use std::mem::take; use crate::timestamp::Timestamp; const SPLIT_COUNT: usize = 128; /// Start balancing the tree when there are N times more items on one side. Must be at least 3. const BALANCE_THRESHOLD: usize = 3; pub struct SelfTimeTree { entries: Vec>, children: Option>>, count: usize, } struct SelfTimeEntry { start: Timestamp, end: Timestamp, item: T, } struct SelfTimeChildren { /// Entries < split_point left: SelfTimeTree, split_point: Timestamp, /// Entries >= split_point right: SelfTimeTree, /// Number of entries in the SelfTimeTree::entries list that overlap the split point spanning_entries: usize, } impl Default for SelfTimeTree { fn default() -> Self { Self { entries: Vec::new(), children: None, count: 0, } } } impl SelfTimeTree { pub fn new() -> Self { Self::default() } pub fn len(&self) -> usize { self.count } pub fn insert(&mut self, start: Timestamp, end: Timestamp, item: T) { self.count += 1; self.entries.push(SelfTimeEntry { start, end, item }); self.check_for_split(); } fn check_for_split(&mut self) { if self.entries.len() >= SPLIT_COUNT { let spanning_entries = if let Some(children) = &mut self.children { children.spanning_entries } else { 0 }; if self.entries.len() - spanning_entries >= SPLIT_COUNT { self.split(); } } } fn split(&mut self) { debug_assert!(!self.entries.is_empty()); self.distribute_entries(); self.rebalance(); } fn distribute_entries(&mut self) { if self.children.is_none() { let start = self.entries.iter().min_by_key(|e| e.start).unwrap().start; let end = self.entries.iter().max_by_key(|e| e.end).unwrap().end; let middle = (start + end) / 2; self.children = Some(Box::new(SelfTimeChildren { left: SelfTimeTree::new(), split_point: middle, right: SelfTimeTree::new(), spanning_entries: 0, })); } let Some(children) = &mut self.children else { unreachable!(); }; let mut i = children.spanning_entries; while i < self.entries.len() { let SelfTimeEntry { start, end, .. } = self.entries[i]; if end <= children.split_point { let SelfTimeEntry { start, end, item } = self.entries.swap_remove(i); children.left.insert(start, end, item); } else if start >= children.split_point { let SelfTimeEntry { start, end, item } = self.entries.swap_remove(i); children.right.insert(start, end, item); } else { self.entries.swap(i, children.spanning_entries); children.spanning_entries += 1; i += 1; } } } fn rebalance(&mut self) { if let Some(box SelfTimeChildren { left, split_point, right, spanning_entries, }) = &mut self.children { let SelfTimeTree { count: left_count, children: left_children, entries: left_entries, } = left; let SelfTimeTree { count: right_count, children: right_children, entries: right_entries, } = right; if *left_count > *right_count * BALANCE_THRESHOLD + *spanning_entries { // The left side has overweight // We want to have a new tree that is: // left' = left.left // right' = (left.right, right) with self.split_point // split_point' = left.split_point // direct entries in self and left are put in self and are redistributed if let Some(box SelfTimeChildren { left: left_left, split_point: left_split_point, right: left_right, spanning_entries: _, }) = left_children { *right = Self { count: left_right.count + right.count, entries: Vec::new(), children: Some(Box::new(SelfTimeChildren { left: take(left_right), split_point: *split_point, right: take(right), spanning_entries: 0, })), }; *split_point = *left_split_point; self.entries.append(left_entries); *left = take(left_left); *spanning_entries = 0; self.distribute_entries(); } } else if *right_count > *left_count * BALANCE_THRESHOLD + *spanning_entries { // The right side has overweight // We want to have a new tree that is: // left' = (left, right.left) with self.split_point // right' = right.right // split_point' = right.split_point // direct entries in self and right are put in self and are redistributed if let Some(box SelfTimeChildren { left: right_left, split_point: right_split_point, right: right_right, spanning_entries: _, }) = right_children { *left = Self { count: left.count + right_left.count, entries: Vec::new(), children: Some(Box::new(SelfTimeChildren { left: take(left), split_point: *split_point, right: take(right_left), spanning_entries: 0, })), }; *split_point = *right_split_point; self.entries.append(right_entries); *right = take(right_right); *spanning_entries = 0; self.check_for_split(); } } } } #[cfg(test)] pub fn lookup_range_count(&self, start: Timestamp, end: Timestamp) -> Timestamp { let mut total_count = Timestamp::ZERO; for entry in &self.entries { if entry.start < end && entry.end > start { let start = std::cmp::max(entry.start, start); let end = std::cmp::min(entry.end, end); let span = end - start; total_count += span; } } if let Some(children) = &self.children { if start < children.split_point { total_count += children.left.lookup_range_count(start, end); } if end > children.split_point { total_count += children.right.lookup_range_count(start, end); } } total_count } pub fn lookup_range_corrected_time(&self, start: Timestamp, end: Timestamp) -> Timestamp { let mut factor_times_1000 = 0u64; #[derive(PartialEq, Eq, PartialOrd, Ord)] enum Change { Start, End, } let mut current_count = 0; let mut changes = Vec::new(); self.for_each_in_range(start, end, |s, e, _| { if s <= start { current_count += 1; } else { changes.push((s, Change::Start)); } if e < end { changes.push((e, Change::End)); } }); changes.sort_unstable(); let mut current_ts = start; for (ts, change) in changes { if current_ts < ts { // Move time let time_diff = ts - current_ts; factor_times_1000 += *time_diff * 1000 / current_count; current_ts = ts; } match change { Change::Start => current_count += 1, Change::End => current_count -= 1, } } if current_ts < end { let time_diff = end - current_ts; factor_times_1000 += *time_diff * 1000 / current_count; } Timestamp::from_value(factor_times_1000 / 1000) } pub fn for_each_in_range( &self, start: Timestamp, end: Timestamp, mut f: impl FnMut(Timestamp, Timestamp, &T), ) { self.for_each_in_range_ref(start, end, &mut f); } fn for_each_in_range_ref( &self, start: Timestamp, end: Timestamp, f: &mut impl FnMut(Timestamp, Timestamp, &T), ) { for entry in &self.entries { if entry.start < end && entry.end > start { f(entry.start, entry.end, &entry.item); } } if let Some(children) = &self.children { if start < children.split_point { children.left.for_each_in_range_ref(start, end, f); } if end > children.split_point { children.right.for_each_in_range_ref(start, end, f); } } } } #[cfg(test)] mod tests { use super::*; fn print_tree(tree: &SelfTimeTree, indent: usize) { if let Some(children) = &tree.children { println!( "{}{} items (split at {}, {} overlapping, {} total)", " ".repeat(indent), tree.entries.len(), children.split_point, children.spanning_entries, tree.count ); print_tree(&children.left, indent + 2); print_tree(&children.right, indent + 2); } else { println!( "{}{} items ({} total)", " ".repeat(indent), tree.entries.len(), tree.count ); } } fn assert_balanced(tree: &SelfTimeTree) { if let Some(children) = &tree.children { let l = children.left.count; let r = children.right.count; let s = children.spanning_entries; if (l > SPLIT_COUNT || r > SPLIT_COUNT) && ((l > r * BALANCE_THRESHOLD + s) || (r > l * BALANCE_THRESHOLD + s)) { print_tree(tree, 0); panic!("Tree is not balanced"); } assert_balanced(&children.left); assert_balanced(&children.right); } } #[test] fn test_simple() { let mut tree = SelfTimeTree::new(); let count = 10000; for i in 0..count { tree.insert(Timestamp::from_micros(i), Timestamp::from_micros(i + 1), i); assert_eq!(tree.count, (i + 1) as usize); assert_balanced(&tree); } assert_eq!( tree.lookup_range_count(Timestamp::ZERO, Timestamp::from_micros(count)), Timestamp::from_micros(count) ); print_tree(&tree, 0); assert_balanced(&tree); } #[test] fn test_evenly() { let mut tree = SelfTimeTree::new(); let count = 10000; for a in 0..10 { for b in 0..10 { for c in 0..10 { for d in 0..10 { let i = d * 1000 + c * 100 + b * 10 + a; tree.insert(Timestamp::from_micros(i), Timestamp::from_micros(i + 1), i); assert_balanced(&tree); } } } } assert_eq!( tree.lookup_range_count(Timestamp::ZERO, Timestamp::from_micros(count)), Timestamp::from_micros(count) ); print_tree(&tree, 0); assert_balanced(&tree); } #[test] fn test_overlapping() { let mut tree = SelfTimeTree::new(); let count = 10000; for i in 0..count { tree.insert( Timestamp::from_micros(i), Timestamp::from_micros(i + 100), i, ); assert_eq!(tree.count, (i + 1) as usize); assert_balanced(&tree); } assert_eq!( tree.lookup_range_count(Timestamp::ZERO, Timestamp::from_micros(count + 100)), Timestamp::from_micros(count * 100) ); print_tree(&tree, 0); assert_balanced(&tree); } #[test] fn test_overlapping_heavy() { let mut tree = SelfTimeTree::new(); let count = 10000; for i in 0..count { tree.insert( Timestamp::from_micros(i), Timestamp::from_micros(i + 500), i, ); assert_eq!(tree.count, (i + 1) as usize); } assert_eq!( tree.lookup_range_count(Timestamp::ZERO, Timestamp::from_micros(count + 500)), Timestamp::from_micros(count * 500) ); print_tree(&tree, 0); assert_balanced(&tree); } }