127 lines
2.4 KiB
C++
127 lines
2.4 KiB
C++
// Copyright (c) 2023 Xi Xu, All rights reserved.
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// SPDX-License-Identifier: GPL-3.0-or-later
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#include <bits/stdc++.h>
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using namespace std;
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class Graph {
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private:
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int n, e;
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int **adj;
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public:
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Graph(istream &in);
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~Graph();
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void print() const;
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bool isEulerian() const;
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void dfs(int u, bool *visited, int v = 0, int w = 0) const;
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bool isBridge(int u, int v) const;
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void fleury() const;
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};
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Graph::Graph(istream &in) {
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in >> n >> e;
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adj = new int *[n];
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for (size_t i = 0; i < n; i++) {
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adj[i] = new int[n];
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for (size_t j = 0; j < n; j++)
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adj[i][j] = 0;
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}
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for (size_t i = 0; i < e; i++) {
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int u, v;
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in >> u >> v;
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adj[u - 1][v - 1]++;
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}
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}
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Graph::~Graph() {
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for (size_t i = 0; i < n; i++)
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delete[] adj[i];
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delete[] adj;
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}
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void Graph::print() const {
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for (size_t i = 0; i < n; i++) {
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for (size_t j = 0; j < n; j++)
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cout << adj[i][j] << " ";
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cout << endl;
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}
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}
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bool Graph::isEulerian() const {
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for (size_t i = 0; i < n; i++) {
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int sum = 0;
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for (size_t j = 0; j < n; j++)
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sum += adj[i][j];
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for (size_t j = 0; j < n; j++)
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sum -= adj[j][i];
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if (sum != 0)
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return false;
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}
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return true;
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}
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void Graph::dfs(int u, bool *visited, int v, int w) const {
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visited[u] = true;
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for (size_t i = 0; i < n; i++)
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if (adj[u][i] && !visited[i] && !(u == v && i == w))
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dfs(i, visited, v, w);
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}
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bool Graph::isBridge(int u, int v) const {
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if (adj[u][v] == 0)
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return false;
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int cnt = 0;
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bool visited[n];
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memset(visited, false, sizeof(visited));
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for (size_t i = 0; i < n; i++)
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if (!visited[i]) {
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dfs(i, visited);
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cnt++;
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}
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memset(visited, false, sizeof(visited));
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for (size_t i = 0; i < n; i++)
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if (!visited[i]) {
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dfs(i, visited, u, v);
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cnt--;
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}
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return cnt < 0;
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}
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void Graph::fleury() const {
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int copyadj[n][n];
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for (size_t i = 0; i < n; i++)
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for (size_t j = 0; j < n; j++)
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copyadj[i][j] = adj[i][j];
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int u = 0;
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while (true) {
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cout << u + 1 << " ";
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bool flag = false;
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for (size_t v = 0; v < n; v++)
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if (copyadj[u][v] && !isBridge(u, v)) {
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copyadj[u][v]--;
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u = v;
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flag = true;
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break;
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}
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if (!flag)
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break;
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}
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}
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int main() {
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ifstream fin("graph.txt");
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Graph g(fin);
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fin.close();
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cout << "Adjacency matrix:" << endl;
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g.print();
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bool is = g.isEulerian();
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if (g.isEulerian()) {
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cout << "The graph is Eulerian." << endl;
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g.fleury();
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}
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else
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cout << "The graph is not Eulerian." << endl;
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return 0;
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} |