#line 1 "test/yukicoder/1069/main.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1069"
#define ERROR 1e-4
#include <cmath>
#include <iomanip>
#include <iostream>
#line 2 "Mylib/Graph/ShortestPath/yen_algorithm.cpp"
#include <functional>
#include <optional>
#include <queue>
#include <utility>
#include <vector>
#line 4 "Mylib/Graph/Template/graph.cpp"
namespace haar_lib {
template <typename T>
struct edge {
int from, to;
T cost;
int index = -1;
edge() {}
edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
edge(int from, int to, T cost, int index) : from(from), to(to), cost(cost), index(index) {}
};
template <typename T>
struct graph {
using weight_type = T;
using edge_type = edge<T>;
std::vector<std::vector<edge<T>>> data;
auto& operator[](size_t i) { return data[i]; }
const auto& operator[](size_t i) const { return data[i]; }
auto begin() const { return data.begin(); }
auto end() const { return data.end(); }
graph() {}
graph(int N) : data(N) {}
bool empty() const { return data.empty(); }
int size() const { return data.size(); }
void add_edge(int i, int j, T w, int index = -1) {
data[i].emplace_back(i, j, w, index);
}
void add_undirected(int i, int j, T w, int index = -1) {
add_edge(i, j, w, index);
add_edge(j, i, w, index);
}
template <size_t I, bool DIRECTED = true, bool WEIGHTED = true>
void read(int M) {
for (int i = 0; i < M; ++i) {
int u, v;
std::cin >> u >> v;
u -= I;
v -= I;
T w = 1;
if (WEIGHTED) std::cin >> w;
if (DIRECTED)
add_edge(u, v, w, i);
else
add_undirected(u, v, w, i);
}
}
};
template <typename T>
using tree = graph<T>;
} // namespace haar_lib
#line 8 "Mylib/Graph/ShortestPath/yen_algorithm.cpp"
namespace haar_lib {
namespace yen_algorithm_impl {
template <typename T>
auto shortest_path(
const graph<T> &g,
int from,
int t,
const std::vector<bool> &usable,
const std::vector<std::vector<bool>> &valid) {
using Path = std::pair<T, std::vector<int>>;
using P = std::pair<T, int>;
const int N = g.size();
std::vector<bool> visited(N, false);
std::vector<std::optional<T>> dist(N);
std::vector<std::pair<int, int>> restore(N);
std::priority_queue<P, std::vector<P>, std::greater<P>> pq;
dist[from] = 0;
pq.emplace(0, from);
while (not pq.empty()) {
auto [d, i] = pq.top();
pq.pop();
if (visited[i]) continue;
visited[i] = true;
for (int k = 0; k < (int) g[i].size(); ++k) {
if (not valid[i][k] or not usable[g[i][k].to]) continue;
auto &e = g[i][k];
if (not dist[e.to] or *dist[e.to] > d + e.cost) {
dist[e.to] = d + e.cost;
restore[e.to] = std::make_pair(i, k);
if (not visited[e.to]) pq.emplace(*dist[e.to], e.to);
}
}
}
std::optional<Path> ret;
if (dist[t]) {
std::vector<int> p;
int cur = t;
while (cur != from) {
auto [i, j] = restore[cur];
p.push_back(j);
cur = i;
}
std::reverse(p.begin(), p.end());
ret = std::make_pair(*dist[t], p);
}
return ret;
}
} // namespace yen_algorithm_impl
template <typename T>
auto yen_algorithm(const graph<T> &g, int s, int t, int K) {
using Path = std::pair<T, std::vector<int>>;
const int N = g.size();
std::vector<std::vector<bool>> valid(N);
std::vector<std::optional<Path>> result(K);
std::priority_queue<Path, std::vector<Path>, std::greater<Path>> stock;
for (int i = 0; i < N; ++i) {
valid[i].assign(g[i].size(), true);
}
for (int i = 0; i < K; ++i) {
if (i == 0) {
std::vector<bool> usable(N, true);
if (auto res = yen_algorithm_impl::shortest_path(g, s, t, usable, valid); res) stock.push(*res);
} else {
std::vector<int> prev_path;
{
int cur = s;
for (auto u : result[i - 1]->second) {
prev_path.push_back(cur);
cur = g[cur][u].to;
}
prev_path.push_back(t);
}
std::vector<bool> check(i, true);
std::vector<bool> usable(N, true);
for (int k = 0; k < (int) prev_path.size() - 1; ++k) {
const int u = prev_path[k];
for (int j = 0; j < i; ++j) {
if (check[j]) {
valid[prev_path[k]][result[j]->second[k]] = false;
}
}
if (auto res = yen_algorithm_impl::shortest_path(g, u, t, usable, valid); res) {
auto [c, p] = *res;
std::vector<int> temp;
for (int j = 0; j < k; ++j) {
int v = result[i - 1]->second[j];
c += g[prev_path[j]][v].cost;
temp.push_back(v);
}
temp.insert(temp.end(), p.begin(), p.end());
stock.emplace(c, temp);
}
usable[u] = false;
for (int j = 0; j < i; ++j) {
if (check[j]) {
valid[prev_path[k]][result[j]->second[k]] = true;
}
}
for (int j = 0; j < i; ++j) {
if (check[j]) {
if (prev_path[k + 1] != g[prev_path[k]][result[j]->second[k]].to) {
check[j] = false;
}
}
}
}
}
if (stock.empty()) break;
result[i] = stock.top();
stock.pop();
while (not stock.empty() and stock.top() == result[i]) {
stock.pop();
}
}
return result;
}
} // namespace haar_lib
#line 2 "Mylib/IO/input_tuple_vector.cpp"
#include <initializer_list>
#line 4 "Mylib/IO/input_tuple_vector.cpp"
#include <tuple>
#line 7 "Mylib/IO/input_tuple_vector.cpp"
namespace haar_lib {
template <typename T, size_t... I>
void input_tuple_vector_init(T &val, int N, std::index_sequence<I...>) {
(void) std::initializer_list<int>{(void(std::get<I>(val).resize(N)), 0)...};
}
template <typename T, size_t... I>
void input_tuple_vector_helper(T &val, int i, std::index_sequence<I...>) {
(void) std::initializer_list<int>{(void(std::cin >> std::get<I>(val)[i]), 0)...};
}
template <typename... Args>
auto input_tuple_vector(int N) {
std::tuple<std::vector<Args>...> ret;
input_tuple_vector_init(ret, N, std::make_index_sequence<sizeof...(Args)>());
for (int i = 0; i < N; ++i) {
input_tuple_vector_helper(ret, i, std::make_index_sequence<sizeof...(Args)>());
}
return ret;
}
} // namespace haar_lib
#line 6 "Mylib/IO/input_tuple.cpp"
namespace haar_lib {
template <typename T, size_t... I>
static void input_tuple_helper(std::istream &s, T &val, std::index_sequence<I...>) {
(void) std::initializer_list<int>{(void(s >> std::get<I>(val)), 0)...};
}
template <typename T, typename U>
std::istream &operator>>(std::istream &s, std::pair<T, U> &value) {
s >> value.first >> value.second;
return s;
}
template <typename... Args>
std::istream &operator>>(std::istream &s, std::tuple<Args...> &value) {
input_tuple_helper(s, value, std::make_index_sequence<sizeof...(Args)>());
return s;
}
} // namespace haar_lib
#line 8 "Mylib/IO/input_tuples.cpp"
namespace haar_lib {
template <typename... Args>
class InputTuples {
struct iter {
using value_type = std::tuple<Args...>;
value_type value;
bool fetched = false;
int N, c = 0;
value_type operator*() {
if (not fetched) {
std::cin >> value;
}
return value;
}
void operator++() {
++c;
fetched = false;
}
bool operator!=(iter &) const {
return c < N;
}
iter(int N) : N(N) {}
};
int N;
public:
InputTuples(int N) : N(N) {}
iter begin() const { return iter(N); }
iter end() const { return iter(N); }
};
template <typename... Args>
auto input_tuples(int N) {
return InputTuples<Args...>(N);
}
} // namespace haar_lib
#line 10 "test/yukicoder/1069/main.test.cpp"
namespace hl = haar_lib;
int main() {
std::cin.tie(0);
std::ios::sync_with_stdio(false);
int N, M, K, X, Y;
std::cin >> N >> M >> K >> X >> Y;
--X, --Y;
auto [p, q] = hl::input_tuple_vector<long double, long double>(N);
hl::graph<long double> g(N);
for (auto [P, Q] : hl::input_tuples<int, int>(M)) {
--P, --Q;
long double dx = p[P] - p[Q];
long double dy = q[P] - q[Q];
long double L = std::sqrt(dx * dx + dy * dy);
g.add_undirected(P, Q, L);
}
auto res = hl::yen_algorithm(g, X, Y, K);
for (auto x : res) {
if (not x) {
std::cout << -1 << "\n";
} else {
std::cout << std::fixed << std::setprecision(12) << x->first << "\n";
}
}
return 0;
}
test/yukicoder/1069/main.test.cpp
Basic graph
(Mylib/Graph/Template/graph.cpp)