/
Treap.rs
192 lines (191 loc) · 6.31 KB
/
Treap.rs
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/// Treap (balanced binary search tree)
/// Reference: https://www.slideshare.net/iwiwi/2-12188757
/// Verified by: ARC061-D (http://arc061.contest.atcoder.jp/submissions/1172709)
/// 2150ms for n = 9*10^5, maybe a bit slow for an O(n * log(n))-time algorithm...
#[derive(Clone, Debug)]
enum Treap<T> {
Bin(
usize, // size
i64, // priority
T, // value
Box<Treap<T>>, // left
Box<Treap<T>>, // right
),
Tip,
}
impl<T: Ord> Treap<T> {
pub fn new() -> Self { Treap::Tip }
pub fn singleton(v: T, pri: i64) -> Self {
use Treap::*;
Bin(1, pri, v, Box::new(Tip), Box::new(Tip))
}
pub fn size(&self) -> usize {
use Treap::*;
match *self {
Tip => 0,
Bin(t, _, _, _, _) => t,
}
}
// Merges two BST. Their ownership is taken.
pub fn merge(left: Self, right: Self) -> Self {
use Treap::*;
match (left, right) {
(Tip, Tip) => Tip,
(Tip, x) => x,
(x, Tip) => x,
(Bin(lsize, lpri, lelem, lleft, lright),
Bin(rsize, rpri, relem, rleft, rright)) => {
if lpri > rpri {
let right = Bin(rsize, rpri, relem, rleft, rright);
let mut ret = Bin(lsize, lpri, lelem, lleft,
Box::new(Self::merge(*lright, right)));
ret.update();
ret
} else {
let left = Bin(lsize, lpri, lelem, lleft, lright);
let mut ret = Bin(rsize, rpri, relem,
Box::new(Self::merge(left, *rleft)),
rright);
ret.update();
ret
}
}
}
}
pub fn split(self, k: usize) -> (Self, Self) {
use Treap::*;
match self {
Tip => (Tip, Tip),
Bin(size, pri, elem, left, right) => {
if k <= left.size() {
let (sl, sr) = Self::split(*left, k);
let mut ret = Bin(size, pri, elem, Box::new(sr), right);
ret.update();
(sl, ret)
} else {
let (sl, sr) = Self::split(*right, k - left.size() - 1);
let mut ret = Bin(size, pri, elem, left, Box::new(sl));
ret.update();
(ret, sr)
}
}
}
}
fn update(&mut self) {
use Treap::*;
match *self {
Tip => (),
Bin(ref mut lsize, ref _pri, ref _elem, ref left, ref right) => {
*lsize = left.size() + right.size() + 1;
},
}
}
fn insert_at(self, v: T, pri: i64, k: usize) -> Self {
use Treap::*;
// Speed up: compare the priority
match self {
Tip => Self::singleton(v, pri),
Bin(size, spri, elem, left, right) => {
let lsize = left.size();
if spri <= pri {
let cself = Bin(size, spri, elem, left, right);
let (left, right) = cself.split(k);
return Bin(size + 1, pri, v,
Box::new(left), Box::new(right));
}
if k < lsize {
return Bin(size + 1, spri, elem,
Box::new((*left).insert_at(v, pri, k)),
right);
}
if k >= lsize + 1 {
return Bin(size + 1, spri, elem,
left,
Box::new((*right)
.insert_at(v, pri, k - lsize - 1)));
}
let cself = Bin(size, spri, elem, left, right);
let sing = Self::singleton(v, pri);
let (left, right) = cself.split(k);
let tmp = Self::merge(left, sing);
Self::merge(tmp, right)
}
}
}
fn erase_at(self, k: usize) -> Self {
use Treap::*;
match self {
Tip => Tip,
Bin(size, pri, elem, left, right) => {
if k < left.size() {
return Bin(size - 1, pri, elem,
Box::new((*left).erase_at(k)), right);
}
if k == left.size() {
return Self::merge(*left, *right); // hit
}
let lsize = left.size();
return Bin(size - 1, pri, elem,
left,
Box::new((*right).erase_at(k - lsize - 1)));
}
}
}
fn find_index(&self, t: &T) -> (usize, bool) {
use Treap::*;
use std::cmp::Ordering;
let mut offset = 0;
let mut tap = self;
loop {
match *tap {
Tip => return (offset, false),
Bin(_, _, ref elem, ref left, ref right) => {
match elem.cmp(t) {
Ordering::Equal => return (offset + left.size(), true),
Ordering::Greater =>
tap = left,
Ordering::Less => {
offset += left.size() + 1;
tap = right;
},
}
}
}
}
}
#[allow(dead_code)]
fn insert(self, v: T, pri: i64) -> Self {
let (idx, found) = self.find_index(&v);
if found {
self
} else {
self.insert_at(v, pri, idx)
}
}
#[allow(dead_code)]
fn erase(self, v: &T) -> Self {
let (idx, found) = self.find_index(v);
if found {
self.erase_at(idx)
} else {
self
}
}
fn into_vec_sub(self, vec: &mut Vec<T>) {
use Treap::*;
match self {
Tip => (),
Bin(_, _, elem, left, right) => {
left.into_vec_sub(vec);
vec.push(elem);
right.into_vec_sub(vec);
}
}
}
#[allow(dead_code)]
pub fn into_vec(self) -> Vec<T> {
let mut ret = Vec::new();
self.into_vec_sub(&mut ret);
ret
}
}