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#![cfg_attr(feature = "nightly", deny(missing_docs))]
#![cfg_attr(feature = "nightly", feature(external_doc))]
#![cfg_attr(feature = "nightly", doc(include = "../README.md"))]
mod iterator;
pub use iterator::Iterator;
/// Returns the flat-tree of the tree node at the specified depth and offset.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::index(0, 0), 0);
/// assert_eq!(flat_tree::index(0, 1), 2);
/// assert_eq!(flat_tree::index(0, 2), 4);
/// assert_eq!(flat_tree::index(1, 2), 9);
/// assert_eq!(flat_tree::index(1, 3), 13);
/// assert_eq!(flat_tree::index(2, 1), 11);
/// assert_eq!(flat_tree::index(2, 2), 19);
/// assert_eq!(flat_tree::index(3, 0), 7);
/// assert_eq!(flat_tree::index(3, 1), 23);
/// ```
#[inline]
pub fn index(depth: usize, offset: usize) -> usize {
(offset << (depth + 1)) | ((1 << depth) - 1)
}
/// Returns the depth of a node.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::depth(0), 0);
/// assert_eq!(flat_tree::depth(1), 1);
/// assert_eq!(flat_tree::depth(2), 0);
/// assert_eq!(flat_tree::depth(3), 2);
/// assert_eq!(flat_tree::depth(4), 0);
/// ```
#[inline]
pub fn depth(i: usize) -> usize {
// Count trailing `1`s of the binary representation of the number.
(!i).trailing_zeros() as usize
}
/// Returns the offset of a node with a depth.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::offset_with_depth(0, 0), 0);
/// assert_eq!(flat_tree::offset_with_depth(1, 1), 0);
/// assert_eq!(flat_tree::offset_with_depth(2, 0), 1);
/// assert_eq!(flat_tree::offset_with_depth(3, 2), 0);
/// assert_eq!(flat_tree::offset_with_depth(4, 0), 2);
/// ```
#[inline]
pub fn offset_with_depth(i: usize, depth: usize) -> usize {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
if is_even(i) {
i / 2
} else {
i >> (depth + 1)
}
}
/// Returns the offset of a node.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::offset(0), 0);
/// assert_eq!(flat_tree::offset(1), 0);
/// assert_eq!(flat_tree::offset(2), 1);
/// assert_eq!(flat_tree::offset(3), 0);
/// assert_eq!(flat_tree::offset(4), 2);
/// ```
#[inline]
pub fn offset(i: usize) -> usize {
offset_with_depth(i, depth(i))
}
/// Returns the parent of a node with a depth.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::parent_with_depth(0, 0), 1);
/// assert_eq!(flat_tree::parent_with_depth(1, 1), 3);
/// assert_eq!(flat_tree::parent_with_depth(2, 0), 1);
/// assert_eq!(flat_tree::parent_with_depth(3, 2), 7);
/// assert_eq!(flat_tree::parent_with_depth(4, 0), 5);
/// ```
#[inline]
pub fn parent_with_depth(i: usize, depth: usize) -> usize {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
index(depth + 1, offset_with_depth(i, depth) >> 1)
}
/// Returns the parent of a node.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::index(1, 0), 1);
/// assert_eq!(flat_tree::index(1, 1), 5);
/// assert_eq!(flat_tree::index(2, 0), 3);
///
/// assert_eq!(flat_tree::parent(0), 1);
/// assert_eq!(flat_tree::parent(2), 1);
/// assert_eq!(flat_tree::parent(1), 3);
/// ```
#[inline]
pub fn parent(i: usize) -> usize {
parent_with_depth(i, depth(i))
}
/// Returns the sibling of a node with a depth.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::sibling_with_depth(0, 0), 2);
/// assert_eq!(flat_tree::sibling_with_depth(1, 1), 5);
/// assert_eq!(flat_tree::sibling_with_depth(2, 0), 0);
/// assert_eq!(flat_tree::sibling_with_depth(3, 2), 11);
/// assert_eq!(flat_tree::sibling_with_depth(4, 0), 6);
/// ```
#[inline]
pub fn sibling_with_depth(i: usize, depth: usize) -> usize {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
index(depth, offset(i) ^ 1)
}
/// Returns the sibling of a node.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::sibling(0), 2);
/// assert_eq!(flat_tree::sibling(2), 0);
/// assert_eq!(flat_tree::sibling(1), 5);
/// assert_eq!(flat_tree::sibling(5), 1);
/// ```
#[inline]
pub fn sibling(i: usize) -> usize {
sibling_with_depth(i, depth(i))
}
/// Returns the parent's sibling, of a node, with a depth.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::uncle_with_depth(0, 0), 5);
/// assert_eq!(flat_tree::uncle_with_depth(1, 1), 11);
/// assert_eq!(flat_tree::uncle_with_depth(2, 0), 5);
/// assert_eq!(flat_tree::uncle_with_depth(5, 1), 11);
/// ```
#[inline]
pub fn uncle_with_depth(i: usize, depth: usize) -> usize {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
sibling_with_depth(parent_with_depth(i, depth), depth + 1)
}
/// Returns the parent's sibling, of a node.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::uncle(0), 5);
/// assert_eq!(flat_tree::uncle(2), 5);
/// assert_eq!(flat_tree::uncle(1), 11);
/// assert_eq!(flat_tree::uncle(5), 11);
/// ```
#[inline]
pub fn uncle(i: usize) -> usize {
uncle_with_depth(i, depth(i))
}
/// Returns both children of a node, with a depth.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::children_with_depth(0, 0), None);
/// assert_eq!(flat_tree::children_with_depth(1, 1), Some((0, 2)));
/// assert_eq!(flat_tree::children_with_depth(3, 2), Some((1, 5)));
/// assert_eq!(flat_tree::children_with_depth(9, 1), Some((8, 10)));
/// ```
#[inline]
pub fn children_with_depth(i: usize, depth: usize) -> Option<(usize, usize)> {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
if is_even(i) {
None
} else if depth == 0 {
Some((i, i))
} else {
let offset = offset_with_depth(i, depth) * 2;
Some((index(depth - 1, offset), index(depth - 1, offset + 1)))
}
}
/// Returns both children of a node.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::children(0), None);
/// assert_eq!(flat_tree::children(1), Some((0, 2)));
/// assert_eq!(flat_tree::children(3), Some((1, 5)));
/// assert_eq!(flat_tree::children(9), Some((8, 10)));
/// ```
#[inline]
pub fn children(i: usize) -> Option<(usize, usize)> {
children_with_depth(i, depth(i))
}
/// Returns only the left child of a node, with a depth
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::left_child_with_depth(0, 0), None);
/// assert_eq!(flat_tree::left_child_with_depth(1, 1), Some(0));
/// assert_eq!(flat_tree::left_child_with_depth(3, 2), Some(1));
/// ```
// TODO: handle errors
#[inline]
pub fn left_child_with_depth(i: usize, depth: usize) -> Option<usize> {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
if is_even(i) {
None
} else if depth == 0 {
Some(i)
} else {
Some(index(depth - 1, offset_with_depth(i, depth) << 1))
}
}
/// Returns only the left child of a node.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::left_child(0), None);
/// assert_eq!(flat_tree::left_child(1), Some(0));
/// assert_eq!(flat_tree::left_child(3), Some(1));
/// ```
#[inline]
pub fn left_child(i: usize) -> Option<usize> {
left_child_with_depth(i, depth(i))
}
/// Returns only the left child of a node, with a depth.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::right_child_with_depth(0, 0), None);
/// assert_eq!(flat_tree::right_child_with_depth(1, 1), Some(2));
/// assert_eq!(flat_tree::right_child_with_depth(3, 2), Some(5));
/// ```
#[inline]
pub fn right_child_with_depth(i: usize, depth: usize) -> Option<usize> {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
if is_even(i) {
None
} else if depth == 0 {
Some(i)
} else {
Some(index(depth - 1, (offset_with_depth(i, depth) << 1) + 1))
}
}
/// Returns only the left child of a node.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::right_child(0), None);
/// assert_eq!(flat_tree::right_child(1), Some(2));
/// assert_eq!(flat_tree::right_child(3), Some(5));
/// ```
// TODO: handle errors
#[inline]
pub fn right_child(i: usize) -> Option<usize> {
right_child_with_depth(i, depth(i))
}
/// Returns the right most node in the tree that the node spans, with a depth.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::right_span_with_depth(0, 0), 0);
/// assert_eq!(flat_tree::right_span_with_depth(1, 1), 2);
/// assert_eq!(flat_tree::right_span_with_depth(3, 2), 6);
/// assert_eq!(flat_tree::right_span_with_depth(23, 3), 30);
/// assert_eq!(flat_tree::right_span_with_depth(27, 2), 30);
/// ```
#[inline]
pub fn right_span_with_depth(i: usize, depth: usize) -> usize {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
if depth == 0 {
i
} else {
(offset_with_depth(i, depth) + 1) * (2 << depth) - 2
}
}
/// Returns the right most node in the tree that the node spans.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::right_span(0), 0);
/// assert_eq!(flat_tree::right_span(1), 2);
/// assert_eq!(flat_tree::right_span(3), 6);
/// assert_eq!(flat_tree::right_span(23), 30);
/// assert_eq!(flat_tree::right_span(27), 30);
/// ```
#[inline]
pub fn right_span(i: usize) -> usize {
right_span_with_depth(i, depth(i))
}
/// Returns the left most node in the tree that the node spans, with a depth.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::left_span_with_depth(0, 0), 0);
/// assert_eq!(flat_tree::left_span_with_depth(1, 1), 0);
/// assert_eq!(flat_tree::left_span_with_depth(3, 2), 0);
/// assert_eq!(flat_tree::left_span_with_depth(23, 3), 16);
/// assert_eq!(flat_tree::left_span_with_depth(27, 2), 24);
/// ```
#[inline]
pub fn left_span_with_depth(i: usize, depth: usize) -> usize {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
if depth == 0 {
i
} else {
offset_with_depth(i, depth) * (2 << depth)
}
}
/// Returns the left most node in the tree that it spans.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::left_span(0), 0);
/// assert_eq!(flat_tree::left_span(1), 0);
/// assert_eq!(flat_tree::left_span(3), 0);
/// assert_eq!(flat_tree::left_span(23), 16);
/// assert_eq!(flat_tree::left_span(27), 24);
/// ```
#[inline]
pub fn left_span(i: usize) -> usize {
left_span_with_depth(i, depth(i))
}
/// Returns the left and right most nodes in the tree that the node spans, with
/// a depth.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::spans_with_depth(0, 0), (0, 0));
/// assert_eq!(flat_tree::spans_with_depth(1, 1), (0, 2));
/// assert_eq!(flat_tree::spans_with_depth(3, 2), (0, 6));
/// assert_eq!(flat_tree::spans_with_depth(23, 3), (16, 30));
/// assert_eq!(flat_tree::spans_with_depth(27, 2), (24, 30));
/// ```
#[inline]
pub fn spans_with_depth(i: usize, depth: usize) -> (usize, usize) {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
(
left_span_with_depth(i, depth),
right_span_with_depth(i, depth),
)
}
/// Returns the left and right most nodes in the tree that the node spans.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::spans(0), (0, 0));
/// assert_eq!(flat_tree::spans(1), (0, 2));
/// assert_eq!(flat_tree::spans(3), (0, 6));
/// assert_eq!(flat_tree::spans(23), (16, 30));
/// assert_eq!(flat_tree::spans(27), (24, 30));
/// ```
#[inline]
pub fn spans(i: usize) -> (usize, usize) {
spans_with_depth(i, depth(i))
}
/// Returns how many nodes are in the tree that the node spans, with a depth.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::count_with_depth(0, 0), 1);
/// assert_eq!(flat_tree::count_with_depth(1, 1), 3);
/// assert_eq!(flat_tree::count_with_depth(3, 2), 7);
/// assert_eq!(flat_tree::count_with_depth(5, 1), 3);
/// assert_eq!(flat_tree::count_with_depth(23, 3), 15);
/// assert_eq!(flat_tree::count_with_depth(27, 2), 7);
/// ```
#[inline]
pub fn count_with_depth(i: usize, depth: usize) -> usize {
debug_assert_eq!(depth, self::depth(i), "Invalid depth.");
(2 << depth) - 1
}
/// Returns how many nodes are in the tree that the node spans.
///
/// ## Examples
/// ```rust
/// assert_eq!(flat_tree::count(0), 1);
/// assert_eq!(flat_tree::count(1), 3);
/// assert_eq!(flat_tree::count(3), 7);
/// assert_eq!(flat_tree::count(5), 3);
/// assert_eq!(flat_tree::count(23), 15);
/// assert_eq!(flat_tree::count(27), 7);
/// ```
#[inline]
pub fn count(i: usize) -> usize {
count_with_depth(i, depth(i))
}
/// Returns a list of all the full roots (subtrees where all nodes have either 2 or 0 children) `<` index.
/// For example `fullRoots(8)` returns `[3]` since the subtree rooted at `3` spans `0 -> 6`,
/// and the tree rooted at `7` has a child located at `9` which is `>= 8`.
///
/// ## Panics
/// If an uneven index is passed.
///
/// ## Examples
/// ```rust
/// use flat_tree::full_roots;
///
/// let mut nodes = Vec::with_capacity(16);
/// full_roots(0, &mut nodes);
/// assert_eq!(nodes, []);
///
/// let mut nodes = Vec::with_capacity(16);
/// full_roots(2, &mut nodes);
/// assert_eq!(nodes, [0]);
///
/// let mut nodes = Vec::with_capacity(16);
/// full_roots(8, &mut nodes);
/// assert_eq!(nodes, [3]);
///
/// let mut nodes = Vec::with_capacity(16);
/// full_roots(20, &mut nodes);
/// assert_eq!(nodes, [7, 17]);
///
/// let mut nodes = Vec::with_capacity(16);
/// full_roots(18, &mut nodes);
/// assert_eq!(nodes, [7, 16]);
///
/// let mut nodes = Vec::with_capacity(16);
/// full_roots(16, &mut nodes);
/// assert_eq!(nodes, [7]);
/// ```
#[inline]
pub fn full_roots(i: usize, nodes: &mut Vec<usize>) {
assert!(
is_even(i),
format!(
"You can only look up roots for depth 0 blocks, got index {}",
i
)
);
let mut tmp = i >> 1;
let mut offset = 0;
let mut factor = 1;
loop {
if tmp == 0 {
break;
}
while factor * 2 <= tmp {
factor *= 2;
}
nodes.push(offset + factor - 1);
offset += 2 * factor;
tmp -= factor;
factor = 1;
}
}
#[inline]
pub(crate) fn is_even(num: usize) -> bool {
(num & 1) == 0
}
#[inline]
pub(crate) fn is_odd(num: usize) -> bool {
(num & 1) != 0
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_is_even() {
assert_eq!(is_even(0), true);
assert_eq!(is_even(1), false);
assert_eq!(is_even(2), true);
assert_eq!(is_even(3), false);
}
#[test]
fn test_is_odd() {
assert_eq!(is_odd(0), false);
assert_eq!(is_odd(1), true);
assert_eq!(is_odd(2), false);
assert_eq!(is_odd(3), true);
}
#[test]
fn test_parent_gt_int32() {
assert_eq!(parent(10_000_000_000), 10_000_000_001);
}
#[test]
fn test_child_to_parent_to_child() {
let mut child = 0;
for _ in 0..50 {
child = parent(child)
}
assert_eq!(child, 1_125_899_906_842_623);
for _ in 0..50 {
child = left_child(child).expect("no valid number returned");
}
assert_eq!(child, 0);
}
}