library
This documentation is automatically generated by online-judge-tools/verification-helper
test/5_atcoder/arc157a.test.cpp
- View this file on GitHub
- Last update: 2024-09-28 04:06:11+09:00
- Problem: https://atcoder.jp/contests/arc157/tasks/arc157_a
Depends on
- ds/hashmap.hpp
- ds/unionfind/unionfind.hpp
- graph/base.hpp
- graph/eulerwalk.hpp
- graph/vs_to_es.hpp
- my_template.hpp
- other/io.hpp
Code
#define PROBLEM "https://atcoder.jp/contests/arc157/tasks/arc157_a"
#include "my_template.hpp"
#include "other/io.hpp"
#include "graph/eulerwalk.hpp"
void solve() {
LL(N, A, B, C, D);
Graph<int, 1> G(2);
FOR(A) G.add(0, 0);
FOR(B) G.add(0, 1);
FOR(C) G.add(1, 0);
FOR(D) G.add(1, 1);
G.build();
auto vs = euler_walk(G).fi;
Yes(!vs.empty());
}
signed main() {
solve();
return 0;
}#line 1 "test/5_atcoder/arc157a.test.cpp"
#define PROBLEM "https://atcoder.jp/contests/arc157/tasks/arc157_a"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 4 "test/5_atcoder/arc157a.test.cpp"
#line 2 "ds/unionfind/unionfind.hpp"
struct UnionFind {
int n, n_comp;
vc<int> dat; // par or (-size)
UnionFind(int n = 0) { build(n); }
void build(int m) {
n = m, n_comp = m;
dat.assign(n, -1);
}
void reset() { build(n); }
int operator[](int x) {
while (dat[x] >= 0) {
int pp = dat[dat[x]];
if (pp < 0) { return dat[x]; }
x = dat[x] = pp;
}
return x;
}
ll size(int x) {
x = (*this)[x];
return -dat[x];
}
bool merge(int x, int y) {
x = (*this)[x], y = (*this)[y];
if (x == y) return false;
if (-dat[x] < -dat[y]) swap(x, y);
dat[x] += dat[y], dat[y] = x, n_comp--;
return true;
}
vc<int> get_all() {
vc<int> A(n);
FOR(i, n) A[i] = (*this)[i];
return A;
}
};
#line 2 "graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
static constexpr bool is_directed = directed;
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
vc<int> vc_deg, vc_indeg, vc_outdeg;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) { return 0; }
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) { return 0; }
return &G->csr_edges[r];
}
private:
const Graph* G;
int l, r;
};
bool is_prepared() { return prepared; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void build(int n) {
N = n, M = 0;
prepared = 0;
edges.clear();
indptr.clear();
csr_edges.clear();
vc_deg.clear();
vc_indeg.clear();
vc_outdeg.clear();
}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
#ifdef FASTIO
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
for (int m = 0; m < M; ++m) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
#endif
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e: edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e: edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed)
csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
vc<int> deg_array() {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
#ifdef FASTIO
void debug() {
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
}
#endif
vc<int> new_idx;
vc<bool> used_e;
// G における頂点 V[i] が、新しいグラフで i になるようにする
// {G, es}
// sum(deg(v)) の計算量になっていて、
// 新しいグラフの n+m より大きい可能性があるので注意
Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
if (len(new_idx) != N) new_idx.assign(N, -1);
int n = len(V);
FOR(i, n) new_idx[V[i]] = i;
Graph<T, directed> G(n);
vc<int> history;
FOR(i, n) {
for (auto&& e: (*this)[V[i]]) {
if (len(used_e) <= e.id) used_e.resize(e.id + 1);
if (used_e[e.id]) continue;
int a = e.frm, b = e.to;
if (new_idx[a] != -1 && new_idx[b] != -1) {
history.eb(e.id);
used_e[e.id] = 1;
int eid = (keep_eid ? e.id : -1);
G.add(new_idx[a], new_idx[b], e.cost, eid);
}
}
}
FOR(i, n) new_idx[V[i]] = -1;
for (auto&& eid: history) used_e[eid] = 0;
G.build();
return G;
}
Graph<T, true> to_directed_tree(int root = -1) {
if (root == -1) root = 0;
assert(!is_directed && prepared && M == N - 1);
Graph<T, true> G1(N);
vc<int> par(N, -1);
auto dfs = [&](auto& dfs, int v) -> void {
for (auto& e: (*this)[v]) {
if (e.to == par[v]) continue;
par[e.to] = v, dfs(dfs, e.to);
}
};
dfs(dfs, root);
for (auto& e: edges) {
int a = e.frm, b = e.to;
if (par[a] == b) swap(a, b);
assert(par[b] == a);
G1.add(a, b, e.cost);
}
G1.build();
return G1;
}
private:
void calc_deg() {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() {
assert(vc_indeg.empty());
vc_indeg.resize(N);
vc_outdeg.resize(N);
for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
}
};
#line 2 "graph/vs_to_es.hpp"
#line 2 "ds/hashmap.hpp"
// u64 -> Val
template <typename Val>
struct HashMap {
// n は入れたいものの個数で ok
HashMap(u32 n = 0) { build(n); }
void build(u32 n) {
u32 k = 8;
while (k < n * 2) k *= 2;
cap = k / 2, mask = k - 1;
key.resize(k), val.resize(k), used.assign(k, 0);
}
// size を保ったまま. size=0 にするときは build すること.
void clear() {
used.assign(len(used), 0);
cap = (mask + 1) / 2;
}
int size() { return len(used) / 2 - cap; }
int index(const u64& k) {
int i = 0;
for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {}
return i;
}
Val& operator[](const u64& k) {
if (cap == 0) extend();
int i = index(k);
if (!used[i]) { used[i] = 1, key[i] = k, val[i] = Val{}, --cap; }
return val[i];
}
Val get(const u64& k, Val default_value) {
int i = index(k);
return (used[i] ? val[i] : default_value);
}
bool count(const u64& k) {
int i = index(k);
return used[i] && key[i] == k;
}
// f(key, val)
template <typename F>
void enumerate_all(F f) {
FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
}
private:
u32 cap, mask;
vc<u64> key;
vc<Val> val;
vc<bool> used;
u64 hash(u64 x) {
static const u64 FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
x += FIXED_RANDOM;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return (x ^ (x >> 31)) & mask;
}
void extend() {
vc<pair<u64, Val>> dat;
dat.reserve(len(used) / 2 - cap);
FOR(i, len(used)) {
if (used[i]) dat.eb(key[i], val[i]);
}
build(2 * len(dat));
for (auto& [a, b]: dat) (*this)[a] = b;
}
};
#line 4 "graph/vs_to_es.hpp"
template <typename GT>
vc<int> vs_to_es(GT& G, vc<int>& vs, bool allow_use_twice = false) {
assert(!vs.empty());
HashMap<int> MP(G.M);
vc<int> nxt(G.M, -1);
auto get = [&](ll a, ll b) -> u64 {
if (!GT::is_directed && a > b) swap(a, b);
return a * G.N + b;
};
FOR(eid, G.M) {
u64 k = get(G.edges[eid].frm, G.edges[eid].to);
int x = MP.get(k, -1);
nxt[eid] = x, MP[k] = eid;
}
int n = len(vs);
vc<int> es(n - 1);
FOR(i, n - 1) {
u64 k = get(vs[i], vs[i + 1]);
int eid = MP.get(k, -1);
assert(eid != -1);
es[i] = eid;
if (!allow_use_twice) { MP[k] = nxt[eid]; }
}
return es;
}
#line 4 "graph/eulerwalk.hpp"
// (vs, es) or empty
template <typename GT>
pair<vc<int>, vc<int>> euler_walk(GT& G, int s = -1) {
const int N = G.N, M = G.M;
assert(G.is_prepared());
assert(N > 0);
if (s == -1) {
vc<int> deg(N);
for (auto&& e: G.edges) {
if constexpr (GT::is_directed) {
deg[e.frm]++, deg[e.to]--;
} else {
deg[e.frm]++, deg[e.to]++;
}
}
if constexpr (GT::is_directed) {
s = max_element(all(deg)) - deg.begin();
if (deg[s] == 0) s = (M == 0 ? 0 : G.edges[0].frm);
} else {
s = [&]() -> int {
FOR(v, N) if (deg[v] & 1) return v;
return (M == 0 ? 0 : G.edges[0].frm);
}();
}
}
if (M == 0) return {{s}, {}};
vc<int> D(N), its(N), eu(M), vs, st = {s};
FOR(v, N) its[v] = G.indptr[v];
++D[s];
while (!st.empty()) {
int x = st.back(), y, e, &it = its[x], end = G.indptr[x + 1];
if (it == end) {
vs.eb(x);
st.pop_back();
continue;
}
auto& ee = G.csr_edges[it++];
y = ee.to, e = ee.id;
if (!eu[e]) {
D[x]--, D[y]++;
eu[e] = 1;
st.eb(y);
}
}
for (auto&& x: D)
if (x < 0) return {{}, {}};
if (len(vs) != M + 1) return {{}, {}};
reverse(all(vs));
auto es = vs_to_es(G, vs, false);
return {vs, es};
}
template <typename GT>
bool has_euler_walk(GT& G, int s = -1) {
int N = G.N, M = G.M;
if (M == 0) return true;
if constexpr (!GT::is_directed) {
vc<int> odd(N);
for (auto& e: G.edges) odd[e.frm] ^= 1, odd[e.to] ^= 1;
int n_odd = 0;
for (auto x: odd) n_odd += x;
if (n_odd >= 4) return false;
if (s != -1 && n_odd == 2 && !odd[s]) return false;
UnionFind uf(N);
for (auto& e: G.edges) uf.merge(e.frm, e.to);
vector<int> cnt_edge(N);
for (auto& e: G.edges) cnt_edge[uf[e.frm]]++;
if (s != -1 && cnt_edge[uf[s]] == 0) return false;
// 辺がある成分を数える
int nc = 0;
for (int v = 0; v < N; ++v) {
if (uf[v] == v && cnt_edge[v] >= 1) ++nc;
}
return nc <= 1;
} else {
int N = G.N;
vc<int> in(N), out(N);
for (auto& e: G.edges) out[e.frm]++, in[e.to]++;
int ng = 0;
FOR(v, N) ng += abs(out[v] - in[v]);
if (ng >= 4) return false;
if (s != -1 && ng == 2 && out[s] != in[s] + 1) return false;
UnionFind uf(N);
for (auto& e: G.edges) uf.merge(e.frm, e.to);
vector<int> cnt_edge(N);
for (auto& e: G.edges) cnt_edge[uf[e.frm]]++;
if (s != -1 && cnt_edge[uf[s]] == 0) return false;
// 辺がある成分を数える
int nc = 0;
for (int v = 0; v < N; ++v) {
if (uf[v] == v && cnt_edge[v] >= 1) ++nc;
}
return nc <= 1;
}
}
#line 6 "test/5_atcoder/arc157a.test.cpp"
void solve() {
LL(N, A, B, C, D);
Graph<int, 1> G(2);
FOR(A) G.add(0, 0);
FOR(B) G.add(0, 1);
FOR(C) G.add(1, 0);
FOR(D) G.add(1, 1);
G.build();
auto vs = euler_walk(G).fi;
Yes(!vs.empty());
}
signed main() {
solve();
return 0;
}