結果
| 問題 |
No.3075 Mex Recurrence Formula
|
| ユーザー |
 atcoder8
|
| 提出日時 | 2025-03-28 22:21:58 |
| 言語 | Rust (1.83.0 + proconio) |
| 結果 |
AC
|
| 実行時間 | 115 ms / 2,000 ms |
| コード長 | 7,793 bytes |
| コンパイル時間 | 13,314 ms |
| コンパイル使用メモリ | 401,604 KB |
| 実行使用メモリ | 11,776 KB |
| 最終ジャッジ日時 | 2025-03-28 22:22:18 |
| 合計ジャッジ時間 | 16,219 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 46 |
ソースコード
use fenwick_tree::FenwickTree;
use proconio::{input, marker::Usize1};
fn main() {
input! {
(n, x): (usize, Usize1),
aa: [usize; n],
}
println!("{}", solve(&aa, x));
}
fn solve(aa: &[usize], x: usize) -> usize {
let n = aa.len();
if x < n {
return aa[x];
}
let find_mex = |ft: &FenwickTree<usize>| {
let mut ok = 0_usize;
let mut ng = n + 1;
while ok.abs_diff(ng) > 1 {
let mid = (ok + ng) / 2;
if ft.sum(..mid) == mid {
ok = mid;
} else {
ng = mid;
}
}
ok
};
let mut counts = vec![0_usize; n + 1];
let mut ft = FenwickTree::<usize>::new(n + 1);
for &a in aa {
if a <= n {
counts[a] += 1;
if counts[a] == 1 {
ft.add(a, 1);
}
}
}
let mut seq = aa.to_vec();
for i in 0..n + 1 {
let mex = find_mex(&ft);
seq.push(mex);
assert_eq!(counts[mex], 0);
counts[mex] = 1;
assert_eq!(ft.get(mex), 0);
ft.add(mex, 1);
let remove = seq[i];
if remove <= n {
counts[remove] -= 1;
if counts[remove] == 0 {
ft.sub(remove, 1);
}
}
}
// 最初のN項を除いたN+1項は繰り返される
seq[n + (x - n) % (n + 1)]
}
pub mod fenwick_tree {
//! Processes the following query in `O(log(n))` time
//! for a sequence of numbers with `n` elements:
//! * Update one element
//! * Calculate the sum of the elements of a range
//! * Gets the elements of a number sequence.
use std::ops::{AddAssign, RangeBounds, Sub, SubAssign};
/// # Examples
///
/// ```
/// use atcoder8_library::fenwick_tree::FenwickTree;
///
/// let ft = FenwickTree::from(vec![3, -1, 4, 1, -5, 9, 2]);
/// assert_eq!(ft.sum(2..), 11);
/// ```
#[derive(Debug, Clone)]
pub struct FenwickTree<T>(Vec<T>);
impl<T> From<Vec<T>> for FenwickTree<T>
where
T: Default + Clone + AddAssign<T>,
{
/// # Examples
///
/// ```
/// use atcoder8_library::fenwick_tree::FenwickTree;
///
/// let ft = FenwickTree::from(vec![3, -1, 4, 1, -5, 9, 2]);
/// assert_eq!(ft.sum(2..6), 9);
/// ```
fn from(t: Vec<T>) -> Self {
let mut ft = FenwickTree::new(t.len());
for (i, x) in t.into_iter().enumerate() {
ft.add(i, x);
}
ft
}
}
impl<T> FenwickTree<T> {
/// Constructs a `FenwickTree<T>` with `n` elements.
///
/// Each element is initialized with `T::default()`.
///
/// # Examples
///
/// ```
/// use atcoder8_library::fenwick_tree::FenwickTree;
///
/// let ft = FenwickTree::<i32>::new(5);
/// assert_eq!(ft.sum(..), 0);
/// ```
pub fn new(n: usize) -> Self
where
T: Default + Clone,
{
FenwickTree(vec![T::default(); n])
}
/// Add `x` to the `p`-th element.
///
/// # Examples
///
/// ```
/// use atcoder8_library::fenwick_tree::FenwickTree;
///
/// let mut ft = FenwickTree::from(vec![3, -1, 4, 1, -5, 9, 2]);
/// assert_eq!(ft.sum(2..6), 9);
///
/// ft.add(3, 100);
/// assert_eq!(ft.sum(2..6), 109);
/// ```
pub fn add(&mut self, p: usize, x: T)
where
T: Clone + AddAssign<T>,
{
let FenwickTree(data) = self;
let n = data.len();
assert!(p < n);
let mut p = p + 1;
while p <= n {
data[p - 1] += x.clone();
p += p & p.overflowing_neg().0;
}
}
/// Subtract `x` from the `p`-th element.
///
/// # Examples
///
/// ```
/// use atcoder8_library::fenwick_tree::FenwickTree;
///
/// let mut ft = FenwickTree::<u32>::from(vec![3, 1, 4, 1, 5, 9, 2]);
/// assert_eq!(ft.sum(2..6), 19);
///
/// ft.sub(3, 1);
/// assert_eq!(ft.sum(2..6), 18);
/// ```
pub fn sub(&mut self, p: usize, x: T)
where
T: Clone + SubAssign<T>,
{
let FenwickTree(data) = self;
let n = data.len();
assert!(p < n);
let mut p = p + 1;
while p <= n {
data[p - 1] -= x.clone();
p += p & p.overflowing_neg().0;
}
}
/// Sets `x` to the `p`-th element.
///
/// # Examples
///
/// ```
/// use atcoder8_library::fenwick_tree::FenwickTree;
///
/// let mut ft = FenwickTree::from(vec![3, -1, 4, 1, -5, 9, 2]);
/// assert_eq!(ft.sum(2..6), 9);
///
/// ft.set(3, 100);
/// assert_eq!(ft.sum(2..6), 108);
/// ```
pub fn set(&mut self, p: usize, x: T)
where
T: Default + Clone + AddAssign<T> + Sub<T, Output = T> + SubAssign<T>,
{
let FenwickTree(data) = self;
let n = data.len();
assert!(p < n);
self.sub(p, self.get(p));
self.add(p, x);
}
/// Compute the sum of the range [0, r).
fn inner_sum(&self, r: usize) -> T
where
T: Default + Clone + AddAssign<T>,
{
let mut s = T::default();
let mut r = r;
while r > 0 {
s += self.0[r - 1].clone();
r -= r & r.wrapping_neg();
}
s
}
/// Calculate the total of the range.
///
/// # Examples
///
/// ```
/// use atcoder8_library::fenwick_tree::FenwickTree;
///
/// let ft = FenwickTree::from(vec![3, -1, 4, 1, -5, 9, 2]);
/// assert_eq!(ft.sum(..), 13);
/// assert_eq!(ft.sum(2..), 11);
/// assert_eq!(ft.sum(..6), 11);
/// assert_eq!(ft.sum(2..6), 9);
/// assert_eq!(ft.sum(6..2), 0);
/// ```
pub fn sum<R>(&self, rng: R) -> T
where
T: Default + Clone + AddAssign<T> + Sub<T, Output = T>,
R: RangeBounds<usize>,
{
let n = self.0.len();
let l = match rng.start_bound() {
std::ops::Bound::Included(&start_bound) => start_bound,
std::ops::Bound::Excluded(&start_bound) => start_bound + 1,
std::ops::Bound::Unbounded => 0,
};
let r = match rng.end_bound() {
std::ops::Bound::Included(&end_bound) => end_bound + 1,
std::ops::Bound::Excluded(&end_bound) => end_bound,
std::ops::Bound::Unbounded => n,
};
assert!(l <= n && r <= n);
if l >= r {
T::default()
} else {
self.inner_sum(r) - self.inner_sum(l)
}
}
/// Returns the value of an element in a sequence of numbers.
/// Calculate the total of the range.
///
/// # Examples
///
/// ```
/// use atcoder8_library::fenwick_tree::FenwickTree;
///
/// let ft = FenwickTree::from(vec![3, -1, 4, -1, 5]);
/// assert_eq!(ft.get(2), 4);
/// ```
pub fn get(&self, p: usize) -> T
where
T: Default + Clone + AddAssign<T> + Sub<T, Output = T>,
{
assert!(p < self.0.len());
self.sum(p..=p)
}
}
}