seg_tree/segment_tree/
persistent.rs

1use crate::nodes::{Node, PersistentNode};
2
3/// Persistent segment tree, it saves every version of itself, it has range queries and point updates.
4/// It uses `O(n+q*log(n))` space, where `q` is the amount of updates, and assuming that each node uses `O(1)` space.
5pub struct Persistent<T: PersistentNode> {
6    nodes: Vec<T>,
7    roots: Vec<usize>,
8    n: usize,
9}
10
11impl<T> Persistent<T>
12where
13    T: PersistentNode + Clone,
14{
15    /// Builds persistent segment tree from slice, each element of the slice will correspond to a leaf of the segment tree.
16    /// It has time complexity of `O(n*log(n))`, assuming that [combine](Node::combine) has constant time complexity.
17    pub fn build(values: &[T]) -> Self {
18        let n = values.len();
19        let mut temp = Self {
20            nodes: Vec::with_capacity(4 * n),
21            roots: Vec::with_capacity(1),
22            n,
23        };
24        if n == 0 {
25            return temp;
26        }
27        let root = temp.build_helper(values, 0, n - 1);
28        temp.roots.push(root);
29        temp
30    }
31
32    fn build_helper(&mut self, values: &[T], i: usize, j: usize) -> usize {
33        let mid = (i + j) / 2;
34        if i == j {
35            let curr_node = self.nodes.len();
36            self.nodes.push(values[i].clone());
37            return curr_node;
38        }
39        let left_node = self.build_helper(values, i, mid);
40        let right_node = self.build_helper(values, mid + 1, j);
41        let curr_node = self.nodes.len();
42        self.nodes
43            .push(Node::combine(&self.nodes[left_node], &self.nodes[right_node]));
44        self.nodes[curr_node].set_children(left_node, right_node);
45        curr_node
46    }
47
48    /// Returns the result from the range `[left,right]` from the version of the segment tree.
49    /// It returns None if and only if range is empty.
50    /// It will **panic** if left or right are not in [0,n), or if version is not in [0,[versions](PersistentSegmentTree::versions)).
51    /// It has time complexity of `O(log(n))`, assuming that [combine](Node::combine) has constant time complexity.
52    #[allow(clippy::must_use_candidate)]
53    pub fn query(&self, version: usize, left: usize, right: usize) -> Option<T> {
54        self.query_helper(self.roots[version], left, right, 0, self.n - 1)
55    }
56
57    fn query_helper(
58        &self,
59        curr_node: usize,
60        left: usize,
61        right: usize,
62        i: usize,
63        j: usize,
64    ) -> Option<T> {
65        if j < left || right < i {
66            return None;
67        }
68        if left <= i && j <= right {
69            return Some(self.nodes[curr_node].clone());
70        }
71        let mid = (i + j) / 2;
72        let left_node = self.nodes[curr_node].left_child();
73        let right_node = self.nodes[curr_node].right_child();
74        match (
75            self.query_helper(left_node, left, right, i, mid),
76            self.query_helper(right_node, left, right, mid + 1, j),
77        ) {
78            (Some(ans_left), Some(ans_right)) => Some(Node::combine(&ans_left, &ans_right)),
79            (Some(ans_left), None) => Some(ans_left),
80            (None, Some(ans_right)) => Some(ans_right),
81            (None, None) => None,
82        }
83    }
84
85    /// Creates a new segment tree version from version were the p-th element of the segment tree to value T and update the segment tree correspondingly.
86    /// It will panic if p is not in `[0,n)`, or if version is not in [0,[versions](PersistentSegmentTree::versions)).
87    /// It has time complexity of `O(log(n))`, assuming that [combine](Node::combine) has constant time complexity.
88    pub fn update(&mut self, version: usize, p: usize, value: &<T as Node>::Value) {
89        let new_root = self.update_helper(self.roots[version], p, value, 0, self.n - 1);
90        self.roots.push(new_root);
91    }
92
93    fn update_helper(
94        &mut self,
95        curr_node: usize,
96        p: usize,
97        value: &<T as Node>::Value,
98        i: usize,
99        j: usize,
100    ) -> usize {
101        if j < p || p < i {
102            return curr_node;
103        }
104        let x = self.nodes.len();
105        self.nodes.push(self.nodes[curr_node].clone());
106        if i == j {
107            self.nodes[x] = Node::initialize(value);
108            return x;
109        }
110        let mid = (i + j) / 2;
111        let left_node = self.update_helper(self.nodes[x].left_child(), p, value, i, mid);
112        let right_node = self.update_helper(self.nodes[x].right_child(), p, value, mid + 1, j);
113        self.nodes[x] = Node::combine(&self.nodes[left_node], &self.nodes[right_node]);
114        self.nodes[x].set_children(left_node, right_node);
115        x
116    }
117    /// Return the amount of different versions the current segment tree has.
118    #[allow(clippy::must_use_candidate)]
119    pub fn versions(&self) -> usize {
120        self.roots.len()
121    }
122
123    /// A method that finds the smallest prefix[^note] `u` such that `predicate(u.value(), value)` is `true`. The following must be true:
124    /// - `predicate` is monotonic over prefixes[^note2].
125    /// - `g` will satisfy the following, given segments `[i,j]` and `[i,k]` with `j<k` we have that `predicate([i,k].value(),value)` implies `predicate([j+1,k].value(),g([i,j].value(),value))`.
126    ///
127    /// These are two examples, the first is finding the smallest prefix which sums at least some value.
128    /// ```
129    /// # use seg_tree::{Persistent,utils::{Sum, PersistentWrapper},nodes::Node};
130    /// # type PSum<T> = PersistentWrapper<Sum<T>>;
131    /// let predicate = |left_value:&usize, value:&usize|{*left_value>=*value}; // Is the sum greater or equal to value?
132    /// let g = |left_node:&usize,value:usize|{value-*left_node}; // Subtract the sum of the prefix.
133    /// # let nodes: Vec<PSum<usize>> = (0..10).map(|x| PSum::initialize(&x)).collect();
134    /// let seg_tree = Persistent::build(&nodes); // [0,1,2,3,4,5,6,7,8,9] with Sum<usize> nodes
135    /// let index = seg_tree.lower_bound(0, predicate, g, 3); // Will return 2 as sum([0,1,2])>=3
136    /// # let sums = vec![0,1,3,6,10,15,21,28,36,45];
137    /// # for i in 0..10{
138    /// #    assert_eq!(seg_tree.lower_bound(0, predicate, g, sums[i]), i);
139    /// # }
140    /// ```
141    /// The second is finding the position of the smallest value greater or equal to some value.
142    /// ```
143    /// # use seg_tree::{Persistent,utils::{Max, PersistentWrapper},nodes::Node};
144    /// # type PMax<T> = PersistentWrapper<Max<T>>;
145    /// let predicate = |left_value:&usize, value:&usize|{*left_value>=*value}; // Is the maximum greater or equal to value?
146    /// let g = |_left_node:&usize,value:usize|{value}; // Do nothing
147    /// # let nodes: Vec<PMax<usize>> = (0..10).map(|x| PMax::initialize(&x)).collect();
148    /// let seg_tree = Persistent::build(&nodes); // [0,1,2,3,4,5,6,7,8,9] with Max<usize> nodes
149    /// let index = seg_tree.lower_bound(0, predicate, g, 3); // Will return 3 as 3>=3
150    /// # for i in 0..10{
151    /// #    assert_eq!(seg_tree.lower_bound(0, predicate, g, i), i);
152    /// # }
153    /// ```
154    ///
155    /// [^note]: A prefix is a segment of the form `[0,i]`.
156    ///
157    /// [^note2]: Given two prefixes `u` and `v` if `u` is contained in `v` then `predicate(u.value(), value)` implies `predicate(v.value(), value)`.
158    pub fn lower_bound<F, G>(
159        &self,
160        version: usize,
161        predicate: F,
162        g: G,
163        value: <T as Node>::Value,
164    ) -> usize
165    where
166        F: Fn(&<T as Node>::Value, &<T as Node>::Value) -> bool,
167        G: Fn(&<T as Node>::Value, <T as Node>::Value) -> <T as Node>::Value,
168    {
169        self.lower_bound_helper(self.roots[version], 0, self.n - 1, predicate, g, value)
170    }
171    fn lower_bound_helper<F, G>(
172        &self,
173        curr_node: usize,
174        i: usize,
175        j: usize,
176        predicate: F,
177        g: G,
178        value: <T as Node>::Value,
179    ) -> usize
180    where
181        F: Fn(&<T as Node>::Value, &<T as Node>::Value) -> bool,
182        G: Fn(&<T as Node>::Value, <T as Node>::Value) -> <T as Node>::Value,
183    {
184        if i == j {
185            return i;
186        }
187        let mid = (i + j) / 2;
188        let left_node = self.nodes[curr_node].left_child();
189        let right_node = self.nodes[curr_node].right_child();
190        let left_value = self.nodes[left_node].value();
191        if predicate(left_value, &value) {
192            self.lower_bound_helper(left_node, i, mid, predicate, g, value)
193        } else {
194            let value = g(left_value, value);
195            self.lower_bound_helper(right_node, mid + 1, j, predicate, g, value)
196        }
197    }
198}
199#[cfg(test)]
200mod tests {
201    use crate::{
202        nodes::Node,
203        segment_tree::Persistent,
204        utils::{PersistentWrapper, Sum},
205    };
206    type PSum<T> = PersistentWrapper<Sum<T>>;
207    #[test]
208    fn non_empty_query_returns_some() {
209        let nodes: Vec<PSum<usize>> = (0..=10).map(|x| PSum::initialize(&x)).collect();
210        let segment_tree = Persistent::build(&nodes);
211        assert!(segment_tree.query(0, 0, 10).is_some());
212    }
213    #[test]
214    fn empty_query_returns_none() {
215        let nodes: Vec<PSum<usize>> = (0..=10).map(|x| PSum::initialize(&x)).collect();
216        let segment_tree = Persistent::build(&nodes);
217        assert!(segment_tree.query(0, 10, 0).is_none());
218    }
219    #[test]
220    fn normal_update_works() {
221        let nodes: Vec<PSum<usize>> = (0..=10).map(|x| PSum::initialize(&x)).collect();
222        let mut segment_tree = Persistent::build(&nodes);
223        let value = 20;
224        segment_tree.update(0, 0, &value);
225        assert_eq!(segment_tree.query(1, 0, 0).unwrap().value(), &value);
226    }
227
228    #[test]
229    fn branched_update_works() {
230        let nodes: Vec<PSum<usize>> = (0..=10).map(|x| PSum::initialize(&x)).collect();
231        let mut segment_tree = Persistent::build(&nodes);
232        let value = 20;
233        segment_tree.update(0, 0, &value);
234        segment_tree.update(0, 1, &value);
235        assert_eq!(segment_tree.query(2, 0, 0).unwrap().value(), &0);
236        assert_eq!(segment_tree.query(2, 1, 1).unwrap().value(), &value);
237    }
238
239    #[test]
240    fn query_works() {
241        let nodes: Vec<PSum<usize>> = (0..=10).map(|x| PSum::initialize(&x)).collect();
242        let segment_tree = Persistent::build(&nodes);
243        assert_eq!(segment_tree.query(0, 0, 10).unwrap().value(), &55);
244    }
245}
seg_tree/segment_tree/persistent.rs

seg_tree/segment_tree/
persistent.rs
