This documentation is automatically generated by competitive-verifier/competitive-verifier
// @brief Minimum Spanning Tree
#define PROBLEM "https://judge.yosupo.jp/problem/minimum_spanning_tree"
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
#include "cp-algo/graph/mst.hpp"
#include <bits/stdc++.h>
using namespace std;
using namespace cp_algo::graph;
void solve() {
int n, m;
cin >> n >> m;
weighted_graph g(n);
g.read_edges(m);
auto [X, E] = mst(g);
cout << X << "\n";
for(int e: E) {cout << e << " ";}
}
signed main() {
//freopen("input.txt", "r", stdin);
ios::sync_with_stdio(0);
cin.tie(0);
int t = 1;
//cin >> t;
while(t--) {
solve();
}
}
#line 1 "verify/graph/mst.test.cpp"
// @brief Minimum Spanning Tree
#define PROBLEM "https://judge.yosupo.jp/problem/minimum_spanning_tree"
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
#line 1 "cp-algo/graph/mst.hpp"
#line 1 "cp-algo/graph/base.hpp"
#line 1 "cp-algo/graph/edge_types.hpp"
#include <iostream>
#include <cstdint>
namespace cp_algo::graph {
using node_index = int;
struct edge_base {
int xor_nodes;
edge_base() {}
edge_base(node_index from, node_index to): xor_nodes(from ^ to) {}
// Given one endpoint, return the other
node_index traverse(node_index from) const {
return xor_nodes ^ from;
}
static auto read(node_index v0 = 0) {
node_index u, v;
std::cin >> u >> v;
u -= v0;
v -= v0;
return std::pair{u, edge_base(u, v)};
}
};
struct weighted_edge: edge_base {
int64_t w;
weighted_edge() {}
weighted_edge(node_index from, node_index to, int64_t w): edge_base(from, to), w(w) {}
static auto read(node_index v0 = 0) {
auto [u, e] = edge_base::read(v0);
int64_t w;
std::cin >> w;
return std::pair{u, weighted_edge(u, e.traverse(u), w)};
}
};
template<typename edge>
concept edge_type = std::is_base_of_v<edge_base, edge>;
template<typename edge>
concept weighted_edge_type = std::is_base_of_v<weighted_edge, edge>;
}
#line 1 "cp-algo/graph/concepts.hpp"
#line 4 "cp-algo/graph/concepts.hpp"
#include <type_traits>
namespace cp_algo::graph {
// Shared graph mode enum for all graph headers
enum graph_mode { directed, undirected };
// Traits: true for types that expose `edge_t` and static `mode`
template<typename T, typename = void>
struct graph_traits : std::false_type {};
template<typename T>
requires requires { typename T::edge_t; T::mode; }
struct graph_traits<T> : std::true_type {
using edge_t = typename T::edge_t;
static constexpr auto mode = T::mode;
static constexpr bool is_directed = mode == directed;
static constexpr bool is_undirected = mode == undirected;
static constexpr bool is_weighted = weighted_edge_type<edge_t>;
};
// Concepts
template<typename G>
concept graph_type = graph_traits<G>::value;
template<typename G>
concept digraph_type = graph_type<G> && graph_traits<G>::is_directed;
template<typename G>
concept undirected_graph_type = graph_type<G> && graph_traits<G>::is_undirected;
template<typename G>
concept weighted_graph_type = graph_type<G> && graph_traits<G>::is_weighted;
template<typename G>
concept weighted_digraph_type = digraph_type<G> && graph_traits<G>::is_weighted;
template<typename G>
concept weighted_undirected_graph_type = undirected_graph_type<G> && graph_traits<G>::is_weighted;
}
#line 1 "cp-algo/structures/stack_union.hpp"
#line 1 "cp-algo/util/big_alloc.hpp"
#include <set>
#include <map>
#include <deque>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#include <cstddef>
#include <bit>
#line 14 "cp-algo/util/big_alloc.hpp"
#include <forward_list>
// Single macro to detect POSIX platforms (Linux, Unix, macOS)
#if defined(__linux__) || defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
#define CP_ALGO_USE_MMAP 1
#include <sys/mman.h>
#else
#define CP_ALGO_USE_MMAP 0
#endif
namespace cp_algo {
template<typename T, size_t Align = 32>
class big_alloc {
static_assert(Align >= alignof(void*), "Align must be at least pointer-size");
static_assert(std::has_single_bit(Align), "Align must be a power of two");
public:
using value_type = T;
template<class U>
struct rebind {
using other = big_alloc<U, Align>;
};
constexpr bool operator==(const big_alloc&) const = default;
big_alloc() noexcept = default;
template<typename U, std::size_t A>
big_alloc(const big_alloc<U, A>&) noexcept {}
[[nodiscard]] T* allocate(std::size_t n) {
std::size_t padded = round_up(n * sizeof(T));
std::size_t align = std::max<std::size_t>(alignof(T), Align);
#if CP_ALGO_USE_MMAP
if(padded >= MEGABYTE) {
void* raw = mmap(nullptr, padded, PROT_READ | PROT_WRITE, MAP_PRIVATE | MAP_ANONYMOUS, -1, 0);
madvise(raw, padded, MADV_HUGEPAGE);
return static_cast<T*>(raw);
}
#endif
return static_cast<T*>(::operator new(padded, std::align_val_t(align)));
}
void deallocate(T* p, std::size_t n) noexcept {
if(!p) {
return;
}
std::size_t padded = round_up(n * sizeof(T));
std::size_t align = std::max<std::size_t>(alignof(T), Align);
#if CP_ALGO_USE_MMAP
if(padded >= MEGABYTE) {
munmap(p, padded);
return;
}
#endif
::operator delete(p, padded, std::align_val_t(align));
}
private:
static constexpr std::size_t MEGABYTE = 1 << 20;
static constexpr std::size_t round_up(std::size_t x) noexcept {
return (x + Align - 1) / Align * Align;
}
};
template<typename T>
using big_vector = std::vector<T, big_alloc<T>>;
template<typename T>
using big_basic_string = std::basic_string<T, std::char_traits<T>, big_alloc<T>>;
template<typename T>
using big_deque = std::deque<T, big_alloc<T>>;
template<typename T>
using big_stack = std::stack<T, big_deque<T>>;
template<typename T>
using big_queue = std::queue<T, big_deque<T>>;
template<typename T>
using big_priority_queue = std::priority_queue<T, big_vector<T>>;
template<typename T>
using big_forward_list = std::forward_list<T, big_alloc<T>>;
using big_string = big_basic_string<char>;
template<typename Key, typename Value, typename Compare = std::less<Key>>
using big_map = std::map<Key, Value, Compare, big_alloc<std::pair<const Key, Value>>>;
template<typename T, typename Compare = std::less<T>>
using big_multiset = std::multiset<T, Compare, big_alloc<T>>;
template<typename T, typename Compare = std::less<T>>
using big_set = std::set<T, Compare, big_alloc<T>>;
}
#line 5 "cp-algo/structures/stack_union.hpp"
#include <iterator>
#include <ranges>
namespace cp_algo::structures {
template<class datatype>
struct stack_union {
stack_union(int n = 0): head(n), next(1), data(1) {}
void push(int v, datatype const& vdata) {
next.push_back(head[v]);
head[v] = (int)std::size(next) - 1;
data.push_back(vdata);
}
template<typename... Args>
void emplace(int v, Args&&... vdata) {
next.push_back(head[v]);
head[v] = (int)std::size(next) - 1;
data.emplace_back(std::forward<Args>(vdata)...);
}
void reserve(int m) {
data.reserve(m);
next.reserve(m);
}
size_t size() const {return std::size(head);}
size_t nodes() const {return std::size(data);}
template<typename Su>
struct _iterator {
using value_type = std::conditional_t<std::is_const_v<Su>, const datatype, datatype>;
using difference_type = std::ptrdiff_t;
Su* su = nullptr;
int sv = 0;
value_type& operator*() const { return su->data[sv]; }
_iterator& operator++() {
sv = su->next[sv];
return *this;
}
_iterator operator++(int) { auto tmp = *this; ++*this; return tmp; }
friend bool operator==(_iterator const& it, std::default_sentinel_t) {
return it.sv == 0;
}
};
using iterator = _iterator<stack_union<datatype>>;
using const_iterator = _iterator<const stack_union<datatype>>;
auto operator[](this auto&& self, int v) {
using Iter = _iterator<std::remove_reference_t<decltype(self)>>;
return std::ranges::subrange(Iter{&self, self.head[v]}, std::default_sentinel);
}
big_vector<int> head, next;
big_vector<datatype> data;
};
}
#line 7 "cp-algo/graph/base.hpp"
namespace cp_algo::graph {
using edge_index = int;
template<edge_type _edge_t = edge_base, graph_mode _mode = undirected>
struct graph {
using edge_t = _edge_t;
static constexpr auto mode = _mode;
using incidence_list = structures::stack_union<edge_index>;
graph(int n, int v0 = 0): v0(v0), adj(n) {}
graph transpose() const {
static_assert(mode == directed, "transpose is only defined for directed graphs");
graph<edge_t, mode> gt(n(), v0);
for(auto v: nodes()) {
for(auto e: outgoing(v)) {
gt.add_edge(edge(e).traverse(v), edge(e));
}
}
return gt;
}
edge_index add_edge(node_index u, edge_t e) {
edge_index idx = (edge_index)size(E);
E.push_back(e);
adj.push(u, idx);
if constexpr (mode == undirected) {
adj.push(e.traverse(u), idx);
}
return idx;
}
edge_index add_edge(node_index u, auto... Args) {
return add_edge(u, edge_t(u, Args...));
}
void read_edges(node_index m) {
adj.reserve(mode == undirected ? 2 * m : m);
for(edge_index i = 0; i < m; i++) {
auto [u, e] = edge_t::read(v0);
add_edge(u, e);
}
}
auto outgoing(node_index v) const {return adj[v];}
auto edges() const {return E | std::views::all;}
auto nodes() const {return std::views::iota(node_index(0), n());}
auto edge_indices() const {return std::views::iota(edge_index(0), m());}
auto&& incidence_lists(this auto&& self) {return self.adj;}
auto&& edge(this auto&& self, edge_index e) {return self.E[e];}
node_index n() const {return (node_index)incidence_lists().size();}
edge_index m() const {return (edge_index)edges().size();}
private:
node_index v0;
big_vector<edge_t> E;
incidence_list adj;
};
// aliases for most standard cases
template<edge_type edge_t = edge_base>
using digraph = graph<edge_t, directed>;
template<weighted_edge_type edge_t = weighted_edge, graph_mode mode = undirected>
using weighted_graph = graph<edge_t, mode>;
template<weighted_edge_type edge_t = weighted_edge>
using weighted_digraph = digraph<edge_t>;
}
#line 1 "cp-algo/structures/dsu.hpp"
#line 4 "cp-algo/structures/dsu.hpp"
#include <numeric>
#line 6 "cp-algo/structures/dsu.hpp"
namespace cp_algo::structures {
struct disjoint_set_union {
disjoint_set_union (int n): par(n) {
std::iota(begin(par), end(par), 0);
}
int get(int v) {
return v == par[v] ? v : par[v] = get(par[v]);
}
bool uni(int a, int b) {
a = get(a);
b = get(b);
par[a] = b;
return a != b;
}
private:
big_vector<int> par;
};
using dsu = disjoint_set_union;
}
#line 1 "cp-algo/util/sort.hpp"
#line 1 "cp-algo/util/bit.hpp"
#line 1 "cp-algo/util/simd.hpp"
#include <experimental/simd>
#line 6 "cp-algo/util/simd.hpp"
#include <memory>
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_SIMD_AVX2_TARGET _Pragma("GCC target(\"avx2,fma\")")
#else
#define CP_ALGO_SIMD_AVX2_TARGET
#endif
#define CP_ALGO_SIMD_PRAGMA_PUSH \
_Pragma("GCC push_options") \
CP_ALGO_SIMD_AVX2_TARGET
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo {
template<typename T, size_t len>
using simd [[gnu::vector_size(len * sizeof(T))]] = T;
using u64x8 = simd<uint64_t, 8>;
using u32x16 = simd<uint32_t, 16>;
using i64x4 = simd<int64_t, 4>;
using u64x4 = simd<uint64_t, 4>;
using u32x8 = simd<uint32_t, 8>;
using u16x16 = simd<uint16_t, 16>;
using i32x4 = simd<int32_t, 4>;
using u32x4 = simd<uint32_t, 4>;
using u16x8 = simd<uint16_t, 8>;
using u16x4 = simd<uint16_t, 4>;
using i16x4 = simd<int16_t, 4>;
using u8x32 = simd<uint8_t, 32>;
using u8x16 = simd<uint8_t, 16>;
using u8x8 = simd<uint8_t, 8>;
using u8x4 = simd<uint8_t, 4>;
using dx4 = simd<double, 4>;
inline dx4 abs(dx4 a) {
return dx4{
std::abs(a[0]),
std::abs(a[1]),
std::abs(a[2]),
std::abs(a[3])
};
}
// https://stackoverflow.com/a/77376595
// works for ints in (-2^51, 2^51)
static constexpr dx4 magic = dx4() + (3ULL << 51);
inline i64x4 lround(dx4 x) {
return i64x4(x + magic) - i64x4(magic);
}
inline dx4 to_double(i64x4 x) {
return dx4(x + i64x4(magic)) - magic;
}
inline dx4 round(dx4 a) {
return dx4{
std::nearbyint(a[0]),
std::nearbyint(a[1]),
std::nearbyint(a[2]),
std::nearbyint(a[3])
};
}
inline u64x4 low32(u64x4 x) {
return x & uint32_t(-1);
}
inline auto swap_bytes(auto x) {
return decltype(x)(__builtin_shufflevector(u32x8(x), u32x8(x), 1, 0, 3, 2, 5, 4, 7, 6));
}
inline u64x4 montgomery_reduce(u64x4 x, uint32_t mod, uint32_t imod) {
#ifdef __AVX2__
auto x_ninv = u64x4(_mm256_mul_epu32(__m256i(x), __m256i() + imod));
x += u64x4(_mm256_mul_epu32(__m256i(x_ninv), __m256i() + mod));
#else
auto x_ninv = u64x4(u32x8(low32(x)) * imod);
x += x_ninv * uint64_t(mod);
#endif
return swap_bytes(x);
}
// x - mod where x >= mod, for x in [0, 2 mod). Unsigned, so it holds up to mod < 2^31;
// zero upper halves of 64-bit lanes stay zero.
inline u32x8 reduce_once(u32x8 x, uint32_t mod) {
auto y = x - mod;
return x < y ? x : y;
}
inline u64x4 reduce_once(u64x4 x, uint32_t mod) {
return u64x4(reduce_once(u32x8(x), mod));
}
inline u64x4 montgomery_mul(u64x4 x, u64x4 y, uint32_t mod, uint32_t imod) {
#ifdef __AVX2__
return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x), __m256i(y))), mod, imod);
#else
return montgomery_reduce(x * y, mod, imod);
#endif
}
inline u32x8 montgomery_mul(u32x8 x, u32x8 y, uint32_t mod, uint32_t imod) {
return u32x8(montgomery_mul(u64x4(x), u64x4(y), mod, imod)) |
u32x8(swap_bytes(montgomery_mul(u64x4(swap_bytes(x)), u64x4(swap_bytes(y)), mod, imod)));
}
inline dx4 rotate_right(dx4 x) {
static constexpr u64x4 shuffler = {3, 0, 1, 2};
return __builtin_shuffle(x, shuffler);
}
template<std::size_t Align = 32>
inline bool is_aligned(const auto *p) noexcept {
return (reinterpret_cast<std::uintptr_t>(p) % Align) == 0;
}
template<class Target>
inline Target& vector_cast(auto &&p) {
return *reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));
}
}
#pragma GCC pop_options
#line 6 "cp-algo/util/bit.hpp"
#include <array>
#line 8 "cp-algo/util/bit.hpp"
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_BIT_OPS_TARGET _Pragma("GCC target(\"avx2,bmi,bmi2,lzcnt,popcnt\")")
#else
#define CP_ALGO_BIT_OPS_TARGET _Pragma("GCC target(\"bmi,bmi2,lzcnt,popcnt\")")
#endif
#define CP_ALGO_BIT_PRAGMA_PUSH \
_Pragma("GCC push_options") \
CP_ALGO_BIT_OPS_TARGET
CP_ALGO_BIT_PRAGMA_PUSH
namespace cp_algo {
template<typename Uint>
constexpr size_t bit_width = sizeof(Uint) * 8;
// n < 64
uint64_t mask(size_t n) {
return (1ULL << n) - 1;
}
size_t order_of_bit(auto x, size_t k) {
return k ? std::popcount(x << (bit_width<decltype(x)> - k)) : 0;
}
inline size_t kth_set_bit(uint64_t x, size_t k) {
return std::countr_zero(_pdep_u64(1ULL << k, x));
}
template<int fl = 0>
void with_bit_floor(size_t n, auto &&callback) {
if constexpr (fl >= 63) {
return;
} else if (n >> (fl + 1)) {
with_bit_floor<fl + 1>(n, callback);
} else {
callback.template operator()<1ULL << fl>();
}
}
void with_bit_ceil(size_t n, auto &&callback) {
with_bit_floor(n, [&]<size_t N>() {
if(N == n) {
callback.template operator()<N>();
} else {
callback.template operator()<N << 1>();
}
});
}
inline uint32_t read_bits(char const* p) {
return _mm256_movemask_epi8(__m256i(vector_cast<u8x32 const>(p[0]) + (127 - '0')));
}
inline uint64_t read_bits64(char const* p) {
return read_bits(p) | (uint64_t(read_bits(p + 32)) << 32);
}
inline void write_bits(char *p, uint32_t bits) {
static constexpr u8x32 shuffler = {
0, 0, 0, 0, 0, 0, 0, 0,
1, 1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2, 2,
3, 3, 3, 3, 3, 3, 3, 3
};
auto shuffled = u8x32(_mm256_shuffle_epi8(__m256i() + bits, __m256i(shuffler)));
static constexpr u8x32 mask = {
1, 2, 4, 8, 16, 32, 64, 128,
1, 2, 4, 8, 16, 32, 64, 128,
1, 2, 4, 8, 16, 32, 64, 128,
1, 2, 4, 8, 16, 32, 64, 128
};
for(int z = 0; z < 32; z++) {
p[z] = shuffled[z] & mask[z] ? '1' : '0';
}
}
inline void write_bits64(char *p, uint64_t bits) {
write_bits(p, uint32_t(bits));
write_bits(p + 32, uint32_t(bits >> 32));
}
}
#pragma GCC pop_options
#line 4 "cp-algo/util/sort.hpp"
#include <algorithm>
#line 8 "cp-algo/util/sort.hpp"
namespace cp_algo {
template<size_t maxc>
void count_sort(auto &a, auto &&proj) {
std::array<int, maxc> cnt = {};
for(auto &x: a) {
cnt[proj(x)]++;
}
std::partial_sum(begin(cnt), end(cnt), begin(cnt));
auto res = a;
for(auto const& it: a | std::views::reverse) {
res[--cnt[proj(it)]] = it;
}
a = std::move(res);
}
template<size_t maxc>
void count_sort(auto &a) {
count_sort<maxc>(a, std::identity{});
}
void radix_sort(auto &a, auto &&proj) {
if(empty(a)) {
return;
}
auto [mn, mx] = std::ranges::minmax(a, {}, proj);
with_bit_floor<1>(size(a), [&]<size_t floor>() {
constexpr int base = std::min<size_t>(floor, 1 << 16);
for(int64_t i = 1; i <= std::invoke(proj, mx) - std::invoke(proj, mn); i *= base) {
count_sort<base>(a, [&](auto const& x) {
return (std::invoke(proj, x) - std::invoke(proj, mn)) / i % base;
});
}
});
}
void radix_sort(auto &a) {
radix_sort(a, std::identity{});
}
}
#line 7 "cp-algo/graph/mst.hpp"
namespace cp_algo::graph {
template<weighted_undirected_graph_type graph>
std::pair<int64_t, big_vector<edge_index>> mst(graph const& g) {
struct edge {
edge_index idx;
node_index v;
};
big_vector<edge> edges;
for(auto v: g.nodes()) {
for(auto e: g.outgoing(v)) {
if (v < g.edge(e).traverse(v)) {
edges.push_back({e, v});
}
}
}
radix_sort(edges, [&](auto e) {
return g.edge(e.idx).w;
});
structures::dsu me(g.n());
int64_t total = 0;
big_vector<edge_index> mst;
for(auto [idx, v]: edges) {
if(me.uni(v, g.edge(idx).traverse(v))) {
total += g.edge(idx).w;
mst.push_back(idx);
}
}
return {total, std::move(mst)};
}
}
#line 6 "verify/graph/mst.test.cpp"
#include <bits/stdc++.h>
using namespace std;
using namespace cp_algo::graph;
void solve() {
int n, m;
cin >> n >> m;
weighted_graph g(n);
g.read_edges(m);
auto [X, E] = mst(g);
cout << X << "\n";
for(int e: E) {cout << e << " ";}
}
signed main() {
//freopen("input.txt", "r", stdin);
ios::sync_with_stdio(0);
cin.tie(0);
int t = 1;
//cin >> t;
while(t--) {
solve();
}
}
| Env | Name | Status | Elapsed | Memory |
|---|---|---|---|---|
| g++ | complete_max_00 |
|
86 ms | 31 MB |
| g++ | complete_max_01 |
|
86 ms | 31 MB |
| g++ | complete_random_00 |
|
2 ms | 4 MB |
| g++ | complete_random_01 |
|
2 ms | 4 MB |
| g++ | complete_random_02 |
|
3 ms | 4 MB |
| g++ | complete_random_03 |
|
8 ms | 5 MB |
| g++ | complete_random_04 |
|
25 ms | 10 MB |
| g++ | example_00 |
|
2 ms | 4 MB |
| g++ | example_01 |
|
2 ms | 4 MB |
| g++ | example_02 |
|
2 ms | 4 MB |
| g++ | max_random_00 |
|
143 ms | 34 MB |
| g++ | max_random_01 |
|
142 ms | 34 MB |
| g++ | max_random_02 |
|
143 ms | 34 MB |
| g++ | max_random_03 |
|
142 ms | 34 MB |
| g++ | max_random_04 |
|
142 ms | 34 MB |
| g++ | random_00 |
|
116 ms | 30 MB |
| g++ | random_01 |
|
141 ms | 33 MB |
| g++ | random_02 |
|
95 ms | 30 MB |
| g++ | random_03 |
|
128 ms | 31 MB |
| g++ | random_04 |
|
103 ms | 27 MB |
| g++ | small_00 |
|
79 ms | 28 MB |
| g++ | small_01 |
|
81 ms | 28 MB |
| g++ | small_02 |
|
74 ms | 25 MB |
| g++ | small_03 |
|
7 ms | 5 MB |
| g++ | small_04 |
|
22 ms | 9 MB |
| g++ | small_c01_00 |
|
2 ms | 4 MB |
| g++ | small_c01_01 |
|
2 ms | 4 MB |
| g++ | small_c01_02 |
|
2 ms | 4 MB |
| g++ | small_c01_03 |
|
2 ms | 4 MB |
| g++ | small_c01_04 |
|
2 ms | 4 MB |
| g++ | star_00 |
|
116 ms | 34 MB |