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//!## Summary //! A library that provides a complete binary tree visitor trait with default implemenations for visiting strategies such as dfs_inorder or dfs_preorder, etc. //! Some adaptors are also provided that let you map, zip, or optionally also produce the depth on every call to next(). //! It also provides two flavors of a complete binary tree data structure with mutable and immutable visitors that implement the visitor trait. //! One laid out in bfs, and one laid out in dfs in order in memory. Both of these flavors assume that every node in the tree is the same type. //! //! This is the trait that this crate revoles around: //!``` //!pub trait Visitor:Sized{ //! type Item; //! fn next(self)->(Self::Item,Option<[Self;2]>); //!} //!``` //! If you have a visitor, you can call next() on it to consume it, and produce a reference to the node it is visiting, plus //! the children nodes. //! //! The fact that the iterator is consumed when calling next(), allows us to return mutable references without fear of the users //! being able to create the same mutable reference some other way. //! So this property provides a way to get mutable references to children nodes simultaneously safely. Useful for parallelizing divide and conquer style problems. //! //!## Goals //! //! To provide a useful complete binary tree visitor trait that has some similar features to the Iterator trait, //! such as zip(), and map(), and that can be used in parallel divide and conquer style problems. //! //!## Unsafety in the provided two tree implementations //! //! With a regular Vec, getting one mutable reference to an element will borrow the //! entire Vec. However a tree has properties that let us make guarentees about //! which elements can be mutably borrowed at the same time. With the bfs tree, the children //! for an element at index k can be found at 2k+1 and 2k+2. This means that we are guarenteed that the parent, //! and the two children are all distinct elements and so mutable references two all of them can exist at the same time. //! With the dfs implementation, on every call to next() we use split_at_mut() to split the current slice we have into three parts: //! the current node, the elements ot the left, and the elements to the right. //! //!## Memory Locality //! //! Ordering the elements in dfs in order is likely better for divide and conquer style problems. //! The main memory access pattern that we want to be fast is the following: If I have a parent, I hope to be able //! to access the children fast. So we want the children to be close to the parent. //! While in bfs order, the root's children are literally right next to it, the children of nodes in the the second //! to last level of the tree could be extremly far apart (possibly n/2 elements away!). //! With dfs order, as you go down the tree, you gain better and better locality. //! //! A downside with dfs ordering is that if not all space is used by the leaf nodes, //! Then that wasted space is interspered throughout the entire data structure. In a bfs ordering, //! All the leaves are at the end of the data structure, so the memory locality penalty may not be as high //! When traversing tree. //! //! For parallel divide and conquer, dfs ordering is likely better than bfs ordering. //! With dfs ordering, once you divide the problem, the memory sections that each task deals with //! do not intersect. With bfs ordering the tasks would still be operating on memory sections that interleave //! #![no_std] extern crate alloc; use alloc::vec::Vec; ///A complete binary tree stored in a Vec<T> laid out in bfs order. pub mod bfs_order; ///A complete binary tree stored in a Vec<T> laid out in dfs in order. ///One advantage of using the dfs order over the bfs order, is that at any point during traversal of the tree, ///you can turn the visitor into a slice representing the rest of the nodes underneath that visitor. pub mod dfs_order; //use core::collections::vec_deque::VecDeque; ///Compute the number of nodes in a complete binary tree based on a height. #[inline] pub fn compute_num_nodes(height: usize) -> usize { (1 << height) - 1 } #[must_use] fn valid_node_num(num: usize) -> bool { (num + 1).is_power_of_two() && num != 0 } ///Computes the height for the number of nodes given. ///Returns the number of trailing zeroes after the last bit in the binary representation. ///For complete binary trees this would be the height. #[inline] pub fn compute_height(num_nodes: usize) -> usize { (num_nodes + 1).trailing_zeros() as usize } ///Dfs in order iterator. Each call to next() will return the next element ///in dfs in order. ///Internally uses a Vec for the stack. pub struct DfsInOrderIter<C: Visitor> { a: Vec<(C::Item, Option<C>)>, length: Option<usize>, min_length: usize, num: usize, } impl<C: Visitor> DfsInOrderIter<C> { fn add_all_lefts(stack: &mut Vec<(C::Item, Option<C>)>, node: C) { let mut target = Some(node); loop { let (i, next) = target.take().unwrap().next(); match next { Some([left, right]) => { let bleep = (i, Some(right)); stack.push(bleep); target = Some(left); } None => { let bleep = (i, None); stack.push(bleep); break; } } } } } impl<C: Visitor> Iterator for DfsInOrderIter<C> { type Item = C::Item; #[inline] fn next(&mut self) -> Option<Self::Item> { match self.a.pop() { Some((i, nl)) => match nl { Some(nl) => { let res = i; DfsInOrderIter::add_all_lefts(&mut self.a, nl); self.num += 1; Some(res) } None => Some(i), }, None => None, } } #[inline] fn size_hint(&self) -> (usize, Option<usize>) { ( self.min_length - self.num, self.length.map(|a| a - self.num), ) } } impl<C: Visitor> core::iter::FusedIterator for DfsInOrderIter<C> {} impl<C: FixedDepthVisitor> core::iter::ExactSizeIterator for DfsInOrderIter<C> {} ///Dfs preorder iterator. Each call to next() will return the next element ///in dfs order. ///Internally uses a Vec for the stack. pub struct DfsPreOrderIter<C: Visitor> { a: Vec<C>, length: Option<usize>, min_length: usize, num: usize, } impl<C: Visitor> core::iter::FusedIterator for DfsPreOrderIter<C> {} impl<C: FixedDepthVisitor> core::iter::ExactSizeIterator for DfsPreOrderIter<C> {} impl<C: Visitor> Iterator for DfsPreOrderIter<C> { type Item = C::Item; #[inline] fn next(&mut self) -> Option<Self::Item> { match self.a.pop() { Some(x) => { let (i, next) = x.next(); if let Some([left, right]) = next { self.a.push(right); self.a.push(left); } self.num += 1; Some(i) } None => None, } } #[inline] fn size_hint(&self) -> (usize, Option<usize>) { ( self.min_length - self.num, self.length.map(|a| a - self.num), ) } } /* Removed since wanted to make crate no_std. ///Bfs Iterator. Each call to next() returns the next ///element in bfs order. ///Internally uses a VecDeque for the queue. pub struct BfsIter<C: Visitor> { a: VecDeque<C>, a:PhantomData<C>, num: usize, min_length: usize, length: Option<usize>, } impl<C: Visitor> core::iter::FusedIterator for BfsIter<C> {} impl<C: FixedDepthVisitor> core::iter::ExactSizeIterator for BfsIter<C> {} impl<C: Visitor> Iterator for BfsIter<C> { type Item = C::Item; #[inline] fn next(&mut self) -> Option<Self::Item> { let queue = &mut self.a; match queue.pop_front() { Some(e) => { let (nn, rest) = e.next(); if let Some([left, right]) = rest { queue.push_back(left); queue.push_back(right); } Some(nn) } None => None, } } #[inline] fn size_hint(&self) -> (usize, Option<usize>) { ( self.min_length - self.num, self.length.map(|a| a - self.num), ) } } */ ///Map iterator adapter pub struct Map<C, F> { func: F, inner: C, } impl<B, C: Visitor, F: Fn(C::Item) -> B + Clone> Visitor for Map<C, F> { type Item = B; #[inline] fn next(self) -> (Self::Item, Option<[Self; 2]>) { let (a, rest) = self.inner.next(); let k = (self.func)(a); match rest { Some([left, right]) => { let ll = Map { func: self.func.clone(), inner: left, }; let rr = Map { func: self.func, inner: right, }; (k, Some([ll, rr])) } None => (k, None), } } } unsafe impl<B, C: FixedDepthVisitor, F: Fn(C::Item) -> B + Clone> FixedDepthVisitor for Map<C, F> {} ///If implemented, then the level_remaining_hint must return the exact height of the tree. ///If this is implemented, then the exact number of nodes that will be returned by a dfs or bfs traversal is known ///so those iterators can implement TrustedLen in this case. pub unsafe trait FixedDepthVisitor: Visitor {} ///The trait this crate revoles around. ///A complete binary tree visitor. pub trait Visitor: Sized { ///The common item produced for both leafs and non leafs. type Item; ///Consume this visitor, and produce the element it was pointing to ///along with it's children visitors. fn next(self) -> (Self::Item, Option<[Self; 2]>); ///Return the levels remaining including the one that will be produced by consuming this iterator. ///So if you first made this object from the root for a tree of size 5, it should return 5. ///Think of is as height-depth. ///This is used to make good allocations when doing dfs and bfs. ///Defaults to (0,None) #[inline] fn level_remaining_hint(&self) -> (usize, Option<usize>) { (0, None) } ///Iterator Adapter to also produce the depth each iteration. #[inline] fn with_depth(self, start_depth: Depth) -> LevelIter<Self> { LevelIter { inner: self, depth: start_depth, } } ///Combine two tree visitors. #[inline] fn zip<F: Visitor>(self, f: F) -> Zip<Self, F> { Zip { a: self, b: f } } ///Map iterator adapter #[inline] fn map<B, F: Fn(Self::Item) -> B>(self, func: F) -> Map<Self, F> { Map { func, inner: self } } ///Only produce children up to num. #[inline] fn take(self, num: usize) -> Take<Self> { Take { a: self, num } } ///Flips left and right children. #[inline] fn flip(self) -> Flip<Self> { Flip(self) } /* ///Provides an iterator that returns each element in bfs order. #[inline] fn bfs_iter(self) -> BfsIter<Self> { let (levels, max_levels) = self.level_remaining_hint(); //Need enough room to fit all the leafs in the queue at once, of which there are n/2. let cap = (2u32.pow(levels as u32)) / 2; let mut a = VecDeque::with_capacity(cap as usize); let min_length = 2usize.pow(levels as u32) - 1; let length = max_levels.map(|max_levels| 2usize.pow(max_levels as u32) - 1); a.push_back(self); BfsIter { a, min_length, length, num: 0, } } */ ///Provides a dfs preorder iterator. Unlike the callback version, ///This one relies on dynamic allocation for its stack. #[inline] fn dfs_preorder_iter(self) -> DfsPreOrderIter<Self> { let (levels, max_levels) = self.level_remaining_hint(); let mut a = Vec::with_capacity(levels); a.push(self); let min_length = 2usize.pow(levels as u32) - 1; let length = max_levels.map(|levels_max| 2usize.pow(levels_max as u32) - 1); DfsPreOrderIter { a, length, min_length, num: 0, } } #[inline] fn dfs_inorder_iter(self) -> DfsInOrderIter<Self> { let (levels, max_levels) = self.level_remaining_hint(); let mut a = Vec::with_capacity(levels); let length = max_levels.map(|levels_max| 2usize.pow(levels_max as u32) - 1); let min_length = 2usize.pow(levels as u32) - 1; DfsInOrderIter::add_all_lefts(&mut a, self); DfsInOrderIter { a, min_length, length, num: 0, } } ///Calls the closure in dfs preorder (root,left,right). ///Takes advantage of the callstack to do dfs. #[inline] fn dfs_preorder(self, mut func: impl FnMut(Self::Item)) { rec_pre(self, &mut func); } ///Calls the closure in dfs preorder (left,right,root). ///Takes advantage of the callstack to do dfs. #[inline] fn dfs_inorder(self, mut func: impl FnMut(Self::Item)) { rec_inorder(self, &mut func); } ///Calls the closure in dfs preorder (left,right,root). ///Takes advantage of the callstack to do dfs. #[inline] fn dfs_postorder(self, mut func: impl FnMut(Self::Item)) { rec_post(self, &mut func); } } fn rec_pre<C: Visitor>(a: C, func: &mut impl FnMut(C::Item)) { let (nn, rest) = a.next(); match rest { Some([left, right]) => { func(nn); rec_pre(left, func); rec_pre(right, func); } None => func(nn), } } fn rec_inorder<C: Visitor>(a: C, func: &mut impl FnMut(C::Item)) { let (nn, rest) = a.next(); match rest { Some([left, right]) => { rec_inorder(left, func); func(nn); rec_inorder(right, func); } None => { func(nn); } } } fn rec_post<C: Visitor>(a: C, func: &mut impl FnMut(C::Item)) { let (nn, rest) = a.next(); match rest { Some([left, right]) => { rec_post(left, func); rec_post(right, func); func(nn); } None => { func(nn); } } } ///Flips left and right children. pub struct Flip<T: Visitor>(T); impl<T: Visitor> Visitor for Flip<T> { type Item = T::Item; fn next(self) -> (Self::Item, Option<[Self; 2]>) { let (a, rest) = self.0.next(); (a, rest.map(|[l, r]| [Flip(r), Flip(l)])) } } unsafe impl<T: FixedDepthVisitor> FixedDepthVisitor for Flip<T> {} ///Only returns children up untill level num. pub struct Take<T: Visitor> { a: T, num: usize, } impl<T: Visitor> Visitor for Take<T> { type Item = T::Item; fn next(self) -> (Self::Item, Option<[Self; 2]>) { let (a, rest) = self.a.next(); let rest = match rest { Some([left, right]) => { if self.num == 0 { None } else { Some([ Take { a: left, num: self.num - 1, }, Take { a: right, num: self.num - 1, }, ]) } } None => None, }; (a, rest) } } ///Tree visitor that zips up two seperate visitors. ///If one of the iterators returns None for its children, this iterator will return None. pub struct Zip<T1: Visitor, T2: Visitor> { a: T1, b: T2, } impl<T1: Visitor, T2: Visitor> Zip<T1, T2> { #[inline] pub fn into_inner(self) -> (T1, T2) { let Zip { a, b } = self; (a, b) } #[inline] pub fn as_inner(&self) -> (&T1, &T2) { (&self.a, &self.b) } #[inline] pub fn as_inner_mut(&mut self) -> (&mut T1, &mut T2) { (&mut self.a, &mut self.b) } } impl<T1: Visitor, T2: Visitor> Visitor for Zip<T1, T2> { type Item = (T1::Item, T2::Item); #[inline] fn next(self) -> (Self::Item, Option<[Self; 2]>) { let (a_item, a_rest) = self.a.next(); let (b_item, b_rest) = self.b.next(); let item = (a_item, b_item); match (a_rest, b_rest) { (Some(a_rest), Some(b_rest)) => { let [aleft, aright] = a_rest; let [bleft, bright] = b_rest; let f1 = Zip { a: aleft, b: bleft }; let f2 = Zip { a: aright, b: bright, }; (item, Some([f1, f2])) } _ => (item, None), } } #[inline] fn level_remaining_hint(&self) -> (usize, Option<usize>) { let a = self.a.level_remaining_hint(); let b = self.b.level_remaining_hint(); let min = a.0.min(b.0); let min2 = match (a.1, b.1) { (Some(a), Some(b)) => Some(a.min(b)), _ => None, }; (min, min2) } } unsafe impl<T1: FixedDepthVisitor, T2: FixedDepthVisitor> FixedDepthVisitor for Zip<T1, T2> {} #[derive(Copy, Clone)] ///A level descriptor. pub struct Depth(pub usize); ///A wrapper iterator that will additionally return the depth of each element. pub struct LevelIter<T> { inner: T, depth: Depth, } impl<T> LevelIter<T> { #[inline] pub fn depth(&self) -> usize { self.depth.0 } #[inline] pub fn into_inner(self) -> T { self.inner } #[inline] pub fn as_inner(&self) -> &T { &self.inner } #[inline] pub fn as_inner_mut(&mut self) -> &mut T { &mut self.inner } } impl<T: Visitor> Visitor for LevelIter<T> { type Item = (Depth, T::Item); #[inline(always)] fn next(self) -> (Self::Item, Option<[Self; 2]>) { let LevelIter { inner, depth } = self; let (nn, rest) = inner.next(); let r = (depth, nn); match rest { Some([left, right]) => { let ln = Depth(depth.0 + 1); let ll = LevelIter { inner: left, depth: ln, }; let rr = LevelIter { inner: right, depth: ln, }; (r, Some([ll, rr])) } None => (r, None), } } #[inline] fn level_remaining_hint(&self) -> (usize, Option<usize>) { self.inner.level_remaining_hint() } } unsafe impl<T: FixedDepthVisitor> FixedDepthVisitor for LevelIter<T> {}