seg-tree 0.3.0

use crate::nodes::{Node, PersistentNode};

/// Persistent segment tree, it saves every version of itself, it has range queries and point updates.
/// It uses `O(n+q*log(n))` space, where `q` is the amount of updates, and assuming that each node uses `O(1)` space.
pub struct Persistent<T: PersistentNode> {
    nodes: Vec<T>,
    roots: Vec<usize>,
    n: usize,
}

impl<T> Persistent<T>
where
    T: PersistentNode + Clone,
{
    /// Builds persistent segment tree from slice, each element of the slice will correspond to a leaf of the segment tree.
    /// It has time complexity of `O(n*log(n))`, assuming that [combine](Node::combine) has constant time complexity.
    pub fn build(values: &[T]) -> Self {
        let n = values.len();
        let mut temp = Self {
            nodes: Vec::with_capacity(4 * n),
            roots: Vec::with_capacity(1),
            n,
        };
        if n == 0 {
            return temp;
        }
        let root = temp.build_helper(values, 0, n - 1);
        temp.roots.push(root);
        temp
    }

    fn build_helper(&mut self, values: &[T], i: usize, j: usize) -> usize {
        let mid = (i + j) / 2;
        if i == j {
            let curr_node = self.nodes.len();
            self.nodes.push(values[i].clone());
            return curr_node;
        }
        let left_node = self.build_helper(values, i, mid);
        let right_node = self.build_helper(values, mid + 1, j);
        let curr_node = self.nodes.len();
        self.nodes
            .push(Node::combine(&self.nodes[left_node], &self.nodes[right_node]));
        self.nodes[curr_node].set_children(left_node, right_node);
        curr_node
    }

    /// Returns the result from the range `[left,right]` from the version of the segment tree.
    /// It returns None if and only if range is empty.
    /// It will **panic** if left or right are not in [0,n), or if version is not in [0,[versions](PersistentSegmentTree::versions)).
    /// It has time complexity of `O(log(n))`, assuming that [combine](Node::combine) has constant time complexity.
    #[allow(clippy::must_use_candidate)]
    pub fn query(&self, version: usize, left: usize, right: usize) -> Option<T> {
        self.query_helper(self.roots[version], left, right, 0, self.n - 1)
    }

    fn query_helper(
        &self,
        curr_node: usize,
        left: usize,
        right: usize,
        i: usize,
        j: usize,
    ) -> Option<T> {
        if j < left || right < i {
            return None;
        }
        if left <= i && j <= right {
            return Some(self.nodes[curr_node].clone());
        }
        let mid = (i + j) / 2;
        let left_node = self.nodes[curr_node].left_child();
        let right_node = self.nodes[curr_node].right_child();
        match (
            self.query_helper(left_node, left, right, i, mid),
            self.query_helper(right_node, left, right, mid + 1, j),
        ) {
            (Some(ans_left), Some(ans_right)) => Some(Node::combine(&ans_left, &ans_right)),
            (Some(ans_left), None) => Some(ans_left),
            (None, Some(ans_right)) => Some(ans_right),
            (None, None) => None,
        }
    }

    /// 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.
    /// It will panic if p is not in `[0,n)`, or if version is not in [0,[versions](PersistentSegmentTree::versions)).
    /// It has time complexity of `O(log(n))`, assuming that [combine](Node::combine) has constant time complexity.
    pub fn update(&mut self, version: usize, p: usize, value: &<T as Node>::Value) {
        let new_root = self.update_helper(self.roots[version], p, value, 0, self.n - 1);
        self.roots.push(new_root);
    }

    fn update_helper(
        &mut self,
        curr_node: usize,
        p: usize,
        value: &<T as Node>::Value,
        i: usize,
        j: usize,
    ) -> usize {
        if j < p || p < i {
            return curr_node;
        }
        let x = self.nodes.len();
        self.nodes.push(self.nodes[curr_node].clone());
        if i == j {
            self.nodes[x] = Node::initialize(value);
            return x;
        }
        let mid = (i + j) / 2;
        let left_node = self.update_helper(self.nodes[x].left_child(), p, value, i, mid);
        let right_node = self.update_helper(self.nodes[x].right_child(), p, value, mid + 1, j);
        self.nodes[x] = Node::combine(&self.nodes[left_node], &self.nodes[right_node]);
        self.nodes[x].set_children(left_node, right_node);
        x
    }
    /// Return the amount of different versions the current segment tree has.
    #[allow(clippy::must_use_candidate)]
    pub fn versions(&self) -> usize {
        self.roots.len()
    }

    /// A method that finds the smallest prefix[^note] `u` such that `predicate(u.value(), value)` is `true`. The following must be true:
    /// - `predicate` is monotonic over prefixes[^note2].
    /// - `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))`.
    ///
    /// These are two examples, the first is finding the smallest prefix which sums at least some value.
    /// ```
    /// # use seg_tree::{Persistent,utils::{Sum, PersistentWrapper},nodes::Node};
    /// # type PSum<T> = PersistentWrapper<Sum<T>>;
    /// let predicate = |left_value:&usize, value:&usize|{*left_value>=*value}; // Is the sum greater or equal to value?
    /// let g = |left_node:&usize,value:usize|{value-*left_node}; // Subtract the sum of the prefix.
    /// # let nodes: Vec<PSum<usize>> = (0..10).map(|x| PSum::initialize(&x)).collect();
    /// let seg_tree = Persistent::build(&nodes); // [0,1,2,3,4,5,6,7,8,9] with Sum<usize> nodes
    /// let index = seg_tree.lower_bound(0, predicate, g, 3); // Will return 2 as sum([0,1,2])>=3
    /// # let sums = vec![0,1,3,6,10,15,21,28,36,45];
    /// # for i in 0..10{
    /// #    assert_eq!(seg_tree.lower_bound(0, predicate, g, sums[i]), i);
    /// # }
    /// ```
    /// The second is finding the position of the smallest value greater or equal to some value.
    /// ```
    /// # use seg_tree::{Persistent,utils::{Max, PersistentWrapper},nodes::Node};
    /// # type PMax<T> = PersistentWrapper<Max<T>>;
    /// let predicate = |left_value:&usize, value:&usize|{*left_value>=*value}; // Is the maximum greater or equal to value?
    /// let g = |_left_node:&usize,value:usize|{value}; // Do nothing
    /// # let nodes: Vec<PMax<usize>> = (0..10).map(|x| PMax::initialize(&x)).collect();
    /// let seg_tree = Persistent::build(&nodes); // [0,1,2,3,4,5,6,7,8,9] with Max<usize> nodes
    /// let index = seg_tree.lower_bound(0, predicate, g, 3); // Will return 3 as 3>=3
    /// # for i in 0..10{
    /// #    assert_eq!(seg_tree.lower_bound(0, predicate, g, i), i);
    /// # }
    /// ```
    ///
    /// [^note]: A prefix is a segment of the form `[0,i]`.
    ///
    /// [^note2]: Given two prefixes `u` and `v` if `u` is contained in `v` then `predicate(u.value(), value)` implies `predicate(v.value(), value)`.
    pub fn lower_bound<F, G>(
        &self,
        version: usize,
        predicate: F,
        g: G,
        value: <T as Node>::Value,
    ) -> usize
    where
        F: Fn(&<T as Node>::Value, &<T as Node>::Value) -> bool,
        G: Fn(&<T as Node>::Value, <T as Node>::Value) -> <T as Node>::Value,
    {
        self.lower_bound_helper(self.roots[version], 0, self.n - 1, predicate, g, value)
    }
    fn lower_bound_helper<F, G>(
        &self,
        curr_node: usize,
        i: usize,
        j: usize,
        predicate: F,
        g: G,
        value: <T as Node>::Value,
    ) -> usize
    where
        F: Fn(&<T as Node>::Value, &<T as Node>::Value) -> bool,
        G: Fn(&<T as Node>::Value, <T as Node>::Value) -> <T as Node>::Value,
    {
        if i == j {
            return i;
        }
        let mid = (i + j) / 2;
        let left_node = self.nodes[curr_node].left_child();
        let right_node = self.nodes[curr_node].right_child();
        let left_value = self.nodes[left_node].value();
        if predicate(left_value, &value) {
            self.lower_bound_helper(left_node, i, mid, predicate, g, value)
        } else {
            let value = g(left_value, value);
            self.lower_bound_helper(right_node, mid + 1, j, predicate, g, value)
        }
    }
}
#[cfg(test)]
mod tests {
    use crate::{
        nodes::Node,
        segment_tree::Persistent,
        utils::{PersistentWrapper, Sum},
    };
    type PSum<T> = PersistentWrapper<Sum<T>>;
    #[test]
    fn non_empty_query_returns_some() {
        let nodes: Vec<PSum<usize>> = (0..=10).map(|x| PSum::initialize(&x)).collect();
        let segment_tree = Persistent::build(&nodes);
        assert!(segment_tree.query(0, 0, 10).is_some());
    }
    #[test]
    fn empty_query_returns_none() {
        let nodes: Vec<PSum<usize>> = (0..=10).map(|x| PSum::initialize(&x)).collect();
        let segment_tree = Persistent::build(&nodes);
        assert!(segment_tree.query(0, 10, 0).is_none());
    }
    #[test]
    fn normal_update_works() {
        let nodes: Vec<PSum<usize>> = (0..=10).map(|x| PSum::initialize(&x)).collect();
        let mut segment_tree = Persistent::build(&nodes);
        let value = 20;
        segment_tree.update(0, 0, &value);
        assert_eq!(segment_tree.query(1, 0, 0).unwrap().value(), &value);
    }

    #[test]
    fn branched_update_works() {
        let nodes: Vec<PSum<usize>> = (0..=10).map(|x| PSum::initialize(&x)).collect();
        let mut segment_tree = Persistent::build(&nodes);
        let value = 20;
        segment_tree.update(0, 0, &value);
        segment_tree.update(0, 1, &value);
        assert_eq!(segment_tree.query(2, 0, 0).unwrap().value(), &0);
        assert_eq!(segment_tree.query(2, 1, 1).unwrap().value(), &value);
    }

    #[test]
    fn query_works() {
        let nodes: Vec<PSum<usize>> = (0..=10).map(|x| PSum::initialize(&x)).collect();
        let segment_tree = Persistent::build(&nodes);
        assert_eq!(segment_tree.query(0, 0, 10).unwrap().value(), &55);
    }
}