#line 1 "verify/verify-aoj-grl/aoj-grl-1-a-fast-dijkstra.test.cpp"
#define PROBLEM \
"http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_A"
#line 2 "template/template.hpp"
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(vector<T> &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
} // namespace Nyaan
#line 58 "template/template.hpp"
// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
#line 61 "template/template.hpp"
// inout
#line 1 "template/inout.hpp"
namespace Nyaan {
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;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
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...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
#line 64 "template/template.hpp"
// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t t) {
if (t == 0) cerr << 0;
if (t < 0) cerr << '-', t = -t;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
void dump(__uint128_t t) {
if (t == 0) cerr << 0;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
cerr << " ";
dump(head);
if (sizeof...(tail) != 0) cerr << ",";
trace(forward<Tail>(tail)...);
}
} // namespace DebugImpl
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"
// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
#line 70 "template/template.hpp"
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 2 "shortest-path/dijkstra-fast.hpp"
#line 2 "data-structure/radix-heap.hpp"
template <typename Key, typename Val>
struct RadixHeap {
using uint = typename make_unsigned<Key>::type;
static constexpr int bit = sizeof(Key) * 8;
array<vector<pair<uint, Val> >, bit + 1> vs;
array<uint, bit + 1> ms;
int s;
uint last;
RadixHeap() : s(0), last(0) { fill(begin(ms), end(ms), uint(-1)); }
bool empty() const { return s == 0; }
int size() const { return s; }
__attribute__((target("lzcnt"))) inline uint64_t getbit(uint a) const {
return 64 - _lzcnt_u64(a);
}
void push(const uint &key, const Val &val) {
s++;
uint64_t b = getbit(key ^ last);
vs[b].emplace_back(key, val);
ms[b] = min(key, ms[b]);
}
pair<uint, Val> pop() {
if (ms[0] == uint(-1)) {
int idx = 1;
while (ms[idx] == uint(-1)) idx++;
last = ms[idx];
for (auto &p : vs[idx]) {
uint64_t b = getbit(p.first ^ last);
vs[b].emplace_back(p);
ms[b] = min(p.first, ms[b]);
}
vs[idx].clear();
ms[idx] = uint(-1);
}
--s;
auto res = vs[0].back();
vs[0].pop_back();
if (vs[0].empty()) ms[0] = uint(-1);
return res;
}
};
/**
* @brief Radix Heap
* @docs docs/data-structure/radix-heap.md
*/
#line 2 "graph/static-graph.hpp"
namespace StaticGraphImpl {
template <typename T, bool Cond = is_void<T>::value>
struct E;
template <typename T>
struct E<T, false> {
int to;
T cost;
E() {}
E(const int& v, const T& c) : to(v), cost(c) {}
operator int() const { return to; }
};
template <typename T>
struct E<T, true> {
int to;
E() {}
E(const int& v) : to(v) {}
operator int() const { return to; }
};
template <typename T = void>
struct StaticGraph {
private:
template <typename It>
struct Es {
It b, e;
It begin() const { return b; }
It end() const { return e; }
int size() const { return int(e - b); }
auto&& operator[](int i) const { return b[i]; }
};
int N, M, ec;
vector<int> head;
vector<pair<int, E<T>>> buf;
vector<E<T>> es;
void build() {
partial_sum(begin(head), end(head), begin(head));
es.resize(M);
for (auto&& [u, e] : buf) es[--head[u]] = e;
}
public:
StaticGraph(int _n, int _m) : N(_n), M(_m), ec(0), head(N + 1, 0) {
buf.reserve(M);
}
template <typename... Args>
void add_edge(int u, Args&&... args) {
#pragma GCC diagnostic ignored "-Wnarrowing"
buf.emplace_back(u, E<T>{std::forward<Args>(args)...});
#pragma GCC diagnostic warning "-Wnarrowing"
++head[u];
if ((int)buf.size() == M) build();
}
Es<typename vector<E<T>>::iterator> operator[](int u) {
return {begin(es) + head[u], begin(es) + head[u + 1]};
}
const Es<typename vector<E<T>>::const_iterator> operator[](int u) const {
return {begin(es) + head[u], begin(es) + head[u + 1]};
}
int size() const { return N; }
};
} // namespace StaticGraphImpl
using StaticGraphImpl::StaticGraph;
/**
* @brief Static Graph
* @docs docs/graph/static-graph.md
*/
#line 5 "shortest-path/dijkstra-fast.hpp"
template <typename T>
vector<T> dijkstra(StaticGraph<T>& g, int start = 0) {
vector<T> d(g.size(), T(-1));
RadixHeap<T, int> Q;
d[start] = 0;
Q.push(0, start);
while (!Q.empty()) {
auto p = Q.pop();
int u = p.second;
if (d[u] < T(p.first)) continue;
T du = d[u];
for (auto&& [v, c] : g[u]) {
if (d[v] == T(-1) || du + c < d[v]) {
d[v] = du + c;
Q.push(d[v], v);
}
}
}
return d;
}
template <typename T>
T dijkstra_point(StaticGraph<T>& g, int start, int goal) {
vector<T> d(g.size(), T(-1));
RadixHeap<T, int> Q;
d[start] = 0;
Q.push(0, start);
while (!Q.empty()) {
auto p = Q.pop();
int u = p.second;
if(u == goal) return d[u];
if (d[u] < T(p.first)) continue;
T du = d[u];
for (auto&& [v, c] : g[u]) {
if (d[v] == T(-1) || du + c < d[v]) {
d[v] = du + c;
Q.push(d[v], v);
}
}
}
return -1;
}
template <typename T>
vector<pair<T, int>> dijkstra_restore(StaticGraph<T>& g, int start = 0) {
vector<pair<T, int>> d(g.size(), {T(-1), -1});
RadixHeap<T, int> Q;
d[start] = {0, -1};
Q.push(0, start);
while (!Q.empty()) {
auto p = Q.pop();
int u = p.second;
if (d[u].first < T(p.first)) continue;
T du = d[u].first;
for (auto&& [v, c] : g[u]) {
if (d[v].first == T(-1) || du + c < d[v].first) {
d[v] = {du + c, u};
Q.push(du + c, v);
}
}
}
return d;
}
/*
* @brief ダイクストラ法(定数倍高速化)
* @docs docs/shortest-path/dijkstra-fast.md
**/
#line 6 "verify/verify-aoj-grl/aoj-grl-1-a-fast-dijkstra.test.cpp"
using namespace Nyaan; void Nyaan::solve() {
ini(N, E, S);
StaticGraph<int> g(N, E);
rep(i, E) {
ini(s, t, d);
g.add_edge(s, t, d);
}
auto d = dijkstra(g, S);
d.resize(N);
each(x, d) {
if (x == -1)
out("INF");
else
out(x);
}
}
verify/verify-aoj-grl/aoj-grl-1-a-fast-dijkstra.test.cpp