fuel_merkle/common/path_iterator.rs
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use crate::common::{
node::{
ChildKeyResult,
ChildResult,
ParentNode,
},
path::{
Path,
Side,
},
};
/// # Path Iterator
///
/// A naturally arising property of binary trees is that a leaf index encodes
/// the unique path needed to traverse from the root of the tree to that leaf.
/// The index's binary representation can be read left to right as a sequence of
/// traversal instructions: a `0` bit means "descend left" and a `1` bit means
/// "descend right". By following the `x` bits composing the index, starting at
/// the root, descending to the left child at each `0`, descending to the right
/// child at each `1`, we arrive at the leaf position, having touched every node
/// position along the path formed by this index. Note that this algorithm does
/// not prescribe how to descend from one node to the next; it describes merely
/// the direction in which to descend at each step.
///
/// Alternatively, this can be interpreted as reading the index's most
/// significant bit (MSB) at an offset `n`: read the `n`th bit to the right of
/// the MSB. Here, `n` is a given step in the tree traversal, starting at 0, and
/// incrementing by 1 at each depth until the leaf is reached. The
/// traversal path is then the list of nodes calculated by traversing the tree
/// using the instruction (`0` or `1`) indicated at `x`<sub>`n`</sub>, where `x`
/// is the index in binary representation, and `n` is the offset for each digit
/// in `x` from the MSB.
///
/// Reversing this path gives us the path from the leaf to the root.
///
/// Imagine a 3-bit integer type `u3` underpinning a tree's leaf indices. 3 bits
/// give our tree a maximum height of 3, and a maximum number of leaf nodes
/// 2<sup>3</sup> = 8. For demonstration, internal nodes are numbered using
/// in-order indices (note that this would require an integer type with 4 bits
/// or more in practice). In-order indexing provides a deterministic way to
/// descend from one node to the next (see [Position](crate::common::Position)).
///
/// ```text
/// 07
/// / \
/// / \
/// / \
/// / \
/// / \
/// / \
/// 03 11
/// / \ / \
/// / \ / \
/// 01 05 09 13
/// / \ / \ / \ / \
/// In-order idx: 00 02 04 06 08 10 12 14
/// Leaf idx: 0 1 2 3 4 5 6 7
/// ```
///
/// Let us now find the path to leaf with index `6`. In the above diagram, this
/// is the seventh leaf in the leaf layer. A priori, we can see that the path
/// from the root to this leaf is represented by the following list of in-order
/// indices: `07, 11, 13, 12` (note that the leaf index that corresponds to the
/// in-order index `12` is `6`).
///
/// ```text
/// 0d6: u3 = 0b110
/// = Right, Right, Left
/// ```
///
/// Starting at the tree's root at index `07`, we can follow the instructions
/// encoded by the binary representation of leaf `6` (`0b110`). In combination
/// with our in-order index rules for descending nodes, we evaluate the
/// following:
///
/// 1. The first bit is `1`; move right from `07` to `11`.
/// 2. The next bit is `1`; move right from `11` to `13`.
/// 3. The next and final bit is `0`; move left from `13` to `12`.
///
/// We have arrived at the desired leaf position with in-order index `12` and
/// leaf index `6`. Indeed, following the instructions at each bit has produced
/// the same list of positional indices that we observed earlier: `07, 11, 13,
/// 12`.
pub struct PathIter<T: ParentNode> {
leaf_key: T::Key,
current: Option<(ChildResult<T>, ChildKeyResult<T>)>,
current_offset: u32,
}
impl<T> PathIter<T>
where
T: ParentNode + Clone,
T::Key: Clone,
{
pub fn new(root: &T, leaf_key: &T::Key) -> Self {
let initial = (Ok(root.clone()), Ok(root.key()));
#[rustfmt::skip]
// The initial offset from the most significant bit (MSB).
//
// The offset from the MSB indicates which bit to read when deducing the
// path from the root to the leaf. As we descend down the tree,
// increasing the traversal depth, we increment this offset and read the
// corresponding bit to get the next traversal instruction.
//
// In the general case, we start by reading the first bit of the path at
// offset 0. This happens when the path fills its allocated memory;
// e.g., a path of 256 instructions is encoded within a 256 bit
// allocation for the leaf key. This also means that the key size in
// bits is equal to the maximum height of the tree.
//
// In the case that the length of the path is less than the number of
// bits in the key, the initial offset from the MSB must be augmented to
// accommodate the shortened path. This occurs when the key is allocated
// with a larger address space to reduce collisions of node addresses.
//
// E.g,
// With an 8-bit key and heights 1 through 7:
//
// Height Depth
// 7 0 127 Offset = Bits - Height = 8 - 7 = 1
// / \
// / \
// ... ... ...
// / \
// / \
// 3 4 07 247 Offset = Bits - Height = 8 - 3 = 5
// / \ / \
// / \ ... \
// / \ \
// / \ \
// / \ \
// / \ \
// 2 5 03 11 251 Offset = Bits - Height = 8 - 2 = 6
// / \ / \ / \
// / \ / \ ... \
// 1 6 01 05 09 13 253 Offset = Bits - Height = 8 - 1 = 7
// / \ / \ / \ / \ / \
// 0 7 00 02 04 06 08 10 12 14 252 254
// 00 01 02 03 04 05 06 07 126 127
//
let initial_offset = T::key_size_bits().checked_sub(root.height())
.expect("Root height more than key size allows, ParentNode impl is incorrect");
Self {
leaf_key: leaf_key.clone(),
current: Some(initial),
current_offset: initial_offset,
}
}
}
impl<T> Iterator for PathIter<T>
where
T: ParentNode,
T::Key: Path,
{
type Item = (ChildResult<T>, ChildKeyResult<T>);
fn next(&mut self) -> Option<Self::Item> {
let value = self.current.take();
if let Some((ref path_node, _)) = value {
match path_node {
Ok(path_node) if path_node.is_node() => {
let path = &self.leaf_key;
let instruction = path.get_instruction(self.current_offset);
self.current = instruction.map(|instruction| {
// get_instruction ensures current_offset is ok
#[allow(clippy::arithmetic_side_effects)]
{
self.current_offset += 1;
}
match instruction {
Side::Left => {
(path_node.left_child(), path_node.right_child_key())
}
Side::Right => {
(path_node.right_child(), path_node.left_child_key())
}
}
});
}
// Terminate the iterator if any of the following are true:
// - The path node is a leaf (traversal is complete)
// - The left or right child was not found and returned a ChildNotFound
// error
// - The left or right child returned any other error
_ => self.current = None,
}
}
value
}
}
pub trait AsPathIterator<T: ParentNode> {
fn as_path_iter(&self, leaf_key: &T::Key) -> PathIter<T>;
}
impl<T> AsPathIterator<T> for T
where
T: ParentNode + Clone,
T::Key: Clone,
{
fn as_path_iter(&self, leaf_key: &T::Key) -> PathIter<T> {
PathIter::new(self, leaf_key)
}
}
#[cfg(test)]
#[allow(
clippy::restriction,
clippy::cast_possible_wrap,
clippy::cast_sign_loss
)]
mod test {
use crate::common::{
node::{
ChildKeyResult,
ChildResult,
Node,
ParentNode,
},
AsPathIterator,
Bytes8,
};
use alloc::vec::Vec;
use core::convert::Infallible;
#[derive(Debug, Clone, PartialEq)]
struct TestNode {
value: u64,
}
impl TestNode {
pub fn in_order_index(&self) -> u64 {
self.value
}
pub fn leaf_index(&self) -> u64 {
assert!(self.is_leaf());
self.value / 2
}
pub fn from_in_order_index(index: u64) -> Self {
Self { value: index }
}
pub fn from_leaf_index(index: u64) -> Self {
Self { value: index * 2 }
}
pub fn height(&self) -> u32 {
(!self.in_order_index()).trailing_zeros()
}
pub fn is_leaf(&self) -> bool {
self.in_order_index() % 2 == 0
}
fn child(&self, direction: i64) -> Self {
assert!(!self.is_leaf());
let shift = 1 << (self.height() - 1);
let index = self.in_order_index() as i64 + shift * direction;
Self::from_in_order_index(index as u64)
}
}
impl Node for TestNode {
type Key = Bytes8;
fn height(&self) -> u32 {
TestNode::height(self)
}
#[allow(clippy::arithmetic_side_effects, clippy::cast_possible_truncation)] // const
fn key_size_bits() -> u32 {
core::mem::size_of::<Self::Key>() as u32 * 8
}
fn leaf_key(&self) -> Self::Key {
TestNode::leaf_index(self).to_be_bytes()
}
fn is_leaf(&self) -> bool {
TestNode::is_leaf(self)
}
fn is_node(&self) -> bool {
!TestNode::is_leaf(self)
}
}
impl ParentNode for TestNode {
type ChildKey = u64;
type Error = Infallible;
fn key(&self) -> Self::ChildKey {
self.in_order_index()
}
fn left_child(&self) -> ChildResult<Self> {
Ok(TestNode::child(self, -1))
}
fn left_child_key(&self) -> ChildKeyResult<Self> {
self.left_child().map(|node| node.in_order_index())
}
fn right_child(&self) -> ChildResult<Self> {
Ok(TestNode::child(self, 1))
}
fn right_child_key(&self) -> ChildKeyResult<Self> {
self.right_child().map(|node| node.in_order_index())
}
}
#[test]
fn test_path_iter_returns_path() {
// 07
// / \
// / \
// / \
// / \
// / \
// / \
// 03 11
// / \ / \
// / \ / \
// 01 05 09 13
// / \ / \ / \ / \
// 00 02 04 06 08 10 12 14
// 00 01 02 03 04 05 06 07
//
type Node = TestNode;
let root = Node::from_in_order_index(7);
{
let leaf = Node::from_leaf_index(0);
let path: Vec<TestNode> = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, _)| path.unwrap())
.collect();
let expected_path = vec![
Node::from_in_order_index(7),
Node::from_in_order_index(3),
Node::from_in_order_index(1),
Node::from_leaf_index(0),
];
assert_eq!(path, expected_path);
}
{
let leaf = Node::from_leaf_index(1);
let path: Vec<TestNode> = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, _)| path.unwrap())
.collect();
let expected_path = vec![
Node::from_in_order_index(7),
Node::from_in_order_index(3),
Node::from_in_order_index(1),
Node::from_leaf_index(1),
];
assert_eq!(path, expected_path);
}
{
let leaf = Node::from_leaf_index(2);
let path: Vec<TestNode> = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, _)| path.unwrap())
.collect();
let expected_path = vec![
Node::from_in_order_index(7),
Node::from_in_order_index(3),
Node::from_in_order_index(5),
Node::from_leaf_index(2),
];
assert_eq!(path, expected_path);
}
{
let leaf = Node::from_leaf_index(3);
let path: Vec<TestNode> = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, _)| path.unwrap())
.collect();
let expected_path = vec![
Node::from_in_order_index(7),
Node::from_in_order_index(3),
Node::from_in_order_index(5),
Node::from_leaf_index(3),
];
assert_eq!(path, expected_path);
}
{
let leaf = Node::from_leaf_index(4);
let path: Vec<TestNode> = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, _)| path.unwrap())
.collect();
let expected_path = vec![
Node::from_in_order_index(7),
Node::from_in_order_index(11),
Node::from_in_order_index(9),
Node::from_leaf_index(4),
];
assert_eq!(path, expected_path);
}
{
let leaf = Node::from_leaf_index(5);
let path: Vec<TestNode> = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, _)| path.unwrap())
.collect();
let expected_path = vec![
Node::from_in_order_index(7),
Node::from_in_order_index(11),
Node::from_in_order_index(9),
Node::from_leaf_index(5),
];
assert_eq!(path, expected_path);
}
{
let leaf = Node::from_leaf_index(6);
let path: Vec<TestNode> = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, _)| path.unwrap())
.collect();
let expected_path = vec![
Node::from_in_order_index(7),
Node::from_in_order_index(11),
Node::from_in_order_index(13),
Node::from_leaf_index(6),
];
assert_eq!(path, expected_path);
}
{
let leaf = Node::from_leaf_index(7);
let path: Vec<TestNode> = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, _)| path.unwrap())
.collect();
let expected_path = vec![
Node::from_in_order_index(7),
Node::from_in_order_index(11),
Node::from_in_order_index(13),
Node::from_leaf_index(7),
];
assert_eq!(path, expected_path);
}
}
#[test]
fn test_path_iter_returns_side_nodes() {
// 07
// / \
// / \
// / \
// / \
// / \
// / \
// 03 11
// / \ / \
// / \ / \
// 01 05 09 13
// / \ / \ / \ / \
// 00 02 04 06 08 10 12 14
// 00 01 02 03 04 05 06 07
//
type Node = TestNode;
let root = Node::from_in_order_index(7); // 2^3 - 1
{
let leaf = Node::from_leaf_index(0);
let side: Vec<_> = root
.as_path_iter(&leaf.leaf_key())
.map(|(_, side)| side.unwrap())
.collect();
let expected_side = vec![
Node::from_in_order_index(7).value, // Root's dummy side
Node::from_in_order_index(11).value, // Sibling of node 3
Node::from_in_order_index(5).value, // Sibling of node 1
Node::from_leaf_index(1).value, // Sibling of leaf 0
];
assert_eq!(side, expected_side);
}
{
let leaf = Node::from_leaf_index(1);
let side: Vec<_> = root
.as_path_iter(&leaf.leaf_key())
.map(|(_, side)| side.unwrap())
.collect();
let expected_side = vec![
Node::from_in_order_index(7).value, // Root's dummy side
Node::from_in_order_index(11).value, // Sibling of node 3
Node::from_in_order_index(5).value, // Sibling of node 1
Node::from_leaf_index(0).value, // Sibling of leaf 1
];
assert_eq!(side, expected_side);
}
{
let leaf = Node::from_leaf_index(2);
let side: Vec<_> = root
.as_path_iter(&leaf.leaf_key())
.map(|(_, side)| side.unwrap())
.collect();
let expected_side = vec![
Node::from_in_order_index(7).value, // Root's dummy side
Node::from_in_order_index(11).value, // Sibling of node 3
Node::from_in_order_index(1).value, // Sibling of node 5
Node::from_leaf_index(3).value, // Sibling of leaf 2
];
assert_eq!(side, expected_side);
}
{
let leaf = Node::from_leaf_index(3);
let side: Vec<_> = root
.as_path_iter(&leaf.leaf_key())
.map(|(_, side)| side.unwrap())
.collect();
let expected_side = vec![
Node::from_in_order_index(7).value, // Root's dummy side
Node::from_in_order_index(11).value, // Sibling of node 3
Node::from_in_order_index(1).value, // Sibling of node 5
Node::from_leaf_index(2).value, // Sibling of leaf 3
];
assert_eq!(side, expected_side);
}
{
let leaf = Node::from_leaf_index(4);
let side: Vec<_> = root
.as_path_iter(&leaf.leaf_key())
.map(|(_, side)| side.unwrap())
.collect();
let expected_side = vec![
Node::from_in_order_index(7).value, // Root's dummy side
Node::from_in_order_index(3).value, // Sibling of node 11
Node::from_in_order_index(13).value, // Sibling of node 9
Node::from_leaf_index(5).value, // Sibling of leaf 4
];
assert_eq!(side, expected_side);
}
{
let leaf = Node::from_leaf_index(5);
let side: Vec<_> = root
.as_path_iter(&leaf.leaf_key())
.map(|(_, side)| side.unwrap())
.collect();
let expected_side = vec![
Node::from_in_order_index(7).value, // Root's dummy side
Node::from_in_order_index(3).value, // Sibling of node 11
Node::from_in_order_index(13).value, // Sibling of node 9
Node::from_leaf_index(4).value, // Sibling of leaf 5
];
assert_eq!(side, expected_side);
}
{
let leaf = Node::from_leaf_index(6);
let side: Vec<_> = root
.as_path_iter(&leaf.leaf_key())
.map(|(_, side)| side.unwrap())
.collect();
let expected_side = vec![
Node::from_in_order_index(7).value, // Root's dummy side
Node::from_in_order_index(3).value, // Sibling of node 11
Node::from_in_order_index(9).value, // Sibling of node 13
Node::from_leaf_index(7).value, // Sibling of leaf 6
];
assert_eq!(side, expected_side);
}
{
let leaf = Node::from_leaf_index(7);
let side: Vec<_> = root
.as_path_iter(&leaf.leaf_key())
.map(|(_, side)| side.unwrap())
.collect();
let expected_side = vec![
Node::from_in_order_index(7).value, // Root's dummy side
Node::from_in_order_index(3).value, // Sibling of node 11
Node::from_in_order_index(9).value, // Sibling of node 13
Node::from_leaf_index(6).value, // Sibling of leaf 7
];
assert_eq!(side, expected_side);
}
}
#[test]
fn test_path_iter_height_4() {
type Node = TestNode;
let root = Node::from_in_order_index(15); // 2^4 - 1
let leaf = Node::from_leaf_index(4); // 0b0100
let path: Vec<TestNode> = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, _)| path.unwrap())
.collect();
let expected_path = vec![
Node::from_in_order_index(15),
Node::from_in_order_index(7),
Node::from_in_order_index(11),
Node::from_in_order_index(9),
Node::from_in_order_index(8),
];
assert_eq!(path, expected_path);
}
#[test]
fn test_path_iter_height_8() {
type Node = TestNode;
let root = Node::from_in_order_index(255); // 2^8 - 1
let leaf = Node::from_leaf_index(61); // 0b00111101
let path: Vec<TestNode> = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, _)| path.unwrap())
.collect();
let expected_path = vec![
Node::from_in_order_index(255),
Node::from_in_order_index(127),
Node::from_in_order_index(63),
Node::from_in_order_index(95),
Node::from_in_order_index(111),
Node::from_in_order_index(119),
Node::from_in_order_index(123),
Node::from_in_order_index(121),
Node::from_leaf_index(61),
];
assert_eq!(path, expected_path);
}
#[test]
fn test_path_iter_returns_root_root_when_root_is_leaf() {
type Node = TestNode;
let root = Node::from_in_order_index(0);
let leaf = Node::from_leaf_index(0);
let (path, side): (Vec<TestNode>, Vec<_>) = root
.as_path_iter(&leaf.leaf_key())
.map(|(path, side)| (path.unwrap(), side.unwrap()))
.unzip();
let expected_path = vec![Node::from_in_order_index(0)];
let expected_side = vec![0];
assert_eq!(path, expected_path);
assert_eq!(side, expected_side);
}
}