結果
| 問題 | No.1641 Tree Xor Query |
| ユーザー |
 nebocco
|
| 提出日時 | 2021-08-27 17:42:09 |
| 言語 | Rust (1.77.0) |
| 結果 |
AC
|
| 実行時間 | 45 ms / 5,000 ms |
| コード長 | 19,117 bytes |
| コンパイル時間 | 13,483 ms |
| コンパイル使用メモリ | 402,008 KB |
| 実行使用メモリ | 17,940 KB |
| 最終ジャッジ日時 | 2024-04-30 21:13:31 |
| 合計ジャッジ時間 | 14,881 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 1 ms
6,816 KB |
| testcase_01 | AC | 1 ms
6,812 KB |
| testcase_02 | AC | 1 ms
6,940 KB |
| testcase_03 | AC | 1 ms
6,940 KB |
| testcase_04 | AC | 1 ms
6,944 KB |
| testcase_05 | AC | 1 ms
6,940 KB |
| testcase_06 | AC | 1 ms
6,940 KB |
| testcase_07 | AC | 1 ms
6,944 KB |
| testcase_08 | AC | 1 ms
6,940 KB |
| testcase_09 | AC | 1 ms
6,944 KB |
| testcase_10 | AC | 1 ms
6,944 KB |
| testcase_11 | AC | 1 ms
6,940 KB |
| testcase_12 | AC | 1 ms
6,940 KB |
| testcase_13 | AC | 45 ms
17,512 KB |
| testcase_14 | AC | 44 ms
17,636 KB |
| testcase_15 | AC | 2 ms
6,944 KB |
| testcase_16 | AC | 4 ms
6,940 KB |
| testcase_17 | AC | 3 ms
6,940 KB |
| testcase_18 | AC | 3 ms
6,944 KB |
| testcase_19 | AC | 2 ms
6,940 KB |
| testcase_20 | AC | 37 ms
17,940 KB |
ソースコード
fn main() {
let mut io = IO::new();
input!{ from io,
n: usize, q: usize,
cl: [i32; n],
ed: [(Usize1, Usize1); n-1],
query: [(i32, Usize1, i32); q]
}
let mut hld = HeavyLightDecomposition::new(n);
for (u, v) in ed {
hld.add_edge(u, v);
}
hld.build(0);
let mut bit = FenwickTree::new(n);
for i in 0..n {
bit.add(hld.id(i), Xor(cl[i]));
}
// io.iterln((0..n).map(|i| hld.id(i)), ", ");
for &(t, x, y) in &query {
if t == 1 {
bit.add(hld.id(x), Xor(y));
// io.iterln((0..n).map(|i| bit.sum(i..=i).0), ", ");
} else {
let rng = hld.subtree_range(x);
// io.println((x, rng.start, rng.end));
let v = bit.sum(rng);
io.println(v.0)
}
}
}
#[derive(Clone, PartialEq)]
struct Xor(i32);
impl Add for Xor {
type Output = Self;
fn add(self, right: Self) -> Self {
Xor(self.0 ^ right.0)
}
}
impl Neg for Xor {
type Output = Self;
fn neg(self) -> Self { self }
}
impl Associative for Xor {}
impl Zero for Xor {
fn zero() -> Self {
Xor(0)
}
fn is_zero(&self) -> bool {
self.0 == 0
}
}
pub struct HeavyLightDecomposition {
graph: Vec<Vec<usize>>,
index: Vec<usize>, // 新しい頂点番号
parent: Vec<usize>, // 親
head: Vec<usize>, // 属するHeavy Pathの根
range: Vec<usize>, // 部分木の開区間右端
}
impl HeavyLightDecomposition {
pub fn new(n: usize) -> Self {
Self {
graph: vec![Vec::new(); n],
index: Vec::new(),
parent: Vec::new(),
head: Vec::new(),
range: Vec::new(),
}
}
pub fn add_edge(&mut self, u: usize, v: usize) {
self.graph[u].push(v);
self.graph[v].push(u);
}
pub fn build(&mut self, root: usize) {
let graph = &mut self.graph;
let n = graph.len();
let mut index = vec![0; n];
let mut parent = vec![n; n];
let mut head = vec![root; n];
let mut range = vec![0; n];
let mut siz = vec![1; n];
let mut st = Vec::new();
st.push(root);
while let Some(v) = st.pop() {
if v < n {
st.push(!v);
if let Some(k) = graph[v].iter().position(|&u| u == parent[v]) {
graph[v].swap_remove(k);
}
graph[v].iter().for_each(|&u| {
parent[u] = v;
st.push(u);
});
} else {
let v = !v;
for i in 0..graph[v].len() {
let u = graph[v][i];
siz[v] += siz[u];
if siz[graph[v][0]] < siz[u] {
graph[v].swap(0, i);
}
}
}
}
st.push(root);
let mut c = 0;
while let Some(v) = st.pop() {
if v < n {
st.push(!v);
index[v] = c;
c += 1;
for &u in graph[v].iter().skip(1) {
head[u] = u;
st.push(u);
}
if let Some(&u) = graph[v].get(0) {
head[u] = head[v];
st.push(u);
}
} else {
range[!v] = c;
}
}
self.index = index;
self.parent = parent;
self.head = head;
self.range = range;
}
pub fn lca(&self, mut u: usize, mut v: usize) -> usize {
let parent = &self.parent;
let head = &self.head;
let index = &self.index;
while head[u] != head[v] {
if index[u] < index[v] {
v = parent[head[v]];
} else {
u = parent[head[u]];
}
}
if index[u] < index[v] {
u
} else {
v
}
}
fn for_each(
&self,
mut u: usize,
mut v: usize,
b: usize,
) -> (Vec<Range<usize>>, Vec<Range<usize>>) {
let parent = &self.parent;
let head = &self.head;
let index = &self.index;
let mut up = Vec::new();
let mut down = Vec::new();
while head[u] != head[v] {
if index[u] < index[v] {
let h = head[v];
down.push(index[h]..index[v] + 1);
v = parent[h];
} else {
let h = head[u];
up.push(index[h]..index[u] + 1);
u = parent[h];
}
}
if index[u] < index[v] {
down.push(index[u] + b..index[v] + 1);
} else if index[v] + b < index[u] + 1 {
up.push(index[v] + b..index[u] + 1);
}
down.reverse();
(up, down)
}
pub fn id(&self, v: usize) -> usize {
self.index[v]
}
pub fn for_each_vertex(&self, u: usize, v: usize) -> (Vec<Range<usize>>, Vec<Range<usize>>) {
self.for_each(u, v, 0)
}
pub fn for_each_edge(&self, u: usize, v: usize) -> (Vec<Range<usize>>, Vec<Range<usize>>) {
self.for_each(u, v, 1)
}
pub fn subtree_range(&self, v: usize) -> Range<usize> {
self.index[v]..self.range[v]
}
}
// ------------ FenwickTree with generics start ------------
#[derive(Clone, Debug)]
pub struct FenwickTree<T>(Vec<T>);
impl<T: Monoid> FenwickTree<T> {
#[inline]
fn lsb(x: usize) -> usize {
x & x.wrapping_neg()
}
pub fn new(n: usize) -> Self {
Self(vec![T::zero(); n + 1])
}
pub fn prefix_sum(&self, i: usize) -> T {
std::iter::successors(Some(i), |&i| Some(i - Self::lsb(i)))
.take_while(|&i| i != 0)
.map(|i| self.0[i].clone())
.fold(T::zero(), |sum, x| sum + x)
}
pub fn add(&mut self, i: usize, x: T) {
let n = self.0.len();
std::iter::successors(Some(i + 1), |&i| Some(i + Self::lsb(i)))
.take_while(|&i| i < n)
.for_each(|i| self.0[i] = self.0[i].clone() + x.clone());
}
/// pred(j, sum(..j)) && !pred(j+1, sum(..j+1))
pub fn partition(&self, pred: impl Fn(usize, &T) -> bool) -> (usize, T) {
assert!(pred(0, &self.0[0]), "need to be pred(0, 0)");
let mut j = 0;
let mut current = self.0[0].clone();
let n = self.0.len();
for d in std::iter::successors(Some(n.next_power_of_two() >> 1), |&d| Some(d >> 1))
.take_while(|&d| d != 0)
{
if j + d < n {
let next = current.clone() + self.0[j + d].clone();
if pred(j + d, &next) {
current = next;
j += d;
}
}
}
(j, current)
}
}
impl<T: Monoid> From<Vec<T>> for FenwickTree<T> {
fn from(src: Vec<T>) -> Self {
let mut table = std::iter::once(T::zero())
.chain(src.into_iter())
.collect::<Vec<T>>();
let n = table.len();
(1..n)
.map(|i| (i, i + Self::lsb(i)))
.filter(|&(_, j)| j < n)
.for_each(|(i, j)| {
table[j] = table[j].clone() + table[i].clone();
});
Self(table)
}
}
impl<T: Group> FenwickTree<T> {
pub fn sum<R: RangeBounds<usize>>(&self, rng: R) -> T {
let Range { start, end } = bounds_within(rng, self.0.len() - 1);
self.prefix_sum(end) + -self.prefix_sum(start)
}
}
// ------------ FenwickTree with generics end ------------
use std::ops::Bound::{Excluded, Included, Unbounded};
use std::ops::{Range, RangeBounds};
pub fn bounds_within<R: RangeBounds<usize>>(r: R, len: usize) -> Range<usize> {
let e_ex = match r.end_bound() {
Included(&e) => e + 1,
Excluded(&e) => e,
Unbounded => len,
}
.min(len);
let s_in = match r.start_bound() {
Included(&s) => s,
Excluded(&s) => s + 1,
Unbounded => 0,
}
.min(e_ex);
s_in..e_ex
}
// ------------ Graph impl start ------------
pub trait Cost:
Element
+ Clone
+ Copy
+ std::fmt::Display
+ Eq
+ Ord
+ Zero
+ One
+ Add<Output = Self>
+ AddAssign
+ Sub<Output = Self>
+ Neg<Output = Self>
{
const MAX: Self;
}
#[derive(Copy, Clone)]
pub struct Edge<C = Void> {
// pub from: usize,
pub to: usize,
pub cost: C,
pub id: usize,
}
pub struct UndirectedGraph<C>(pub Vec<Vec<Edge<C>>>, pub usize);
pub struct DirectedGraph<C> {
pub forward: Vec<Vec<Edge<C>>>,
pub backward: Vec<Vec<Edge<C>>>,
pub count: usize,
}
pub trait Graph<C: Element> {
fn new(size: usize) -> Self;
fn size(&self) -> usize;
fn add_edge(&mut self, u: usize, v: usize, cost: C);
fn edges_from(&self, v: usize) -> std::slice::Iter<Edge<C>>;
}
impl<C: Element> Graph<C> for UndirectedGraph<C> {
fn new(size: usize) -> Self {
Self(vec![Vec::<Edge<C>>::new(); size], 0)
}
fn size(&self) -> usize {
self.0.len()
}
fn add_edge(&mut self, u: usize, v: usize, cost: C) {
self.0[u].push(Edge {
to: v,
cost: cost.clone(),
id: self.1,
});
self.0[v].push(Edge {
to: u,
cost,
id: self.1,
});
self.1 += 1;
}
fn edges_from(&self, v: usize) -> std::slice::Iter<Edge<C>> {
self.0[v].iter()
}
}
impl<C: Element> Graph<C> for DirectedGraph<C> {
fn new(size: usize) -> Self {
Self {
forward: vec![Vec::<Edge<C>>::new(); size],
backward: vec![Vec::<Edge<C>>::new(); size],
count: 0,
}
}
fn size(&self) -> usize {
self.forward.len()
}
fn add_edge(&mut self, u: usize, v: usize, cost: C) {
self.forward[u].push(Edge {
to: v,
cost: cost.clone(),
id: self.count,
});
self.backward[v].push(Edge {
to: u,
cost,
id: self.count,
});
self.count += 1;
}
fn edges_from(&self, v: usize) -> std::slice::Iter<Edge<C>> {
self.forward[v].iter()
}
}
impl<C: Element> DirectedGraph<C> {
pub fn edges_to(&self, u: usize) -> std::slice::Iter<Edge<C>> {
self.backward[u].iter()
}
pub fn reverse(&self) -> Self {
Self {
forward: self.backward.clone(),
backward: self.forward.clone(),
count: self.count,
}
}
}
macro_rules! impl_cost {
($($T:ident,)*) => {
$(
impl Cost for $T { const MAX: Self = std::$T::MAX; }
)*
};
}
impl_cost! {
i8, i16, i32, i64, i128, isize,
}
#[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord)]
pub struct Void();
impl std::fmt::Display for Void {
fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
write!(f, "")
}
}
impl Zero for Void {
fn zero() -> Self {
Void()
}
fn is_zero(&self) -> bool {
true
}
}
impl One for Void {
fn one() -> Self {
Void()
}
fn is_one(&self) -> bool {
true
}
}
impl Add for Void {
type Output = Self;
fn add(self, _: Self) -> Self {
Void()
}
}
impl AddAssign for Void {
fn add_assign(&mut self, _: Self) {}
}
impl Sub for Void {
type Output = Self;
fn sub(self, _: Self) -> Self {
Void()
}
}
impl Neg for Void {
type Output = Self;
fn neg(self) -> Self {
Void()
}
}
impl Cost for Void {
const MAX: Self = Void();
}
// ------------ Graph impl end ------------
// ------------ algebraic traits start ------------
use std::marker::Sized;
use std::ops::*;
/// 元
pub trait Element: Sized + Clone + PartialEq {}
impl<T: Sized + Clone + PartialEq> Element for T {}
/// 結合性
pub trait Associative: Magma {}
/// マグマ
pub trait Magma: Element + Add<Output = Self> {}
impl<T: Element + Add<Output = Self>> Magma for T {}
/// 半群
pub trait SemiGroup: Magma + Associative {}
impl<T: Magma + Associative> SemiGroup for T {}
/// モノイド
pub trait Monoid: SemiGroup + Zero {}
impl<T: SemiGroup + Zero> Monoid for T {}
pub trait ComMonoid: Monoid + AddAssign {}
impl<T: Monoid + AddAssign> ComMonoid for T {}
/// 群
pub trait Group: Monoid + Neg<Output = Self> {}
impl<T: Monoid + Neg<Output = Self>> Group for T {}
pub trait ComGroup: Group + ComMonoid {}
impl<T: Group + ComMonoid> ComGroup for T {}
/// 半環
pub trait SemiRing: ComMonoid + Mul<Output = Self> + One {}
impl<T: ComMonoid + Mul<Output = Self> + One> SemiRing for T {}
/// 環
pub trait Ring: ComGroup + SemiRing {}
impl<T: ComGroup + SemiRing> Ring for T {}
pub trait ComRing: Ring + MulAssign {}
impl<T: Ring + MulAssign> ComRing for T {}
/// 体
pub trait Field: ComRing + Div<Output = Self> + DivAssign {}
impl<T: ComRing + Div<Output = Self> + DivAssign> Field for T {}
/// 加法単元
pub trait Zero: Element {
fn zero() -> Self;
fn is_zero(&self) -> bool {
*self == Self::zero()
}
}
/// 乗法単元
pub trait One: Element {
fn one() -> Self;
fn is_one(&self) -> bool {
*self == Self::one()
}
}
macro_rules! impl_integer {
($($T:ty,)*) => {
$(
impl Associative for $T {}
impl Zero for $T {
fn zero() -> Self { 0 }
fn is_zero(&self) -> bool { *self == 0 }
}
impl<'a> Zero for &'a $T {
fn zero() -> Self { &0 }
fn is_zero(&self) -> bool { *self == &0 }
}
impl One for $T {
fn one() -> Self { 1 }
fn is_one(&self) -> bool { *self == 1 }
}
impl<'a> One for &'a $T {
fn one() -> Self { &1 }
fn is_one(&self) -> bool { *self == &1 }
}
)*
};
}
impl_integer! {
i8, i16, i32, i64, i128, isize,
u8, u16, u32, u64, u128, usize,
}
// ------------ algebraic traits end ------------
// ------------ io module start ------------
use std::io::{stdout, BufWriter, Read, StdoutLock, Write};
pub struct IO {
iter: std::str::SplitAsciiWhitespace<'static>,
buf: BufWriter<StdoutLock<'static>>,
}
impl IO {
pub fn new() -> Self {
let mut input = String::new();
std::io::stdin().read_to_string(&mut input).unwrap();
let input = Box::leak(input.into_boxed_str());
let out = Box::new(stdout());
IO {
iter: input.split_ascii_whitespace(),
buf: BufWriter::new(Box::leak(out).lock()),
}
}
fn scan_str(&mut self) -> &'static str {
self.iter.next().unwrap()
}
pub fn scan<T: Scan>(&mut self) -> <T as Scan>::Output {
<T as Scan>::scan(self)
}
pub fn scan_vec<T: Scan>(&mut self, n: usize) -> Vec<<T as Scan>::Output> {
(0..n).map(|_| self.scan::<T>()).collect()
}
pub fn print<T: Print>(&mut self, x: T) {
<T as Print>::print(self, x);
}
pub fn println<T: Print>(&mut self, x: T) {
self.print(x);
self.print("\n");
}
pub fn iterln<T: Print, I: Iterator<Item = T>>(&mut self, mut iter: I, delim: &str) {
if let Some(v) = iter.next() {
self.print(v);
for v in iter {
self.print(delim);
self.print(v);
}
}
self.print("\n");
}
pub fn flush(&mut self) {
self.buf.flush().unwrap();
}
}
impl Default for IO {
fn default() -> Self {
Self::new()
}
}
pub trait Scan {
type Output;
fn scan(io: &mut IO) -> Self::Output;
}
macro_rules! impl_scan {
($($t:tt),*) => {
$(
impl Scan for $t {
type Output = Self;
fn scan(s: &mut IO) -> Self::Output {
s.scan_str().parse().unwrap()
}
}
)*
};
}
impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String, f32, f64);
impl Scan for char {
type Output = char;
fn scan(s: &mut IO) -> Self::Output {
s.scan_str().chars().next().unwrap()
}
}
pub enum Bytes {}
impl Scan for Bytes {
type Output = &'static [u8];
fn scan(s: &mut IO) -> Self::Output {
s.scan_str().as_bytes()
}
}
pub enum Chars {}
impl Scan for Chars {
type Output = Vec<char>;
fn scan(s: &mut IO) -> Self::Output {
s.scan_str().chars().collect()
}
}
pub enum Usize1 {}
impl Scan for Usize1 {
type Output = usize;
fn scan(s: &mut IO) -> Self::Output {
s.scan::<usize>().wrapping_sub(1)
}
}
impl<T: Scan, U: Scan> Scan for (T, U) {
type Output = (T::Output, U::Output);
fn scan(s: &mut IO) -> Self::Output {
(T::scan(s), U::scan(s))
}
}
impl<T: Scan, U: Scan, V: Scan> Scan for (T, U, V) {
type Output = (T::Output, U::Output, V::Output);
fn scan(s: &mut IO) -> Self::Output {
(T::scan(s), U::scan(s), V::scan(s))
}
}
impl<T: Scan, U: Scan, V: Scan, W: Scan> Scan for (T, U, V, W) {
type Output = (T::Output, U::Output, V::Output, W::Output);
fn scan(s: &mut IO) -> Self::Output {
(T::scan(s), U::scan(s), V::scan(s), W::scan(s))
}
}
pub trait Print {
fn print(w: &mut IO, x: Self);
}
macro_rules! impl_print_int {
($($t:ty),*) => {
$(
impl Print for $t {
fn print(w: &mut IO, x: Self) {
w.buf.write_all(x.to_string().as_bytes()).unwrap();
}
}
)*
};
}
impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize, f32, f64);
impl Print for u8 {
fn print(w: &mut IO, x: Self) {
w.buf.write_all(&[x]).unwrap();
}
}
impl Print for &[u8] {
fn print(w: &mut IO, x: Self) {
w.buf.write_all(x).unwrap();
}
}
impl Print for &str {
fn print(w: &mut IO, x: Self) {
w.print(x.as_bytes());
}
}
impl Print for String {
fn print(w: &mut IO, x: Self) {
w.print(x.as_bytes());
}
}
impl<T: Print, U: Print> Print for (T, U) {
fn print(w: &mut IO, (x, y): Self) {
w.print(x);
w.print(" ");
w.print(y);
}
}
impl<T: Print, U: Print, V: Print> Print for (T, U, V) {
fn print(w: &mut IO, (x, y, z): Self) {
w.print(x);
w.print(" ");
w.print(y);
w.print(" ");
w.print(z);
}
}
mod neboccoio_macro {
#[macro_export]
macro_rules! input {
(@start $io:tt @read @rest) => {};
(@start $io:tt @read @rest, $($rest: tt)*) => {
input!(@start $io @read @rest $($rest)*)
};
(@start $io:tt @read @rest mut $($rest:tt)*) => {
input!(@start $io @read @mut [mut] @rest $($rest)*)
};
(@start $io:tt @read @rest $($rest:tt)*) => {
input!(@start $io @read @mut [] @rest $($rest)*)
};
(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [[$kind:tt; $len1:expr]; $len2:expr] $($rest:tt)*) => {
let $($mut)* $var = (0..$len2).map(|_| $io.scan_vec::<$kind>($len1)).collect::<Vec<Vec<$kind>>>();
input!(@start $io @read @rest $($rest)*)
};
(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:expr] $($rest:tt)*) => {
let $($mut)* $var = $io.scan_vec::<$kind>($len);
input!(@start $io @read @rest $($rest)*)
};
(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => {
let $($mut)* $var = $io.scan::<$kind>();
input!(@start $io @read @rest $($rest)*)
};
(from $io:tt $($rest:tt)*) => {
input!(@start $io @read @rest $($rest)*)
};
}
}
// ------------ io module end ------------