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#include "cp-algo/graph/euler.hpp"
#ifndef CP_ALGO_GRAPH_EULER_HPP
#define CP_ALGO_GRAPH_EULER_HPP
#include "base.hpp"
#include <algorithm>
#include <utility>
#include <vector>
namespace cp_algo::graph {
template<typename graph>
int euler_start(graph const& g) {
std::vector<int> deg(g.n());
constexpr bool undirected = graph::undirected;
int res = 0;
g.call_edges([&](edge_index e) {
int u = g.edge(e ^ 1).to;
int v = g.edge(e).to;
res = u;
deg[u]++;
deg[v]--;
});
if constexpr (undirected) {
for(auto &it: deg) {
it = bool(it % 2);
}
}
auto nodes = g.nodes_view();
auto is_start = [&](int v) {return deg[v] > 0;};
auto starts = std::ranges::count_if(nodes, is_start);
if(starts > 1 + undirected) {
res = -1;
} else if(starts == 1 + undirected) {
auto start = *std::ranges::find_if(nodes, is_start);
res = deg[start] == 1 ? start : -1;
}
return res;
}
auto euler_trail(auto const& g) {
int v0 = euler_start(g);
std::vector<int> trail;
if(~v0) {
std::vector<bool> used(g.m());
auto& adj = g.incidence_lists();
auto head = adj.head;
auto dfs = [&](auto &&self, int v) -> void {
while(head[v]) {
int e = adj.data[std::exchange(head[v], adj.next[head[v]])];
if(!used[e / 2]) {
used[e / 2] = 1;
self(self, g.edge(e).to);
trail.push_back(e);
}
}
};
dfs(dfs, v0);
std::ranges::reverse(trail);
}
return std::pair{v0, trail};
}
}
#endif // CP_ALGO_GRAPH_EULER_HPP
#line 1 "cp-algo/graph/euler.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 {
node_index to;
edge_base() {}
edge_base(node_index v): to(v) {}
static auto read(node_index v0 = 0) {
node_index u, v;
std::cin >> u >> v;
return std::pair{u - v0, edge_base(v - v0)};
}
edge_base backedge(int from) const {
return {from};
}
};
struct weighted_edge: edge_base {
int64_t w;
weighted_edge() {}
weighted_edge(node_index v, int64_t w): edge_base(v), w(w) {}
static auto read(node_index v0 = 0) {
node_index u, v;
int64_t w;
std::cin >> u >> v >> w;
return std::pair{u - v0, weighted_edge{v - v0, w}};
}
weighted_edge backedge(node_index from) const {
return {from, 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/data_structures/stack_union.hpp"
#include <cstddef>
#include <vector>
namespace cp_algo::data_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] = std::size(next) - 1;
data.push_back(vdata);
}
template<typename... Args>
void emplace(int v, Args&&... vdata) {
next.push_back(head[v]);
head[v] = 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);}
std::vector<int> head, next;
std::vector<datatype> data;
};
}
#line 5 "cp-algo/graph/base.hpp"
#include <ranges>
#line 7 "cp-algo/graph/base.hpp"
namespace cp_algo::graph {
using edge_index = int;
enum type {directed = 0, undirected = 1};
template<type _undirected, edge_type edge_t = edge_base>
struct graph {
static constexpr bool undirected = _undirected;
graph(int n, int v0 = 0): v0(v0), adj(n) {}
void add_edge(node_index u, edge_t e) {
adj.push(u, size(edges));
edges.push_back(e);
if constexpr (undirected) {
adj.push(e.to, size(edges));
}
edges.push_back(e.backedge(u));
}
void read_edges(node_index m) {
adj.reserve(m);
for(edge_index i = 0; i < m; i++) {
auto [u, e] = edge_t::read(v0);
add_edge(u, e);
}
}
void call_adjacent(node_index v, auto &&callback, auto &&terminate) const {
for(int sv = adj.head[v]; sv && !terminate(); sv = adj.next[sv]) {
callback(adj.data[sv]);
}
}
void call_adjacent(node_index v, auto &&callback) const {
call_adjacent(v, callback, [](){return false;});
}
void call_edges(auto &&callback) const {
for(edge_index e: edges_view()) {
callback(e);
}
}
auto nodes_view() const {
return std::views::iota(0, n());
}
auto edges_view() const {
return std::views::filter(
std::views::iota(0, 2 * m()),
[](edge_index e) {return !(e % 2);}
);
}
auto const& incidence_lists() const {return adj;}
edge_t const& edge(edge_index e) const {return edges[e];}
node_index n() const {return adj.size();}
edge_index m() const {return size(edges) / 2;}
private:
node_index v0;
std::vector<edge_t> edges;
data_structures::stack_union<edge_index> adj;
};
}
#line 4 "cp-algo/graph/euler.hpp"
#include <algorithm>
#include <utility>
#line 7 "cp-algo/graph/euler.hpp"
namespace cp_algo::graph {
template<typename graph>
int euler_start(graph const& g) {
std::vector<int> deg(g.n());
constexpr bool undirected = graph::undirected;
int res = 0;
g.call_edges([&](edge_index e) {
int u = g.edge(e ^ 1).to;
int v = g.edge(e).to;
res = u;
deg[u]++;
deg[v]--;
});
if constexpr (undirected) {
for(auto &it: deg) {
it = bool(it % 2);
}
}
auto nodes = g.nodes_view();
auto is_start = [&](int v) {return deg[v] > 0;};
auto starts = std::ranges::count_if(nodes, is_start);
if(starts > 1 + undirected) {
res = -1;
} else if(starts == 1 + undirected) {
auto start = *std::ranges::find_if(nodes, is_start);
res = deg[start] == 1 ? start : -1;
}
return res;
}
auto euler_trail(auto const& g) {
int v0 = euler_start(g);
std::vector<int> trail;
if(~v0) {
std::vector<bool> used(g.m());
auto& adj = g.incidence_lists();
auto head = adj.head;
auto dfs = [&](auto &&self, int v) -> void {
while(head[v]) {
int e = adj.data[std::exchange(head[v], adj.next[head[v]])];
if(!used[e / 2]) {
used[e / 2] = 1;
self(self, g.edge(e).to);
trail.push_back(e);
}
}
};
dfs(dfs, v0);
std::ranges::reverse(trail);
}
return std::pair{v0, trail};
}
}