(2, 16).unwrap(); // Will return aggregated sum of all values between those keys.
//! assert_eq!(val, 10);
//! ```
#![forbid(unsafe_code)]
#![feature(test)]
use std::ops::{Deref, DerefMut};
mod fixed_size_tree;
mod growing_tree;
pub use fixed_size_tree::FixedSizeFenwickTree;
pub use growing_tree::GrowingFenwickTree;
/// Contains all public types
pub mod prelude {
pub use crate::FenwickTreeValue;
pub use crate::fixed_size_tree::FixedSizeFenwickTree;
pub use crate::growing_tree::GrowingFenwickTree;
pub use crate::FenwickTree;
pub use crate::TreeError;
}
fn least_significant_bit(idx: usize) -> usize {
let int_idx = idx as i32;
(int_idx & -int_idx) as usize
}
/// Types that implement that trait can be stored and aggregated within Fenwick tree.
pub trait FenwickTreeValue:
Default + Clone //
+ core::cmp::PartialEq
{
fn store_value(&mut self, other: &Self);
fn substract(self, other: Self) -> Self;
}
impl<T> FenwickTreeValue for T
where T: Default + Copy //
+ std::ops::AddAssign
+ std::ops::Sub<Output = Self>
+ core::cmp::PartialEq
{
fn store_value(&mut self, other: &Self) {
*self += *other
}
fn substract(self, other: Self) -> Self {
self - other
}
}
/// Fenwick tree trait, API of that data structure
pub trait FenwickTree {
type Value: FenwickTreeValue;
/// Returns sum of values across all indexes lesser or equal than `idx`.
///
/// # Errors
///
/// This function will returns an error if idx is out of bounds.
/// GrowingFenwick tree implementation never returns error.
///
fn query(&self, idx: usize) -> Result<Self::Value, TreeError>;
/// Add new value to the `idx` stored value, which is 0 by default.
///
/// # Errors
///
/// This function will return an error if idx is out of bounds.
/// GrowingFenwick tree implementation never returns error.
///
fn update(&mut self, idx: usize, value: Self::Value) -> Result<(), TreeError>;
/// Returns sum of values across all indexes in between `from` and `to` indexes
/// (including edges).
///
/// # Errors
///
/// This function will return an error if any index is out of bounds.
/// GrowingFenwick tree implementation never return error.
///
fn range_query(&self, from: usize, to: usize) -> Result<Self::Value, TreeError> {
let from_sum = self.query(from)?;
let to_sum = self.query(to)?;
Ok(to_sum.substract(from_sum))
}
}
/// For the sake of clarity Tree supports 2 types of indexing. [`TreeIndex::External`] is meant to be used
/// by library consumer. While [`TreeIndex::Internal`] is used for purposes to make tree reindexing code more
/// understable and maintainable. [`usize`] can be automatically converted using `into()` into the [`TreeIndex::External`]
#[derive(Debug, Clone, Copy)]
enum TreeIndex {
Internal { val: usize },
External { val: usize },
}
#[derive(Debug, PartialEq)]
pub enum TreeError {
IndexOutOfBounds( usize )
}
impl TreeIndex {
fn to_internal(self) -> Self {
match self {
TreeIndex::Internal { val: _ } => self,
TreeIndex::External { val } => TreeIndex::Internal { val: val + 1 },
}
}
fn to_external(self) -> Result<Self, String> {
match self {
TreeIndex::Internal { val } => {
if val == 0 {
return Err("Index is out of bounds.".to_string());
}
Ok(TreeIndex::External { val: val - 1 })
}
TreeIndex::External { val: _ } => Ok(self),
}
}
/// Starts with the initial value and then moves down to zero returning result of
/// deduction of the least significant bit
fn lsb_descending(self) -> LeastSignificantBitDescentingChain {
LeastSignificantBitDescentingChain {
idx: self.to_internal(),
}
}
/// Starts with the initial value and then moves up until upper bound is reached
/// returning the result of deduction of the least significant bit
fn lsb_ascending(self, upper_bound: usize) -> LeastSignificantBitAscendingChain {
LeastSignificantBitAscendingChain {
idx: self.to_internal(),
max: upper_bound,
}
}
fn is_power_of_2(self) -> bool {
let idx = *self;
idx.is_power_of_two()
}
}
impl From<usize> for TreeIndex {
fn from(value: usize) -> Self {
Self::External { val: value }
}
}
impl Deref for TreeIndex {
type Target = usize;
fn deref(&self) -> &Self::Target {
match self {
TreeIndex::External { val } => val,
TreeIndex::Internal { val } => val,
}
}
}
impl PartialEq for TreeIndex {
fn eq(&self, other: &Self) -> bool {
match (self, other) {
(Self::Internal { val: l_val }, Self::Internal { val: r_val }) => l_val == r_val,
(Self::External { val: l_val }, Self::External { val: r_val }) => l_val == r_val,
_ => false,
}
}
}
impl DerefMut for TreeIndex {
fn deref_mut(&mut self) -> &mut Self::Target {
match self {
TreeIndex::External { val } => val,
TreeIndex::Internal { val } => val,
}
}
}
/// Iterator that implements changing value by deduction of the least significant bit and
/// returning result
struct LeastSignificantBitDescentingChain {
idx: TreeIndex,
}
impl Iterator for LeastSignificantBitDescentingChain {
type Item = TreeIndex;
fn next(&mut self) -> Option<Self::Item> {
if *self.idx == 0 {
return None;
}
// TODO: implement COpy?
let res = TreeIndex::Internal { val: *self.idx };
*self.idx -= least_significant_bit(*self.idx);
Some(res)
}
}
/// Iterator that implements changing value by addition of the least significant bit and
/// returning result
struct LeastSignificantBitAscendingChain {
idx: TreeIndex,
max: usize,
}
impl Iterator for LeastSignificantBitAscendingChain {
type Item = TreeIndex;
fn next(&mut self) -> Option<Self::Item> {
if *self.idx > self.max {
return None;
}
// TODO: implement COpy?
let res = TreeIndex::Internal { val: *self.idx };
*self.idx += least_significant_bit(*self.idx);
Some(res)
}
}
#[cfg(test)]
mod tests {
use pretty_assertions::assert_eq;
use crate::{least_significant_bit, TreeIndex};
fn to_internal_index_vec(indexes: &[usize]) -> Vec<TreeIndex> {
indexes
.into_iter()
.map(|i| TreeIndex::Internal { val: *i })
.collect::<Vec<TreeIndex>>()
}
#[test]
fn test_index_transform_from_internal_to_external_with_error() {
let idx = TreeIndex::Internal { val: 0 };
idx.to_external().expect_err("Index is out of bounds.");
}
#[test]
fn test_index_transform_from_internal_to_external() {
for val in 1..100 {
let idx = TreeIndex::Internal { val: val };
assert_eq!(
idx.to_external().unwrap(),
TreeIndex::External { val: val - 1 }
);
}
}
#[test]
fn test_index_transform_from_external_to_internal() {
for val in 0..100 {
let idx = TreeIndex::External { val: val };
assert_eq!(idx.to_internal(), TreeIndex::Internal { val: val + 1 });
}
}
#[test]
fn test_index_transform_to_itseld() {
for val in 0..100 {
let idx = TreeIndex::External { val: val };
assert_eq!(idx.to_external().unwrap(), TreeIndex::External { val });
}
for val in 0..100 {
let idx = TreeIndex::Internal { val: val };
assert_eq!(idx.to_internal(), TreeIndex::Internal { val: val });
}
}
#[test]
fn test_ascending_lsb_chain() {
let idx: TreeIndex = 0.into();
assert_eq!(
idx.lsb_ascending(64).collect::<Vec<TreeIndex>>(),
to_internal_index_vec(&[1, 2, 4, 8, 16, 32, 64])
);
let idx: TreeIndex = 1.into();
assert_eq!(
idx.lsb_ascending(64).collect::<Vec<TreeIndex>>(),
to_internal_index_vec(&[2, 4, 8, 16, 32, 64])
);
let idx: TreeIndex = 6.into();
assert_eq!(
idx.lsb_ascending(64).collect::<Vec<TreeIndex>>(),
to_internal_index_vec(&[7, 8, 16, 32, 64])
);
let idx: TreeIndex = 6.into();
assert_eq!(idx.lsb_ascending(0).collect::<Vec<TreeIndex>>(), vec![]);
}
#[test]
fn test_descending_lsb_chain() {
let idx: TreeIndex = 5.into();
assert_eq!(idx, TreeIndex::External { val: 5 });
assert_eq!(
idx.lsb_descending().collect::<Vec<TreeIndex>>(),
to_internal_index_vec(&[6, 4])
);
let idx: TreeIndex = 4.into();
assert_eq!(
idx.lsb_descending().collect::<Vec<TreeIndex>>(),
to_internal_index_vec(&[5, 4])
);
let idx = TreeIndex::Internal { val: 3 };
assert_eq!(
idx.lsb_descending().collect::<Vec<TreeIndex>>(),
to_internal_index_vec(&[3, 2])
);
let idx = TreeIndex::Internal { val: 12 };
assert_eq!(
idx.lsb_descending().collect::<Vec<TreeIndex>>(),
to_internal_index_vec(&[12, 8])
);
}
#[test]
fn test_lsb() {
assert_eq!(least_significant_bit(12), 4)
}
#[test]
fn test_bitwise_op() {
assert_eq!(12usize.next_power_of_two(), 16);
assert_eq!(12usize.next_power_of_two() >> 1, 8);
}
}