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arq_tree.rs
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arq_tree.rs
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//! Associative Range Query Tree based on [Al.Cash's compact representation]
//! (http://codeforces.com/blog/entry/18051).
/// Colloquially known as a "segtree" in the sport programming literature, it
/// represents a sequence of elements a_i (0 <= i < size) from a monoid (M, +) on
/// which we want to support fast range operations:
///
/// - modify(l, r, f) replaces a_i (l <= i <= r) by f(a_i) for a homomorphism f
/// - query(l, r) returns the aggregate a_l + a_{l+1} + ... + a_r
///
/// To customize, simply change the commented lines.
/// In this example, we chose to support range sum queries and range constant
/// assignments. Since constant assignment f_c(a) = c is not a homomorphism over
/// integers, we have to augment the monoid type, using the 2D vector (a_i, 1)
/// instead of a_i. You may check that f_c((a, s)) = (c*s, s) is a homomorphism.
pub struct ArqTree {
d: Vec<Option<i64>>,
t: Vec<i64>,
s: Vec<i64>,
}
impl ArqTree {
/// Initializes a sequence of identity elements.
pub fn new(size: usize) -> Self {
let mut s = vec![1; 2 * size];
for i in (0..size).rev() {
s[i] = s[i << 1] + s[i << 1 | 1];
}
Self {
d: vec![None; size],
t: vec![0; 2 * size], // monoid identity
s: s,
}
}
fn apply(&mut self, p: usize, f: i64) {
self.t[p] = f * self.s[p]; // hom application
if p < self.d.len() {
self.d[p] = Some(f); // hom composition
}
}
fn push(&mut self, p: usize) {
for s in (1..32).rev() {
let i = p >> s;
if let Some(f) = self.d[i] {
self.apply(i << 1, f);
self.apply(i << 1 | 1, f);
self.d[i] = None;
}
}
}
fn pull(&mut self, mut p: usize) {
while p > 1 {
p >>= 1;
if self.d[p] == None {
self.t[p] = self.t[p << 1] + self.t[p << 1 | 1]; // monoid op
}
}
}
/// Performs the homomorphism f on all entries from l to r, inclusive.
pub fn modify(&mut self, mut l: usize, mut r: usize, f: i64) {
l += self.d.len();
r += self.d.len();
let (l0, r0) = (l, r);
self.push(l0);
self.push(r0);
while l <= r {
if l & 1 == 1 {
self.apply(l, f);
l += 1;
}
if r & 1 == 0 {
self.apply(r, f);
r -= 1;
}
l >>= 1;
r >>= 1;
}
self.pull(l0);
self.pull(r0);
}
/// Returns the aggregate range query on all entries from l to r, inclusive.
pub fn query(&mut self, mut l: usize, mut r: usize) -> i64 {
l += self.d.len();
r += self.d.len();
self.push(l);
self.push(r);
let mut res = 0; // monoid identity
while l <= r {
if l & 1 == 1 {
res = res + self.t[l]; // monoid op
l += 1;
}
if r & 1 == 0 {
res = self.t[r] + res; // monoid op
r -= 1;
}
l >>= 1;
r >>= 1;
}
res
}
}
#[cfg(test)]
mod test {
use super::*;
#[test]
fn test_arq_tree() {
let mut arq = ArqTree::new(10);
arq.modify(1, 3, 10);
arq.modify(3, 5, 1);
assert_eq!(arq.query(0, 9), 23);
}
}