This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub kmyk/competitive-programming-library
#include "graph/euler_graph.hpp"
#pragma once
#include <algorithm>
#include <tuple>
#include <utility>
#include <vector>
#include "../utils/macros.hpp"
/**
* @param g must be an undirected graph. Loops and multiple edges are acceptable.
* @param root specifies the component to find an Eulerian cycle
* @return indices of edges. It's empty if g is not a Eulerian graph.
*/
std::vector<int> find_eulerian_cycle_with_root(int n, const std::vector<std::pair<int, int> > & edges, int root) {
int m = edges.size();
std::vector<std::vector<int> > g(n);
std::vector<int> degree(n);
REP (i, m) {
int x, y; std::tie(x, y) = edges[i];
g[x].push_back(i);
g[y].push_back(i);
++ degree[x];
++ degree[y]; // This is required even if x == y
}
std::vector<int> order;
std::vector<bool> used(m);
auto go = [&](auto && go, int x) -> bool {
if (degree[x] % 2 != 0) {
return false;
}
while (not g[x].empty()) {
int i = g[x].back();
g[x].pop_back();
if (not used[i]) {
used[i] = true;
int y = x ^ edges[i].first ^ edges[i].second;
if (not go(go, y)) {
return false;
}
order.push_back(i);
}
}
return true;
};
if (not go(go, root)) {
return std::vector<int>(); // not a Eulerian graph
}
return order;
}
/**
* @brief Eulerian cycle (無向, 復元)
* @param g must be an undirected and connected graph.
* @return indices of edges. It's empty if g is not a Eulerian graph.
*/
std::vector<int> find_eulerian_cycle(int n, const std::vector<std::pair<int, int> > & edges) {
auto order = find_eulerian_cycle_with_root(n, edges, 0);
if (order.size() != edges.size()) {
return std::vector<int>();
}
return order;
}
#line 2 "graph/euler_graph.hpp"
#include <algorithm>
#include <tuple>
#include <utility>
#include <vector>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 7 "graph/euler_graph.hpp"
/**
* @param g must be an undirected graph. Loops and multiple edges are acceptable.
* @param root specifies the component to find an Eulerian cycle
* @return indices of edges. It's empty if g is not a Eulerian graph.
*/
std::vector<int> find_eulerian_cycle_with_root(int n, const std::vector<std::pair<int, int> > & edges, int root) {
int m = edges.size();
std::vector<std::vector<int> > g(n);
std::vector<int> degree(n);
REP (i, m) {
int x, y; std::tie(x, y) = edges[i];
g[x].push_back(i);
g[y].push_back(i);
++ degree[x];
++ degree[y]; // This is required even if x == y
}
std::vector<int> order;
std::vector<bool> used(m);
auto go = [&](auto && go, int x) -> bool {
if (degree[x] % 2 != 0) {
return false;
}
while (not g[x].empty()) {
int i = g[x].back();
g[x].pop_back();
if (not used[i]) {
used[i] = true;
int y = x ^ edges[i].first ^ edges[i].second;
if (not go(go, y)) {
return false;
}
order.push_back(i);
}
}
return true;
};
if (not go(go, root)) {
return std::vector<int>(); // not a Eulerian graph
}
return order;
}
/**
* @brief Eulerian cycle (無向, 復元)
* @param g must be an undirected and connected graph.
* @return indices of edges. It's empty if g is not a Eulerian graph.
*/
std::vector<int> find_eulerian_cycle(int n, const std::vector<std::pair<int, int> > & edges) {
auto order = find_eulerian_cycle_with_root(n, edges, 0);
if (order.size() != edges.size()) {
return std::vector<int>();
}
return order;
}