結果
| 問題 | No.2726 Rooted Tree Nim |
| ユーザー |
 noya2
|
| 提出日時 | 2024-04-14 22:05:46 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 112 ms / 2,000 ms |
| コード長 | 17,381 bytes |
| コンパイル時間 | 3,024 ms |
| コンパイル使用メモリ | 276,804 KB |
| 実行使用メモリ | 29,832 KB |
| 最終ジャッジ日時 | 2024-10-04 01:50:51 |
| 合計ジャッジ時間 | 5,317 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / 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 | 2 ms
6,820 KB |
| testcase_01 | AC | 84 ms
6,816 KB |
| testcase_02 | AC | 69 ms
6,820 KB |
| testcase_03 | AC | 108 ms
29,708 KB |
| testcase_04 | AC | 112 ms
29,832 KB |
| testcase_05 | AC | 67 ms
11,020 KB |
| testcase_06 | AC | 66 ms
11,020 KB |
| testcase_07 | AC | 73 ms
11,020 KB |
| testcase_08 | AC | 73 ms
11,020 KB |
| testcase_09 | AC | 62 ms
6,816 KB |
| testcase_10 | AC | 63 ms
6,816 KB |
| testcase_11 | AC | 63 ms
6,816 KB |
| testcase_12 | AC | 69 ms
10,132 KB |
| testcase_13 | AC | 62 ms
6,816 KB |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template<typename T>
void out(const vector<vector<T>> &vv){
int s = (int)vv.size();
for (int i = 0; i < s; i++) out(vv[i]);
}
struct IoSetup {
IoSetup(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetup_noya2;
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{
const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 = 998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{
unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
if (a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a); a >>= n;
int m = __builtin_ctzll(b); b >>= m;
while (a != b) {
int mm = __builtin_ctzll(a - b);
bool f = a > b;
unsigned long long c = f ? a : b;
b = f ? b : a;
a = (c - b) >> mm;
}
return a << min(n, m);
}
template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(abs(a),abs(b))); }
long long sqrt_fast(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((x + 1) * (x + 1) <= n) x++;
while (x * x > n) x--;
return x;
}
template<typename T> T floor_div(const T n, const T d) {
assert(d != 0);
return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}
template<typename T> T ceil_div(const T n, const T d) {
assert(d != 0);
return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}
template<typename T> void uniq(vector<T> &v){
sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }
} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
#line 2 "c.cpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/tree/heavy_light_decomposition.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/tree/simple_tree.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
#include<ranges>
#line 7 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
namespace noya2::internal {
template<class E>
struct csr final {
csr () {}
csr (int _n) : n(_n) {}
csr (int _n, int m) : n(_n){
start.reserve(m);
elist.reserve(m);
}
// ACL style constructor (do not have to call build)
csr (int _n, const std::vector<std::pair<int,E>> &idx_elem) : n(_n), start(_n + 2), elist(idx_elem.size()) {
for (auto &[i, e] : idx_elem){
start[i + 2]++;
}
for (int i = 1; i < n; i++){
start[i + 2] += start[i + 1];
}
for (auto &[i, e] : idx_elem){
elist[start[i + 1]++] = e;
}
prepared = true;
}
int add(int idx, E elem){
int eid = start.size();
start.emplace_back(idx);
elist.emplace_back(elem);
return eid;
}
void build(){
if (prepared) return ;
int m = start.size();
std::vector<E> nelist(m);
std::vector<int> nstart(n + 2, 0);
for (int i = 0; i < m; i++){
nstart[start[i] + 2]++;
}
for (int i = 1; i < n; i++){
nstart[i + 2] += nstart[i + 1];
}
for (int i = 0; i < m; i++){
nelist[nstart[start[i] + 1]++] = elist[i];
}
swap(elist,nelist);
swap(start,nstart);
prepared = true;
}
const auto operator[](int idx) const {
return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
}
auto operator[](int idx){
return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
}
const auto operator()(int idx, int l, int r) const {
return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
}
auto operator()(int idx, int l, int r){
return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
}
int n;
std::vector<int> start;
std::vector<E> elist;
bool prepared = false;
};
} // namespace noya2::internal
#line 5 "/Users/noya2/Desktop/Noya2_library/tree/simple_tree.hpp"
namespace noya2 {
struct simple_tree {
internal::csr<int> g;
simple_tree () {}
simple_tree (int _n) : g(_n, (_n - 1)*2) {}
void add_edge(int u, int v){
g.add(u, v);
int id = g.add(v, u);
if (id + 1 == (g.n - 1)*2) g.build();
}
void input(int indexed = 1){
for (int i = 0; i < g.n - 1; i++){
int u, v; cin >> u >> v;
u -= indexed, v -= indexed;
add_edge(u, v);
}
}
void input_parents(int indexed = 1){
for (int i = 0; i < g.n - 1; i++){
int v; cin >> v;
v -= indexed;
add_edge(i + 1, v);
}
}
const auto operator[](int v) const {
return g[v];
}
auto operator[](int v){
return g[v];
}
};
} // namespace noya2
#line 4 "/Users/noya2/Desktop/Noya2_library/tree/heavy_light_decomposition.hpp"
namespace noya2 {
struct hld_tree {
internal::csr<int> g;
hld_tree () {}
hld_tree (int _n, int _root = 0) : g(_n,(_n - 1)*2), n(_n), root(_root) {}
hld_tree (simple_tree _g, int _root = 0) : g(_g.g), n(_g.g.n), root(_root){
build();
}
void add_edge(int u, int v){
g.add(u, v);
int id = g.add(v, u);
if (id + 1 == (n - 1)*2) build();
}
void input(int indexed = 1){
for (int i = 0; i < n - 1; i++){
int u, v; cin >> u >> v;
u -= indexed, v -= indexed;
add_edge(u, v);
}
}
void input_parents(int indexed = 1){
for (int i = 0; i < n - 1; i++){
int v; cin >> v;
v -= indexed;
add_edge(i + 1, v);
}
}
int depth(int v) const {
return dep[v];
}
int parent(int v) const {
if (v == root) return -1;
return g[v].back();
}
int degree(int v) const {
return g[v].size();
}
int subtree_size(int v) const {
return sub[v];
}
// if d > dep[v], return -1
int la(int v, int d) const {
while (v != -1){
int u = nxt[v];
if (down[v] - d >= down[u]){
v = tour[down[v] - d];
break;
}
d -= down[v] - down[u] + 1;
v = parent(u);
}
return v;
}
int lca(int u, int v) const {
while (nxt[u] != nxt[v]){
if (down[u] < down[v]) swap(u,v);
u = parent(nxt[u]);
}
return dep[u] < dep[v] ? u : v;
}
int dist(int u, int v) const {
return dep[u] + dep[v] - 2*dep[lca(u,v)];
}
// if d > dist(from, to), return -1
int jump(int from, int to, int d) const {
int l = lca(from,to);
if (d <= dep[from] - dep[l]){
return la(from, d);
}
d -= dep[from] - dep[l];
if (d <= dep[to] - dep[l]){
return la(to, dep[to] - dep[l] - d);
}
return -1;
}
// seg.set(index(v), X[v]);
int index(int vertex) const {
return down[vertex];
}
int index_from_edge(int u, int v) const {
return (dep[u] < dep[v] ? down[v] : down[u]);
}
// X[vertex(i)] = seg.get(i);
int vertex(int index) const {
return tour[index];
}
int subtree_l(int v) const {
return down[v];
}
int subtree_r(int v) const {
return down[v] + sub[v];
}
// if r == v, return true
bool is_in_subtree(int r, int v) const {
return subtree_l(r) <= subtree_l(v) && subtree_l(v) < subtree_r(r);
}
bool is_in_path(int lv, int mv, int rv) const {
return dist(lv,mv) + dist(mv,rv) == dist(lv,rv);
}
// dist, v1, v2
tuple<int,int,int> diameter(){
int v1 = max_element(dep.begin(),dep.end()) - dep.begin();
vector<int> dist_from_v1(n,numeric_limits<int>::max());
queue<int> que;
que.push(v1);
dist_from_v1[v1] = 0;
while (!que.empty()){
int v = que.front(); que.pop();
for (int u : g[v]){
if (dist_from_v1[u] > dist_from_v1[v]+1){
dist_from_v1[u] = dist_from_v1[v]+1;
que.push(u);
}
}
}
int v2 = max_element(dist_from_v1.begin(),dist_from_v1.end()) - dist_from_v1.begin();
return make_tuple(dist_from_v1[v2],v1,v2);
}
// vertex array : vector<int> {from, v1, v2, ... , to}
vector<int> path(int from, int to){
int l = lca(from,to);
const int sizf = dep[from]-dep[l], sizt = dep[to]-dep[l];
vector<int> pf = {from}, pt;
pf.reserve(sizf+1); pt.reserve(sizt);
for (int i = 0; i < sizf; i++){
from = parent(from);
pf.push_back(from);
}
for (int i = 0; i < sizt; i++){
pt.push_back(to);
to = parent(to);
}
pf.insert(pf.end(),pt.rbegin(),pt.rend());
return pf;
}
template<typename F>
void path_query(int u, int v, bool vertex, const F &f){
int l = lca(u,v);
for (auto [s, t] : ascend(u, l)){
f(t, s + 1);
}
if (vertex) f(down[l], down[l] + 1);
for (auto [s, t] : descend(l, v)){
f(s, t + 1);
}
}
template<typename F>
void path_noncommutative_query(int u, int v, bool vertex, const F &f){
int l = lca(u,v);
for (auto [s, t] : ascend(u, l)){
f(s + 1, t); // l > r ok
}
if (vertex) f(down[l],down[l] + 1);
for (auto [s, t] : descend(l, v)){
f(s, t + 1); // l > r ok
}
}
template<typename F>
void subtree_query(int v, bool vertex, const F &f){
f(down[v] + (vertex ? 0 : 1), down[v] + sub[v]);
}
// adjacent to v
const auto operator[](int v) const {
return g[v];
}
auto operator[](int v){
return g[v];
}
// only child
const auto operator()(int v) const {
return g(v, 0, degree(v) - (v == root ? 0 : 1));
}
auto operator()(int v){
return g(v, 0, degree(v) - (v == root ? 0 : 1));
}
private:
int n, root;
vector<int> dep, sub, down, tour, nxt;
// v is ancestor of u.
// enumerate [closed] intervals of down ( interval [l, r] may hold l > r ).
vector<pair<int,int>> ascend(int u, int v){
vector<pair<int,int>> res;
while (nxt[u] != nxt[v]){
res.emplace_back(down[u], down[nxt[u]]);
u = parent(nxt[u]);
}
if (u != v) res.emplace_back(down[u], down[v]+1);
return res;
}
// u is ancestor of v.
// enumerate [closed] intervals of down ( interval [l, r] may hold l > r ).
vector<pair<int,int>> descend(int u, int v){
if (u == v) return {};
if (nxt[u] == nxt[v]){
return {pair<int,int>(down[u]+1, down[v])};
}
vector<pair<int,int>> res = descend(u, parent(nxt[v]));
res.emplace_back(down[nxt[v]], down[v]);
return res;
}
void build(){
g.build();
init_sz();
init_hld();
}
/*
setup dep, sub
if v is not root, g[v].back() is parent of v.
if v is not leaf (i.e. v has child), g[v].front() is heavy child of v.
*/
void init_sz(){
dep.resize(n, 0);
sub.resize(n, 1);
auto dfs = [&](auto sfs, int v, int f) -> void {
for (int &u : g[v]){
// only one chance to take parent as u.
if (u == f) swap(g[v].back(), u);
// twice means u is the last element of g[v], i.e. parent of v.
if (u == f) break;
dep[u] = dep[v]+1;
sfs(sfs, u, v);
sub[v] += sub[u];
if (sub[g[v].front()] < sub[u]){
swap(g[v].front(), u);
}
}
};
dfs(dfs, root, -1);
}
/*
setup down, tour, nxt
only heavy child c of v, nxt[c] = nxt[v]. for other child c, nxt[c] = c.
*/
void init_hld(){
down.resize(n);
tour.resize(n);
nxt.resize(n);
nxt[root] = root;
int clock = 0;
auto dfs = [&](auto sfs, int v) -> void {
down[v] = clock++;
tour[down[v]] = v;
// in case of no child, nothing to do
if ((*this)(v).empty()) return ;
// heavy child
nxt[(*this)(v).front()] = nxt[v];
sfs(sfs, (*this)(v).front());
// other child
for (int u : (*this)(v).next()){
nxt[u] = u;
sfs(sfs, u);
}
};
dfs(dfs, root);
}
public:
struct compressed_tree : public simple_tree {
using simple_tree::simple_tree;
using simple_tree::operator=;
hld_tree &g;
compressed_tree (hld_tree &g_, vector<int> vs) : g(g_){
auto comp = [&](int lv, int rv){
return g.index(lv) < g.index(rv);
};
sort(vs.begin(),vs.end(),comp);
int sz = vs.size();
for (int i = 0; i < sz-1; i++){
vs.emplace_back(g.lca(vs[i],vs[i+1]));
}
sort(vs.begin(),vs.end(),comp);
vs.erase(unique(vs.begin(),vs.end()),vs.end());
sz = vs.size();
(*this) = simple_tree(sz);
real_vertex = vs;
for (int i = 0; i < sz; i++){
g.virtual_vertex[real_vertex[i]] = i;
}
stack<int> st;
st.push(0);
for (int i = 1; i < sz; i++){
while (!g.is_in_subtree(real_vertex[st.top()], real_vertex[i])) st.pop();
(*this).add_edge(st.top(),i);
st.push(i);
}
}
vector<int> real_vertex;
int real_v(int virtual_v) const {
return real_vertex[virtual_v];
}
int virtual_v(int real_v) const {
return g.virtual_vertex[real_v];
}
size_t size() const {
return real_vertex.size();
}
};
compressed_tree compressed_tree_gen(const vector<int> &vs){
if ((int)virtual_vertex.size() != n) virtual_vertex.resize(n);
return compressed_tree(*this, vs);
}
vector<int> virtual_vertex;
};
} // namespace noya2
#line 4 "c.cpp"
void solve(){
int n; in(n);
ll k; in(k);
hld_tree g(n);
g.input();
vector<ll> a(n); in(a);
ll x = 0;
rep(i,n){
if (g.depth(i) % 2 == 0) continue;
x ^= (a[i] % (k+1));
}
out(x == 0 ? "P" : "K");
}
int main(){
int t = 1; in(t);
while (t--) { solve(); }
}