cplib-cpp
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data_structure/test/fibonacci_heap_shortestpath.test.cpp
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- Last update: 2022-01-08 20:23:44+09:00
- Problem: https://judge.yosupo.jp/problem/shortest_path
Depends on
Code
#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"
#include "../fibonacci_heap.hpp"
#include <iostream>
#include <stack>
#include <utility>
#include <vector>
int main() {
std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
int N, M, s, t;
std::cin >> N >> M >> s >> t;
using P = std::pair<long long, int>;
fibonacci_heap<P> heap;
constexpr long long INF = 1e18;
std::vector<long long> D(N, INF);
std::vector<int> prev(N, -1);
D[s] = 0;
std::vector<fibonacci_heap<P>::Node *> handler(N);
for (int i = 0; i < N; i++) { handler[i] = heap.push(std::make_pair(D[i], i)); }
std::vector<std::vector<std::pair<int, int>>> to(N);
while (M--) {
int a, b, c;
std::cin >> a >> b >> c;
to[a].emplace_back(b, c);
}
while (heap.size()) {
int now = heap.top().second;
if (now == t) break;
heap.pop();
for (const auto &nxtlen : to[now]) {
const auto nxt = nxtlen.first, len = nxtlen.second;
if (D[nxt] > D[now] + len) {
D[nxt] = D[now] + len, prev[nxt] = now;
heap.decrease(handler[nxt], std::make_pair(D[nxt], nxt));
}
}
}
if (D[t] == INF) {
std::cout << -1 << '\n';
return 0;
}
std::stack<int> path;
int now = t;
while (now != s) { path.push(now), now = prev[now], path.push(now); }
std::cout << D[t] << ' ' << path.size() / 2 << '\n';
while (path.size()) {
std::cout << path.top() << ' ';
path.pop();
std::cout << path.top() << '\n';
path.pop();
}
}#line 1 "data_structure/test/fibonacci_heap_shortestpath.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"
#line 2 "data_structure/fibonacci_heap.hpp"
#include <array>
#include <cassert>
#include <iostream>
#include <list>
// CUT begin
// Fibonacci heap
// - Complexity:
// - empty(), size(), top(), push(), meld(): O(1)
// - pop(), decrease(): O(lg N) amortized
// - Reference:
// - "Introduction to Algorithms, Third Edition", Chapter 19
// - <https://www.cs.princeton.edu/~wayne/teaching/fibonacci-heap.pdf>
// - <https://rsk0315.hatenablog.com/entry/2019/10/29/151823>
template <typename Tp> struct fibonacci_heap {
struct Node {
Tp val;
int deg;
Node *parent, *left, *right, *child;
bool mark;
Node() = default;
Node(Node const &) = default;
Node(Node &&) = default;
Node &operator=(Node const &) = default;
Node &operator=(Node &&) = default;
Node(Tp v)
: val(v), deg(0), parent(nullptr), left(nullptr), right(nullptr), child(nullptr),
mark(false) {}
friend std::ostream &operator<<(std::ostream &os, const Node &n) {
os << '(' << n.val << ',';
if (n.child != nullptr) os << *(n.child) << ',';
Node *now = n.right;
while (now != &n) {
os << now->val << ',';
if (now->child != nullptr) os << *now->child << ',';
now = now->right;
}
os << ')';
return os;
}
};
int sz;
std::list<Node *> roots;
Node *ptop;
inline void _chmin(Node *cand) noexcept {
if (ptop == nullptr or cand->val < ptop->val) ptop = cand;
}
fibonacci_heap() : sz(0), roots({}), ptop(nullptr) {}
bool empty() const noexcept { return sz == 0; }
int size() const noexcept { return sz; }
std::array<Node *, 30> _arr;
void _fmerge(Node *ptr) {
int d = ptr->deg;
if (_arr[d] == nullptr)
_arr[d] = ptr;
else {
Node *cptr = _arr[d];
if (cptr->val < ptr->val) std::swap(ptr, cptr);
ptr->deg++;
cptr->parent = ptr;
if (ptr->child == nullptr)
ptr->child = cptr;
else {
Node *cl = ptr->child, *cr = ptr->child->right;
assert(cl->right == cr and cr->left == cl);
cptr->left = cl, cptr->right = cr, cl->right = cr->left = cptr;
}
_arr[d] = nullptr;
_fmerge(ptr);
}
}
void _consolidate() {
_arr.fill(nullptr);
for (auto ptr : roots)
if (ptr != nullptr) {
if (ptr->deg < 0)
delete ptr;
else
_fmerge(ptr);
}
roots.clear(), ptop = nullptr;
for (auto ptr : _arr)
if (ptr != nullptr) _add_tree(ptr);
}
void _add_tree(Node *root) noexcept {
root->parent = nullptr;
root->left = root->right = root;
roots.emplace_back(root);
_chmin(root);
}
Node *push(const Tp &val) noexcept {
sz++;
Node *ptr = new Node(val);
_add_tree(ptr);
return ptr;
}
void meld(fibonacci_heap &&hp) {
sz += hp.sz;
roots.splice(roots.end(), hp.roots);
if (hp.ptop != nullptr) _chmin(hp.ptop);
}
void pop() {
assert(sz > 0);
sz--;
Node *ch1 = ptop->child;
if (ch1 != nullptr) {
Node *now = ch1;
while (true) {
Node *nxt = now->right;
_add_tree(now);
now = nxt;
if (now == ch1) break;
}
}
ptop->deg = -1;
_consolidate();
}
void _deldfs(Node *now) {
while (now != nullptr) {
if (now->child != nullptr) _deldfs(now->child);
Node *nxt = now->right;
delete now;
now = nxt;
}
}
void clear() {
for (auto root : roots) _deldfs(root);
sz = 0;
roots.clear();
ptop = nullptr;
}
void _cut(Node *x) noexcept {
Node *y = x->parent;
assert(y != nullptr and y->deg > 0);
Node *xr = x->right, *xl = x->left;
if (x == xr) {
y->child = nullptr;
} else {
y->child = xr;
xl->right = xr, xr->left = xl;
}
y->deg--;
_add_tree(x);
x->mark = false;
}
void _cascading_cut(Node *now) noexcept {
assert(now != nullptr);
Node *par = now->parent;
if (par == nullptr) return;
if (!now->mark)
now->mark = true;
else {
_cut(now);
_cascading_cut(par);
}
}
void erase(Node *r) {
if (r->parent != nullptr) {
Node *rpar = r->parent;
_cut(r);
_cascading_cut(rpar);
}
ptop = r;
pop();
}
bool decrease(Node *r, const Tp new_val) {
assert(r != nullptr);
if (!(new_val < r->val)) return false;
r->val = new_val;
if (r->parent != nullptr and new_val < r->parent->val) {
Node *rpar = r->parent;
_cut(r);
_cascading_cut(rpar);
}
_chmin(r);
return true;
}
Tp top() const {
assert(ptop != nullptr);
return ptop->val;
}
friend std::ostream &operator<<(std::ostream &os, const fibonacci_heap &hp) {
os << "[(fibonacci_heap: sz=" << hp.sz << ", top=" << hp.ptop->val
<< ", #tree = " << hp.roots.size() << ")";
for (auto x : hp.roots) { os << *x << ", "; }
os << ']';
return os;
}
};
#include <utility>
#include <vector>
template <typename Tp> struct heap {
using P = std::pair<Tp, int>;
fibonacci_heap<P> _heap;
std::vector<typename fibonacci_heap<P>::Node *> vp;
std::vector<Tp> result;
void initialize(int N, Tp initval) {
_heap.clear();
vp.resize(N);
result.assign(N, initval);
for (int i = 0; i < N; i++) { vp[i] = _heap.push(std::make_pair(initval, i)); }
}
heap(int N, Tp initval) { initialize(N, initval); }
bool chmin(int i, Tp val) {
if (val < result[i]) {
result[i] = val;
if (vp[i] == nullptr) {
vp[i] = _heap.push(std::make_pair(result[i], i));
} else {
_heap.decrease(vp[i], std::make_pair(result[i], i));
}
return true;
}
return false;
}
Tp operator[](int i) const { return result.at(i); }
P top() { return _heap.top(); }
P pop() {
P ret = _heap.top();
_heap.pop();
return ret;
}
int size() { return _heap.size(); }
bool empty() { return _heap.empty(); }
};
#line 5 "data_structure/test/fibonacci_heap_shortestpath.test.cpp"
#include <stack>
#line 8 "data_structure/test/fibonacci_heap_shortestpath.test.cpp"
int main() {
std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
int N, M, s, t;
std::cin >> N >> M >> s >> t;
using P = std::pair<long long, int>;
fibonacci_heap<P> heap;
constexpr long long INF = 1e18;
std::vector<long long> D(N, INF);
std::vector<int> prev(N, -1);
D[s] = 0;
std::vector<fibonacci_heap<P>::Node *> handler(N);
for (int i = 0; i < N; i++) { handler[i] = heap.push(std::make_pair(D[i], i)); }
std::vector<std::vector<std::pair<int, int>>> to(N);
while (M--) {
int a, b, c;
std::cin >> a >> b >> c;
to[a].emplace_back(b, c);
}
while (heap.size()) {
int now = heap.top().second;
if (now == t) break;
heap.pop();
for (const auto &nxtlen : to[now]) {
const auto nxt = nxtlen.first, len = nxtlen.second;
if (D[nxt] > D[now] + len) {
D[nxt] = D[now] + len, prev[nxt] = now;
heap.decrease(handler[nxt], std::make_pair(D[nxt], nxt));
}
}
}
if (D[t] == INF) {
std::cout << -1 << '\n';
return 0;
}
std::stack<int> path;
int now = t;
while (now != s) { path.push(now), now = prev[now], path.push(now); }
std::cout << D[t] << ' ' << path.size() / 2 << '\n';
while (path.size()) {
std::cout << path.top() << ' ';
path.pop();
std::cout << path.top() << '\n';
path.pop();
}
}