competitive-programming-library
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test/yosupo/shortest_path.test.cpp
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- Last update: 2023-06-25 16:24:15+09:00
- Problem: https://judge.yosupo.jp/problem/shortest_path
Depends on
- Fast IO library
(basic/FastIO.hpp)
- basic/template.hpp
- Prioritizable Binary Heap
(data-structure/PrioritizableBinaryHeap.hpp)
- Dijkstra's algorithm
(graph/Dijkstra.hpp)
- graph/Graph.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"
#include "../../basic/template.hpp"
#include "../../basic/FastIO.hpp"
#include "../../graph/Dijkstra.hpp"
FastIO::Scanner cin;
FastIO::Printer cout;
int N, M, s, t, a, b, c;
int main() {
cin >> N >> M >> s >> t;
Graph<true, lint> g(N);
rep(i, M) {
cin >> a >> b >> c;
g.add_edge(a, b, c, 1);
}
Dijkstra<lint> d(g);
auto res = d.dist_and_path(s, t);
if (res.first == LLONG_MAX)
puts("-1");
else {
cout << res.first << ' ' << res.second.size() - 1 << '\n';
rep(i, res.second.size() - 1) cout << res.second[i] << ' '
<< res.second[i + 1] << '\n';
}
}#line 1 "test/yosupo/shortest_path.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"
#line 2 "basic/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()
using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;
constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON * 10;
constexpr double PI = 3.141592653589793238462643383279;
template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
int popcount(uint x) {
#if __cplusplus >= 202002L
return std::popcount(x);
#else
#ifndef __clang__
return __builtin_popcount(x);
#endif
#endif
x = (x & 0x55555555) + (x >> 1 & 0x55555555);
x = (x & 0x33333333) + (x >> 2 & 0x33333333);
x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
return [f = std::forward<F>(f)](auto&&... args) {
return f(f, std::forward<decltype(args)>(args)...);
};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
return std::vector<decltype(make_vec<T>(args...))>(n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U, class Stream>
Stream& operator>>(Stream& ist, std::pair<T, U>& x) {
return ist >> x.first >> x.second;
}
template <class T, class U, class Stream>
Stream& operator<<(Stream& ost, const std::pair<T, U>& x) {
return ost << x.first << " " << x.second;
}
template <class Container,
std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator>>(std::istream& ist, Container& cont)
-> decltype(typename Container::iterator(), std::cin)& {
Container tmp;
while (true) {
typename Container::value_type t;
ist >> t;
tmp.emplace_back(t);
if (getchar() == '\n') break;
}
cont = Container(std::move(tmp));
return ist;
}
template <class Container, class Stream,
std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator<<(Stream& ost, const Container& cont)
-> decltype(typename Container::iterator(), ost)& {
for (auto it = cont.begin(); it != cont.end(); it++) {
if (it != cont.begin()) ost << ' ';
ost << *it;
}
return ost;
}
template <class Container>
auto sum(const Container& cont) -> decltype(typename Container::iterator(), 0LL) {
lint res = 0;
for (auto it = cont.begin(); it != cont.end(); it++) res += *it;
return res;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
if (lhs < rhs) {
lhs = rhs;
return true;
}
return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
if (lhs > rhs) {
lhs = rhs;
return true;
}
return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
while (b) {
lint c = a;
a = b;
b = c % b;
}
return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
if (n == 1) return false;
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) return false;
}
return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
T res(1);
while (true) {
if (b & 1) res *= a;
b >>= 1;
if (!b) break;
a *= a;
}
return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
a %= m;
lint res(1);
while (b) {
if (b & 1) res *= a, res %= m;
a *= a, a %= m, b >>= 1;
}
return res;
}
LP extGcd(lint a, lint b) noexcept {
if (b == 0) return {1, 0};
LP s = extGcd(b, a % b);
std::swap(s.first, s.second);
s.second -= a / b * s.first;
return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) noexcept {
auto p = extGcd(m1, m2);
lint g = gcd(m1, m2), l = m1 / g * m2;
lint tmp = (b2 - b1) / g * p.first % (m2 / g);
lint r = (b1 + m1 * tmp + l) % l;
return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
rep(i, a.size()) {
rep(j, b.size()) {
chmax(dp[i + 1][j], dp[i][j]);
chmax(dp[i][j + 1], dp[i][j]);
if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
}
chmax(dp[i + 1][b.size()], dp[i][b.size()]);
}
rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value, std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
auto tmp = vec;
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
std::vector<T> tmp(l, r);
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (auto i = l; i < r; i++) {
*i = std::lower_bound(all(tmp), *i) - tmp.begin();
}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
std::vector<typename InputIter::value_type> tmp(l, r);
std::sort(all(tmp));
tmp.erase(std::unique(all(tmp)), tmp.end());
for (auto i = l; i < r; i++) {
*i = std::lower_bound(all(tmp), *i) - tmp.begin();
}
}
template <class InputIter,
std::enable_if_t<std::is_same<typename InputIter::value_type, std::pair<IP, int>>::value,
std::nullptr_t> = nullptr>
void mo_sort(InputIter l, InputIter r, int N) {
const int M = std::max(1.0, std::sqrt(lint(N) * N / std::distance(l, r)));
std::sort(l, r, [M](const auto& lhs, const auto& rhs) {
if (lhs.first.first / M < rhs.first.first / M) return true;
if (lhs.first.first / M == rhs.first.first / M) return lhs.first.second < rhs.first.second;
return false;
});
int before = -1, cnt = 0;
bool f = false;
for (InputIter i = l; i != r; i++) {
if (before != i->first.first / M) {
if (f) std::reverse(i - cnt, i);
f ^= true, before = i->first.first / M, cnt = 1;
} else
cnt++;
}
if (f) std::reverse(r - cnt, r);
}
template <class T>
std::vector<T> xor_bases(const std::vector<T>& vec) {
std::vector<T> res;
for (T i : vec) {
for (T j : res) {
chmin(i, i ^ j);
}
if (i) res.emplace_back(i);
}
return res;
}
#line 3 "basic/FastIO.hpp"
namespace FastIO {
static constexpr size_t buf_size = 1 << 18;
static constexpr size_t integer_size = 19;
static char inbuf[buf_size + 1] = {};
static char outbuf[buf_size + 1] = {};
class Scanner {
size_t pos = 0, end = buf_size;
void load() {
end = fread(inbuf, 1, buf_size, stdin);
inbuf[end] = '\0';
}
void ignore_space() {
while (inbuf[pos] <= ' ') {
if (__builtin_expect(++pos == end, 0)) reload();
}
}
char next() { return inbuf[pos++]; }
char next_nonspace() {
ignore_space();
return inbuf[pos++];
}
public:
Scanner() { load(); }
void reload() {
size_t length = end - pos;
memmove(inbuf, inbuf + pos, length);
end = length + fread(inbuf + length, 1, buf_size - length, stdin);
inbuf[end] = '\0';
pos = 0;
}
void scan() {}
void scan(char& c) { c = next_nonspace(); }
void scan(std::string& s) {
ignore_space();
s = "";
do {
size_t start = pos;
while (inbuf[pos] > ' ') pos++;
s += std::string(inbuf + start, inbuf + pos);
if (inbuf[pos] != '\0') break;
reload();
} while (true);
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
void scan(T& x) {
char c = next_nonspace();
if (__builtin_expect(pos + integer_size >= end, 0)) reload();
bool minus = false;
if (c == '-')
minus = true, x = 0;
else
x = c & 15;
while ((c = next()) >= '0') x = x * 10 + (c & 15);
if (minus) x = -x;
}
template <typename T, class... Args>
void scan(T& x, Args&... args) {
scan(x);
scan(args...);
}
template <typename T,
std::enable_if_t<std::is_same_v<T, char> || std::is_same_v<T, std::string> ||
std::is_integral_v<T>,
std::nullptr_t> = nullptr>
Scanner& operator>>(T& x) {
scan(x);
return *this;
}
};
class Printer {
static constexpr size_t block_size = 10000;
static const std::unique_ptr<char[]> block_str;
size_t pos = 0;
static constexpr lint powers[] = {1,
10,
100,
1000,
10000,
100000,
1000000,
10000000,
100000000,
1000000000,
10000000000,
100000000000,
1000000000000,
10000000000000,
100000000000000,
1000000000000000,
10000000000000000,
100000000000000000,
1000000000000000000};
static std::unique_ptr<char[]> precompute() {
std::unique_ptr<char[]> res(new char[block_size * 4]);
rep(i, block_size) {
size_t j = 4, k = i;
while (j--) {
res[i * 4 + j] = k % 10 + '0';
k /= 10;
}
}
return res;
}
template <typename T>
size_t integer_digits(T n) {
if (n >= powers[9]) {
if (n >= powers[13]) {
if (n >= powers[16]) {
if (n >= powers[17]) {
if (n >= powers[18]) return 19;
return 18;
}
return 17;
}
if (n >= powers[14]) {
if (n >= powers[15]) return 16;
return 15;
}
return 14;
}
if (n >= powers[11]) {
if (n >= powers[12]) return 13;
return 12;
}
if (n >= powers[10]) return 11;
return 10;
}
if (n >= powers[4]) {
if (n >= powers[7]) {
if (n >= powers[8]) return 9;
return 8;
}
if (n >= powers[5]) {
if (n >= powers[6]) return 7;
return 6;
}
return 5;
}
if (n >= powers[2]) {
if (n >= powers[3]) return 4;
return 3;
}
if (n >= powers[1]) return 2;
return 1;
}
public:
Printer() = default;
~Printer() { flush(); }
void flush() {
fwrite(outbuf, 1, pos, stdout);
pos = 0;
}
void print() {}
void print(char c) {
outbuf[pos++] = c;
if (__builtin_expect(pos == buf_size, 0)) flush();
}
void print(char* s) {
while (*s != 0) {
outbuf[pos++] = *s++;
if (pos == buf_size) flush();
}
}
void print(const std::string& x) {
for (char c : x) {
outbuf[pos++] = c;
if (pos == buf_size) flush();
}
}
template <typename T,
std::enable_if_t<std::is_integral<T>::value, std::nullptr_t> = nullptr>
void print(T x) {
if (__builtin_expect(pos + integer_size >= buf_size, 0)) flush();
if (x < 0) print('-'), x = -x;
size_t digit = integer_digits(x);
size_t len = digit;
while (len >= 4) {
len -= 4;
memcpy(outbuf + pos + len, block_str.get() + (x % block_size) * 4, 4);
x /= 10000;
}
memcpy(outbuf + pos, block_str.get() + x * 4 + 4 - len, len);
pos += digit;
}
template <typename T, class... Args>
void print(const T& x, const Args&... args) {
print(x);
print(' ');
print(args...);
}
template <class... Args>
void println(const Args&... args) {
print(args...);
print('\n');
}
template <typename T,
std::enable_if_t<std::is_same_v<T, char> || std::is_same_v<T, char*> ||
std::is_same_v<T, std::string> || std::is_integral_v<T>,
std::nullptr_t> = nullptr>
Printer& operator<<(const T& x) {
print(x);
return *this;
}
};
const std::unique_ptr<char[]> Printer::block_str = Printer::precompute();
}; // namespace FastIO
/**
* @title Fast IO library
*/
#line 3 "graph/Graph.hpp"
template <typename>
class Dijkstra;
template <bool weighted, typename W = std::conditional_t<weighted, int, void>>
class Graph {
size_t N;
std::vector<
std::vector<std::conditional_t<weighted, std::pair<int, W>, int>>>
vec;
using weight_type = W;
public:
Graph(int N_) : N(N_), vec(N_) {}
Graph(decltype(vec) v_) : N(v_.size()), vec(v_) {}
size_t size() const { return N; }
void add_edge(int s, int t, bool directed) {
if (directed)
vec[s].emplace_back(t);
else
vec[s].emplace_back(t), vec[t].emplace_back(s);
}
void add_edge(int s, int t, W w, bool directed) {
if (directed)
vec[s].emplace_back(t, w);
else
vec[s].emplace_back(t, w), vec[t].emplace_back(s, w);
}
Graph<weighted, W> rev() const {
Graph<weighted, W> res(N);
rep(i, N) {
for (const auto& j : vec[i]) {
#if __cplusplus >= 201703L
if constexpr (weighted)
#else
if (weighted)
#endif
res.vec[j.first].emplace_back(i, j.second);
else
res.vec[j].emplace_back(i);
}
}
return res;
}
friend Dijkstra<W>;
};
#line 3 "data-structure/PrioritizableBinaryHeap.hpp"
// assign priorities to indexed nodes
template <class T, class Compare = std::less<>>
class PrioritizableBinaryHeap {
std::vector<std::pair<int, T>> heap;
std::vector<int> rev;
Compare comp;
void up_heap(int id = -1) {
if (id == -1) id = heap.size() - 1;
while (id > 1) {
auto &vp = heap[id >> 1], &vx = heap[id];
if (comp(vp.second, vx.second)) {
std::swap(rev[vp.first], rev[vx.first]);
std::swap(vp, vx);
id >>= 1;
} else
return;
}
}
void down_heap(int id = 1) {
while ((id << 1) < heap.size()) {
int il = id << 1, ir = id << 1 | 1, swap = -1;
auto &vl = heap[il], &vx = heap[id];
if (comp(vx.second, vl.second)) swap = il;
if (ir < heap.size()) {
auto& vr = heap[ir];
if (comp(vx.second, vr.second)) {
if (swap == -1 || comp(vl.second, vr.second)) swap = ir;
}
}
if (swap == -1) return;
std::swap(rev[vx.first], rev[heap[swap].first]);
std::swap(vx, heap[swap]);
id = swap;
}
}
public:
PrioritizableBinaryHeap(int n) : heap(1), rev(n, -1) {}
[[nodiscard]] bool empty() const noexcept { return heap.size() == 1; }
[[nodiscard]] size_t size() const noexcept { return heap.size() - 1; }
[[nodiscard]] auto top() const noexcept { return heap[1]; }
auto pop() {
const auto tmp = heap[1];
rev[heap.back().first] = 1;
rev[heap[1].first] = -1;
heap[1] = std::move(heap.back());
heap.pop_back();
down_heap();
return tmp;
}
void push(int id, const T& x) {
rev[id] = heap.size();
heap.emplace_back(id, x);
up_heap();
}
void prioritize(int id, const T& x) {
if (heap[rev[id]].second > x)
decrease_key(id, x);
else
increase_key(id, x);
}
void decrease_key(int id, const T& x) {
if (rev[id] == -1) {
push(id, x);
return;
}
heap[rev[id]].second = x;
down_heap(rev[id]);
}
void increase_key(int id, const T& x) {
if (rev[id] == -1) {
push(id, x);
return;
}
heap[rev[id]].second = x;
up_heap(rev[id]);
}
};
/**
* @title Prioritizable Binary Heap
*/
#line 5 "graph/Dijkstra.hpp"
template <typename W>
class Dijkstra {
Graph<true, W> G;
public:
Dijkstra() {}
Dijkstra(const Graph<true, W>& G_) : G(G_) {}
Dijkstra(Graph<true, W>&& G_) : G(G_) {}
void set(const Graph<true, W>& G_) { G = G_; }
std::vector<W> operator()(int s) {
std::vector<W> dist(G.N, std::numeric_limits<W>::max());
dist[s] = 0;
PrioritizableBinaryHeap<W, std::greater<W>> que(G.N);
que.push(s, 0);
while (!que.empty()) {
auto p = que.pop();
for (const auto& i : G.vec[p.first]) {
if (chmin(dist[i.first], p.second + i.second))
que.increase_key(i.first, dist[i.first]);
}
}
return dist;
}
W operator()(int s, int t) {
std::vector<W> dist(G.N, std::numeric_limits<W>::max());
dist[s] = 0;
PrioritizableBinaryHeap<W, std::greater<W>> que(G.N);
que.push(s, 0);
while (!que.empty()) {
auto p = que.pop();
if (p.first == t) break;
for (const auto& i : G.vec[p.first]) {
if (chmin(dist[i.first], p.second + i.second))
que.increase_key(i.first, dist[i.first]);
}
}
return dist[t];
}
std::pair<W, std::vector<int>> dist_and_path(int s, int t) {
std::vector<W> from(G.N), dist(G.N, std::numeric_limits<W>::max());
dist[s] = 0;
PrioritizableBinaryHeap<W, std::greater<W>> que(G.N);
que.push(s, 0);
while (!que.empty()) {
auto p = que.top();
que.pop();
if (p.first == t) break;
for (auto i : G.vec[p.first]) {
if (chmin(dist[i.first], p.second + i.second)) {
from[i.first] = p.first;
que.increase_key(i.first, dist[i.first]);
}
}
}
if (dist[t] == std::numeric_limits<W>::max()) return {dist[t], {}};
W res_dist = dist[t];
std::vector<int> res_vec = {t};
while (t != s) res_vec.emplace_back(t = from[t]);
std::reverse(all(res_vec));
return {res_dist, res_vec};
}
};
/**
* @title Dijkstra's algorithm
*/
#line 5 "test/yosupo/shortest_path.test.cpp"
FastIO::Scanner cin;
FastIO::Printer cout;
int N, M, s, t, a, b, c;
int main() {
cin >> N >> M >> s >> t;
Graph<true, lint> g(N);
rep(i, M) {
cin >> a >> b >> c;
g.add_edge(a, b, c, 1);
}
Dijkstra<lint> d(g);
auto res = d.dist_and_path(s, t);
if (res.first == LLONG_MAX)
puts("-1");
else {
cout << res.first << ' ' << res.second.size() - 1 << '\n';
rep(i, res.second.size() - 1) cout << res.second[i] << ' '
<< res.second[i + 1] << '\n';
}
}