結果
| 問題 | No.2912 ０次パーシステントホモロジー |
| ユーザー |
 atcoder8
|
| 提出日時 | 2024-10-05 00:26:11 |
| 言語 | Rust (1.77.0 + proconio) |
| 結果 |
AC
|
| 実行時間 | 143 ms / 2,000 ms |
| コード長 | 12,297 bytes |
| コンパイル時間 | 11,714 ms |
| コンパイル使用メモリ | 406,892 KB |
| 実行使用メモリ | 11,264 KB |
| 最終ジャッジ日時 | 2024-10-05 00:26:27 |
| 合計ジャッジ時間 | 13,845 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（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
6,820 KB |
| testcase_02 | AC | 1 ms
6,816 KB |
| testcase_03 | AC | 1 ms
6,820 KB |
| testcase_04 | AC | 1 ms
6,820 KB |
| testcase_05 | AC | 1 ms
6,820 KB |
| testcase_06 | AC | 1 ms
6,820 KB |
| testcase_07 | AC | 1 ms
6,820 KB |
| testcase_08 | AC | 0 ms
6,820 KB |
| testcase_09 | AC | 1 ms
6,816 KB |
| testcase_10 | AC | 1 ms
6,816 KB |
| testcase_11 | AC | 1 ms
6,816 KB |
| testcase_12 | AC | 0 ms
6,816 KB |
| testcase_13 | AC | 1 ms
6,816 KB |
| testcase_14 | AC | 1 ms
6,820 KB |
| testcase_15 | AC | 15 ms
6,820 KB |
| testcase_16 | AC | 115 ms
7,040 KB |
| testcase_17 | AC | 44 ms
6,820 KB |
| testcase_18 | AC | 64 ms
7,168 KB |
| testcase_19 | AC | 143 ms
11,264 KB |
| testcase_20 | AC | 143 ms
11,264 KB |
| testcase_21 | AC | 140 ms
11,264 KB |
| testcase_22 | AC | 140 ms
11,264 KB |
ソースコード
use proconio::input;
use union_find::UnionFind;
fn main() {
input! {
(n, m): (usize, usize),
mut ijw: [(usize, usize, usize); m],
t: usize,
rr: [usize; t],
}
ijw.sort_unstable_by_key(|&(_, _, w)| w);
let mut uf = UnionFind::new(n);
let mut ir = rr.iter().cloned().enumerate().collect::<Vec<_>>();
ir.sort_unstable_by_key(|&(_, r)| r);
let mut num_components_vec = vec![0_usize; t];
let mut progress = 0;
for &(i, r) in &ir {
while progress < m && ijw[progress].2 <= r {
let (u, v, _) = ijw[progress];
uf.merge(u, v);
progress += 1;
}
num_components_vec[i] = uf.group_num();
}
for &num_components in &num_components_vec {
println!("{}", num_components);
}
}
pub mod union_find {
//! Union-Find processes the following queries on undirected graphs.
//! * Merge two connected components.
//! * Determine whether two given nodes are in the same connected component.
//!
//! To seed up processing, merge optimization using the number of nodes
//! of the connected components and path compression are performed.
//!
//! The time complexity of each query is `O(A(n))`.
//! where `n` is the number of nodes in the graph and
//! `A(n)` is the inverse of the Ackermann function.
/// This is the value that will be associated with each nodes of the graph.
#[derive(Debug, Clone, Copy)]
enum ParentOrSize {
/// It is used for non-representative nodes and stores the parent node.
Parent(usize),
/// It is used for the representative node and
/// stores the number of nodes of the connected component.
Size(usize),
}
/// Union-Find processes the following queries on undirected graphs.
/// * Merge two connected components.
/// * Determine whether two given nodes are in the same connected component.
///
/// To seed up processing, merge optimization using the number of nodes
/// of the connected components and path compression are performed.
///
/// The time complexity of each query is `O(A(n))`.
/// where `n` is the number of nodes in the graph and
/// `A(n)` is the inverse of the Ackermann function.
///
/// # Examples
///
/// ```
/// use atcoder8_library::union_find::UnionFind;
///
/// let mut uf = UnionFind::new(3);
/// assert_eq!(uf.same(0, 2), false);
/// uf.merge(0, 1);
/// assert_eq!(uf.same(0, 2), false);
/// uf.merge(1, 2);
/// assert_eq!(uf.same(0, 2), true);
/// ```
#[derive(Debug, Default, Clone)]
pub struct UnionFind {
/// For each node, one of the following is stored.
/// * The number of nodes of the connected component to which it belongs.
/// (If it is a representative node of the connected component.)
/// * Index of the parent node. (Otherwise.)
parent_or_size: Vec<ParentOrSize>,
/// Number of connected components.
group_num: usize,
}
impl UnionFind {
/// Create an undirected graph with `n` nodes and `0` edges.
///
/// # Examples
///
/// ```
/// use atcoder8_library::union_find::UnionFind;
///
/// let mut uf = UnionFind::new(3);
/// assert_eq!(uf.same(0, 2), false);
/// uf.merge(0, 1);
/// assert_eq!(uf.same(0, 2), false);
/// uf.merge(2, 1);
/// assert_eq!(uf.same(0, 2), true);
/// ```
pub fn new(n: usize) -> Self {
UnionFind {
parent_or_size: vec![ParentOrSize::Size(1); n],
group_num: n,
}
}
/// Return the representative node of the connected component containing node `a`.
///
/// At that time, perform path compression on the nodes on the path from node `a` to the representative node.
///
/// # Examples
///
/// ```
/// use atcoder8_library::union_find::UnionFind;
///
/// let mut uf = UnionFind::new(3);
/// uf.merge(1, 2);
/// assert_eq!(uf.leader(0), 0);
/// assert_eq!(uf.leader(1), uf.leader(2));
/// ```
pub fn leader(&mut self, a: usize) -> usize {
// If node `a` is a representative node of the connected component, return `a`.
if let ParentOrSize::Size(_) = self.parent_or_size[a] {
return a;
}
// Path from node `a` to the representative node.
let mut path = vec![];
// Current node.
let mut current = a;
// Record the path to the representative node.
while let ParentOrSize::Parent(parent) = self.parent_or_size[current] {
// Add current node to the path.
path.push(current);
// Move to the parent node.
current = parent;
}
// The representative node of the connected component.
let leader = current;
// Set nodes on the path as direct children of the representative node.
path.iter().for_each(|&node| {
self.parent_or_size[node] = ParentOrSize::Parent(leader);
});
// Return the representative node of the connected component.
leader
}
/// Return whether two nodes `a` and `b` are in the same connected component.
///
/// # Examples
///
/// ```
/// use atcoder8_library::union_find::UnionFind;
///
/// let mut uf = UnionFind::new(3);
/// assert_eq!(uf.same(0, 2), false);
/// uf.merge(0, 1);
/// assert_eq!(uf.same(0, 2), false);
/// uf.merge(2, 1);
/// assert_eq!(uf.same(0, 2), true);
/// ```
pub fn same(&mut self, a: usize, b: usize) -> bool {
self.leader(a) == self.leader(b)
}
/// Merge each connected component containing nodes `a` and `b`.
///
/// Return `true` if different connected components are newly merged.
///
/// # Examples
///
/// ```
/// use atcoder8_library::union_find::UnionFind;
///
/// let mut uf = UnionFind::new(3);
/// assert_eq!(uf.same(0, 2), false);
/// uf.merge(0, 1);
/// assert_eq!(uf.same(0, 2), false);
/// uf.merge(2, 1);
/// assert_eq!(uf.same(0, 2), true);
/// ```
pub fn merge(&mut self, a: usize, b: usize) -> bool {
// Representative node of the connected component that contains the node `a`.
let leader_a = self.leader(a);
// Representative node of the connected component that contains the node `b`.
let leader_b = self.leader(b);
// If nodes `a` and `b` are in the same connected component, return `false` without processing.
if leader_a == leader_b {
return false;
}
// Number of nodes of the component containing node `a`.
let component_size_a = self.size(leader_a);
// Number of nodes of the component containing node `b`.
let component_size_b = self.size(leader_b);
// Number of nodes of the merged component.
let merged_component_size = component_size_a + component_size_b;
// Set the parent of the representative node of the smaller sized connected component
// to be the parent of the other connected component.
if component_size_a <= component_size_b {
self.parent_or_size[leader_a] = ParentOrSize::Parent(leader_b);
self.parent_or_size[leader_b] = ParentOrSize::Size(merged_component_size);
} else {
self.parent_or_size[leader_b] = ParentOrSize::Parent(leader_a);
self.parent_or_size[leader_a] = ParentOrSize::Size(merged_component_size);
}
// Decrease the number of connected components by one.
self.group_num -= 1;
// Return `true` because different connected components are newly combined.
true
}
/// Return a list of connected components.
///
/// Each connected component consists of indexes of nodes.
/// The indexes of the nodes in each connected component are arranged in ascending order.
/// The list of connected components is sorted in ascending order
/// with respect to the smallest index of the included nodes.
///
/// # Examples
///
/// ```
/// use atcoder8_library::union_find::UnionFind;
///
/// let mut uf = UnionFind::new(5);
/// uf.merge(1, 2);
/// uf.merge(2, 3);
/// assert_eq!(uf.groups(), vec![vec![0], vec![1, 2, 3], vec![4]]);
/// ```
pub fn groups(&mut self) -> Vec<Vec<usize>> {
// Number of nodes in graph.
let element_num = self.parent_or_size.len();
// List of connected components.
let mut groups: Vec<Vec<usize>> = vec![];
// Correspondence between the representative node and group index.
let mut leader_to_idx: Vec<Option<usize>> = vec![None; element_num];
// Assign each node in the graph to a group.
for node in 0..element_num {
// Representative node of the connected component to which the `node` belongs.
let leader = self.leader(node);
if let Some(group_idx) = leader_to_idx[leader] {
// Assign to an existing group.
groups[group_idx].push(node);
} else {
// Adding a new group.
leader_to_idx[leader] = Some(groups.len());
groups.push(vec![node]);
}
}
// Return a list of groups.
groups
}
/// Return the number of nodes in the connected component to which node `a` belongs.
///
/// # Examples
///
/// ```
/// use atcoder8_library::union_find::UnionFind;
///
/// let mut uf = UnionFind::new(3);
/// assert_eq!(uf.size(0), 1);
/// uf.merge(0, 1);
/// assert_eq!(uf.size(0), 2);
/// uf.merge(2, 1);
/// assert_eq!(uf.size(0), 3);
/// ```
pub fn size(&mut self, a: usize) -> usize {
let leader = self.leader(a);
match self.parent_or_size[leader] {
ParentOrSize::Parent(_) => panic!(),
ParentOrSize::Size(size) => size,
}
}
/// Add a new node with degree `0`.
///
/// # Examples
///
/// ```
/// use atcoder8_library::union_find::UnionFind;
///
/// let mut uf = UnionFind::new(4);
/// uf.merge(1, 2);
/// uf.merge(2, 3);
/// assert_eq!(uf.groups(), vec![vec![0], vec![1, 2, 3]]);
/// uf.add();
/// assert_eq!(uf.groups(), vec![vec![0], vec![1, 2, 3], vec![4]]);
/// ```
pub fn add(&mut self) {
self.parent_or_size.push(ParentOrSize::Size(1));
self.group_num += 1;
}
/// Return the number of connected components.
///
/// # Examples
///
/// ```
/// use atcoder8_library::union_find::UnionFind;
///
/// let mut uf = UnionFind::new(3);
/// assert_eq!(uf.group_num(), 3);
/// uf.merge(0, 1);
/// assert_eq!(uf.group_num(), 2);
/// uf.merge(2, 1);
/// assert_eq!(uf.group_num(), 1);
/// ```
pub fn group_num(&self) -> usize {
self.group_num
}
/// Return the number of nodes in the graph.
///
/// # Examples
///
/// ```
/// use atcoder8_library::union_find::UnionFind;
///
/// let mut uf = UnionFind::new(5);
/// assert_eq!(uf.elem_num(), 5);
/// ```
pub fn elem_num(&self) -> usize {
self.parent_or_size.len()
}
}
}