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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 const 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 const 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. /// /// ## 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 { let depth = self::depth(i); if is_even(i) { i / 2 } else { i >> (depth + 1) } } /// Returns the parent of a node with a depth. /// /// ## Examples /// ```rust /// assert_eq!(flat_tree::parent(0), 1); /// assert_eq!(flat_tree::parent(1), 3); /// assert_eq!(flat_tree::parent(2), 1); /// assert_eq!(flat_tree::parent(3), 7); /// assert_eq!(flat_tree::parent(4), 5); /// ``` #[inline] pub fn parent(i: usize) -> usize { let depth = self::depth(i); index(depth + 1, 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 { let depth = self::depth(i); index(depth, offset(i) ^ 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 { let depth = self::depth(i); index(depth + 1, offset(parent(i)) ^ 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)> { let depth = self::depth(i); if is_even(i) { None } else if depth == 0 { Some((i, i)) } else { let offset = offset(i) * 2; Some((index(depth - 1, offset), index(depth - 1, offset + 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> { let depth = self::depth(i); if is_even(i) { None } else if depth == 0 { Some(i) } else { Some(index(depth - 1, offset(i) << 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> { let depth = self::depth(i); if is_even(i) { None } else if depth == 0 { Some(i) } else { Some(index(depth - 1, (offset(i) << 1) + 1)) } } /// 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 { let depth = self::depth(i); if depth == 0 { i } else { (offset(i) + 1) * (2 << depth) - 2 } } /// 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 { let depth = self::depth(i); if depth == 0 { i } else { offset(i) * (2 << 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) { (left_span(i), right_span(i)) } /// 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 const fn count(i: usize) -> usize { let depth = self::depth(i); (2 << depth) - 1 } /// 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) const fn is_even(num: usize) -> bool { (num & 1) == 0 } #[inline] pub(crate) const 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); } }