use std::{
collections::HashSet,
io::{self, BufRead, Write},
vec,
};
use std::collections::HashMap;
use std::hash::Hash;
pub struct UnionFind<T> {
elem_to_idx: HashMap<T, usize>,
idx_to_elem: Vec<T>,
parent: Vec<usize>,
size: Vec<usize>,
}
impl<T: Clone + Eq + Hash> UnionFind<T> {
pub fn new() -> Self {
Self {
elem_to_idx: HashMap::new(),
idx_to_elem: Vec::new(),
parent: Vec::new(),
size: Vec::new(),
}
}
pub fn len(&self) -> usize {
self.idx_to_elem.len()
}
pub fn is_empty(&self) -> bool {
self.idx_to_elem.is_empty()
}
pub fn contains(&self, item: &T) -> bool {
self.elem_to_idx.contains_key(item)
}
/// Inserts `item` as its own singleton set if it is not already present.
pub fn make_set(&mut self, item: T) {
if self.elem_to_idx.contains_key(&item) {
return;
}
let idx = self.idx_to_elem.len();
self.elem_to_idx.insert(item.clone(), idx);
self.idx_to_elem.push(item);
self.parent.push(idx);
self.size.push(1);
}
/// Root representative for `item`’s set, or `None` if `item` is unknown.
pub fn find(&mut self, item: &T) -> Option<&T> {
let idx = *self.elem_to_idx.get(item)?;
let root = self.find_root(idx);
Some(&self.idx_to_elem[root])
}
/// Number of elements in the component containing `item`, or `None` if unknown.
pub fn component_size(&mut self, item: &T) -> Option<usize> {
let idx = *self.elem_to_idx.get(item)?;
let root = self.find_root(idx);
Some(self.size[root])
}
/// Merges the sets of `a` and `b`. Returns `true` if they were separate and are now merged.
pub fn union(&mut self, a: &T, b: &T) -> bool {
let Some(&ia) = self.elem_to_idx.get(a) else {
return false;
};
let Some(&ib) = self.elem_to_idx.get(b) else {
return false;
};
let ra = self.find_root(ia);
let rb = self.find_root(ib);
if ra == rb {
return false;
}
let (small, large) = if self.size[ra] < self.size[rb] {
(ra, rb)
} else {
(rb, ra)
};
self.parent[small] = large;
self.size[large] += self.size[small];
true
}
pub fn same_set(&mut self, a: &T, b: &T) -> bool {
match (self.elem_to_idx.get(a), self.elem_to_idx.get(b)) {
(Some(&ia), Some(&ib)) => self.find_root(ia) == self.find_root(ib),
_ => false,
}
}
fn find_root(&mut self, mut idx: usize) -> usize {
let mut root = idx;
while self.parent[root] != root {
root = self.parent[root];
}
while self.parent[idx] != root {
let p = self.parent[idx];
self.parent[idx] = root;
idx = p;
}
root
}
}
impl<T: Clone + Eq + Hash> Default for UnionFind<T> {
fn default() -> Self {
Self::new()
}
}
const TAK: &str = "TAK";
const NIE: &str = "NIE";
fn parse_first_line(line: &str) -> i32 {
let mut parts = line.split_whitespace();
parts.next().unwrap().parse().unwrap()
}
fn parse_district_start(line: &str) -> (usize, i32, usize) {
let mut parts = line.split_whitespace();
let n = parts.next().unwrap().parse().unwrap();
let m = parts.next().unwrap().parse().unwrap();
let k = parts.next().unwrap().parse().unwrap();
(n, m, k)
}
fn parse_winners(line: &str) -> Vec<usize> {
line.split_whitespace()
.map(|part| part.parse::<usize>().unwrap() - 1)
.collect()
}
fn parse_graph_pairs(line: &str) -> (usize, usize) {
let mut parts = line.split_whitespace();
let u = parts.next().unwrap().parse().unwrap();
let v = parts.next().unwrap().parse().unwrap();
(u, v)
}
fn process_district(lines: &mut std::io::Lines<std::io::StdinLock<'_>>) -> &'static str {
let first_line = lines.next().unwrap().unwrap();
let second_line = lines.next().unwrap().unwrap();
let (n, m, k) = parse_district_start(&first_line);
let winners = parse_winners(&second_line);
let mut pairs = Vec::new();
for _ in 0..m {
pairs.push(parse_graph_pairs(&lines.next().unwrap().unwrap()));
}
let mut graph = vec![HashSet::new(); n];
for (u, v) in pairs {
graph[u - 1].insert(v - 1);
graph[v - 1].insert(u - 1);
}
let mut party_chunks = UnionFind::new();
let mut party_chunk_count = vec![0; k];
let mut party_wins = vec![Vec::new(); k];
for city in 0..n {
party_chunks.make_set(city);
party_chunk_count[winners[city]] += 1;
}
let mut one_chunkers = Vec::new();
let mut removed_parties = HashSet::new();
for city in 0..n {
for neighbor in &graph[city] {
if winners[city] == winners[*neighbor] && !party_chunks.same_set(&city, neighbor) {
party_chunks.union(&city, neighbor);
party_chunk_count[winners[city]] -= 1;
}
}
party_wins[winners[city]].push(city);
}
for (party, chunk_count) in party_chunk_count.iter().enumerate() {
if *chunk_count == 1 {
one_chunkers.push(party);
} else if *chunk_count == 0 {
removed_parties.insert(party);
}
}
let mut removed_uf = UnionFind::new();
for city in 0..n {
removed_uf.make_set(city);
}
let mut removed_in_this_chunk = vec![false; n];
let mut chunk_reps: Vec<Option<HashMap<usize, usize>>> = vec![None; n];
while let Some(party) = one_chunkers.pop() {
if !removed_parties.contains(&party) {
let mut old_roots = Vec::new();
for city in &party_wins[party] {
for &neighbor in &graph[*city] {
if removed_in_this_chunk[neighbor] {
old_roots.push(*removed_uf.find(&neighbor).unwrap());
}
}
}
old_roots.sort_unstable();
old_roots.dedup();
for city in &party_wins[party] {
removed_in_this_chunk[*city] = true;
}
for city in &party_wins[party] {
for &neighbor in &graph[*city] {
if removed_in_this_chunk[neighbor] {
removed_uf.union(city, &neighbor);
}
}
}
let mut best_idx = None;
let mut best_len = 0;
for (i, oroot) in old_roots.iter().enumerate() {
let len = chunk_reps[*oroot].as_ref().map_or(0, |m| m.len());
if len > best_len {
best_len = len;
best_idx = Some(i);
}
}
let mut collected_reps: HashMap<usize, usize> = if let Some(bi) = best_idx {
chunk_reps[old_roots[bi]].take().unwrap_or_default()
} else {
HashMap::new()
};
collected_reps.remove(&party);
for (i, oroot) in old_roots.iter().enumerate() {
if Some(i) == best_idx {
continue;
}
if let Some(old_reps) = chunk_reps[*oroot].take() {
for (neighbor_party, rep) in old_reps {
if !removed_parties.contains(&neighbor_party) && neighbor_party != party {
if let Some(part_rep) = collected_reps.get(&neighbor_party) {
if !party_chunks.same_set(part_rep, &rep) {
party_chunks.union(part_rep, &rep);
party_chunk_count[neighbor_party] -= 1;
if party_chunk_count[neighbor_party] == 1 {
one_chunkers.push(neighbor_party);
}
}
} else {
collected_reps.insert(neighbor_party, rep);
}
}
}
}
}
for city in &party_wins[party] {
for &neighbor in &graph[*city] {
let neighbor_party = winners[neighbor];
if neighbor_party != party
&& !removed_parties.contains(&neighbor_party)
&& !removed_in_this_chunk[neighbor]
{
if let Some(part_rep) = collected_reps.get(&neighbor_party) {
if !party_chunks.same_set(part_rep, &neighbor) {
party_chunks.union(part_rep, &neighbor);
party_chunk_count[neighbor_party] -= 1;
if party_chunk_count[neighbor_party] == 1 {
one_chunkers.push(neighbor_party);
}
}
} else {
collected_reps.insert(neighbor_party, neighbor);
}
}
}
}
let root = *removed_uf.find(&party_wins[party][0]).unwrap();
chunk_reps[root] = Some(collected_reps);
removed_parties.insert(party);
}
}
if removed_parties.len() != k {
return NIE;
}
TAK
}
fn main() {
let stdin = io::stdin().lock();
let mut stdout = io::stdout().lock();
let mut lines = stdin.lines();
let first_line = lines.next().unwrap().unwrap();
let t = parse_first_line(&first_line);
for _ in 0..t {
writeln!(stdout, "{}", process_district(&mut lines)).expect("write stdout");
}
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 | use std::{ collections::HashSet, io::{self, BufRead, Write}, vec, }; use std::collections::HashMap; use std::hash::Hash; pub struct UnionFind<T> { elem_to_idx: HashMap<T, usize>, idx_to_elem: Vec<T>, parent: Vec<usize>, size: Vec<usize>, } impl<T: Clone + Eq + Hash> UnionFind<T> { pub fn new() -> Self { Self { elem_to_idx: HashMap::new(), idx_to_elem: Vec::new(), parent: Vec::new(), size: Vec::new(), } } pub fn len(&self) -> usize { self.idx_to_elem.len() } pub fn is_empty(&self) -> bool { self.idx_to_elem.is_empty() } pub fn contains(&self, item: &T) -> bool { self.elem_to_idx.contains_key(item) } /// Inserts `item` as its own singleton set if it is not already present. pub fn make_set(&mut self, item: T) { if self.elem_to_idx.contains_key(&item) { return; } let idx = self.idx_to_elem.len(); self.elem_to_idx.insert(item.clone(), idx); self.idx_to_elem.push(item); self.parent.push(idx); self.size.push(1); } /// Root representative for `item`’s set, or `None` if `item` is unknown. pub fn find(&mut self, item: &T) -> Option<&T> { let idx = *self.elem_to_idx.get(item)?; let root = self.find_root(idx); Some(&self.idx_to_elem[root]) } /// Number of elements in the component containing `item`, or `None` if unknown. pub fn component_size(&mut self, item: &T) -> Option<usize> { let idx = *self.elem_to_idx.get(item)?; let root = self.find_root(idx); Some(self.size[root]) } /// Merges the sets of `a` and `b`. Returns `true` if they were separate and are now merged. pub fn union(&mut self, a: &T, b: &T) -> bool { let Some(&ia) = self.elem_to_idx.get(a) else { return false; }; let Some(&ib) = self.elem_to_idx.get(b) else { return false; }; let ra = self.find_root(ia); let rb = self.find_root(ib); if ra == rb { return false; } let (small, large) = if self.size[ra] < self.size[rb] { (ra, rb) } else { (rb, ra) }; self.parent[small] = large; self.size[large] += self.size[small]; true } pub fn same_set(&mut self, a: &T, b: &T) -> bool { match (self.elem_to_idx.get(a), self.elem_to_idx.get(b)) { (Some(&ia), Some(&ib)) => self.find_root(ia) == self.find_root(ib), _ => false, } } fn find_root(&mut self, mut idx: usize) -> usize { let mut root = idx; while self.parent[root] != root { root = self.parent[root]; } while self.parent[idx] != root { let p = self.parent[idx]; self.parent[idx] = root; idx = p; } root } } impl<T: Clone + Eq + Hash> Default for UnionFind<T> { fn default() -> Self { Self::new() } } const TAK: &str = "TAK"; const NIE: &str = "NIE"; fn parse_first_line(line: &str) -> i32 { let mut parts = line.split_whitespace(); parts.next().unwrap().parse().unwrap() } fn parse_district_start(line: &str) -> (usize, i32, usize) { let mut parts = line.split_whitespace(); let n = parts.next().unwrap().parse().unwrap(); let m = parts.next().unwrap().parse().unwrap(); let k = parts.next().unwrap().parse().unwrap(); (n, m, k) } fn parse_winners(line: &str) -> Vec<usize> { line.split_whitespace() .map(|part| part.parse::<usize>().unwrap() - 1) .collect() } fn parse_graph_pairs(line: &str) -> (usize, usize) { let mut parts = line.split_whitespace(); let u = parts.next().unwrap().parse().unwrap(); let v = parts.next().unwrap().parse().unwrap(); (u, v) } fn process_district(lines: &mut std::io::Lines<std::io::StdinLock<'_>>) -> &'static str { let first_line = lines.next().unwrap().unwrap(); let second_line = lines.next().unwrap().unwrap(); let (n, m, k) = parse_district_start(&first_line); let winners = parse_winners(&second_line); let mut pairs = Vec::new(); for _ in 0..m { pairs.push(parse_graph_pairs(&lines.next().unwrap().unwrap())); } let mut graph = vec![HashSet::new(); n]; for (u, v) in pairs { graph[u - 1].insert(v - 1); graph[v - 1].insert(u - 1); } let mut party_chunks = UnionFind::new(); let mut party_chunk_count = vec![0; k]; let mut party_wins = vec![Vec::new(); k]; for city in 0..n { party_chunks.make_set(city); party_chunk_count[winners[city]] += 1; } let mut one_chunkers = Vec::new(); let mut removed_parties = HashSet::new(); for city in 0..n { for neighbor in &graph[city] { if winners[city] == winners[*neighbor] && !party_chunks.same_set(&city, neighbor) { party_chunks.union(&city, neighbor); party_chunk_count[winners[city]] -= 1; } } party_wins[winners[city]].push(city); } for (party, chunk_count) in party_chunk_count.iter().enumerate() { if *chunk_count == 1 { one_chunkers.push(party); } else if *chunk_count == 0 { removed_parties.insert(party); } } let mut removed_uf = UnionFind::new(); for city in 0..n { removed_uf.make_set(city); } let mut removed_in_this_chunk = vec![false; n]; let mut chunk_reps: Vec<Option<HashMap<usize, usize>>> = vec![None; n]; while let Some(party) = one_chunkers.pop() { if !removed_parties.contains(&party) { let mut old_roots = Vec::new(); for city in &party_wins[party] { for &neighbor in &graph[*city] { if removed_in_this_chunk[neighbor] { old_roots.push(*removed_uf.find(&neighbor).unwrap()); } } } old_roots.sort_unstable(); old_roots.dedup(); for city in &party_wins[party] { removed_in_this_chunk[*city] = true; } for city in &party_wins[party] { for &neighbor in &graph[*city] { if removed_in_this_chunk[neighbor] { removed_uf.union(city, &neighbor); } } } let mut best_idx = None; let mut best_len = 0; for (i, oroot) in old_roots.iter().enumerate() { let len = chunk_reps[*oroot].as_ref().map_or(0, |m| m.len()); if len > best_len { best_len = len; best_idx = Some(i); } } let mut collected_reps: HashMap<usize, usize> = if let Some(bi) = best_idx { chunk_reps[old_roots[bi]].take().unwrap_or_default() } else { HashMap::new() }; collected_reps.remove(&party); for (i, oroot) in old_roots.iter().enumerate() { if Some(i) == best_idx { continue; } if let Some(old_reps) = chunk_reps[*oroot].take() { for (neighbor_party, rep) in old_reps { if !removed_parties.contains(&neighbor_party) && neighbor_party != party { if let Some(part_rep) = collected_reps.get(&neighbor_party) { if !party_chunks.same_set(part_rep, &rep) { party_chunks.union(part_rep, &rep); party_chunk_count[neighbor_party] -= 1; if party_chunk_count[neighbor_party] == 1 { one_chunkers.push(neighbor_party); } } } else { collected_reps.insert(neighbor_party, rep); } } } } } for city in &party_wins[party] { for &neighbor in &graph[*city] { let neighbor_party = winners[neighbor]; if neighbor_party != party && !removed_parties.contains(&neighbor_party) && !removed_in_this_chunk[neighbor] { if let Some(part_rep) = collected_reps.get(&neighbor_party) { if !party_chunks.same_set(part_rep, &neighbor) { party_chunks.union(part_rep, &neighbor); party_chunk_count[neighbor_party] -= 1; if party_chunk_count[neighbor_party] == 1 { one_chunkers.push(neighbor_party); } } } else { collected_reps.insert(neighbor_party, neighbor); } } } } let root = *removed_uf.find(&party_wins[party][0]).unwrap(); chunk_reps[root] = Some(collected_reps); removed_parties.insert(party); } } if removed_parties.len() != k { return NIE; } TAK } fn main() { let stdin = io::stdin().lock(); let mut stdout = io::stdout().lock(); let mut lines = stdin.lines(); let first_line = lines.next().unwrap().unwrap(); let t = parse_first_line(&first_line); for _ in 0..t { writeln!(stdout, "{}", process_district(&mut lines)).expect("write stdout"); } } |
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