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#include <iostream>
#include <vector>
#include <queue>
#include <stack>
#include <fstream>
#include <algorithm>
using namespace std;
class Graph {
int nrNodes, nrEdges;
bool oriented;
vector<vector<int>> edges;
vector<vector<int>> transposedGraph;
stack<int> topoSort;
public:
Graph(int nrNodes, bool oriented = true) ;
void addEdge(int x, int y); // sets edge between x and y
void BFS(int startingNode, ostream& g);
int connectedComponents(); // returns the number of conencted components from the graph
void DFS(int node, vector<int>& visited);
void topologicalSort(int x, vector<int> &visited);
stack<int> getTopologicalSortedGraph();
void stronglyConnectedComponents(ofstream & g); // outputs the strongly connected components
bool havelHakim(vector<int> grades);
~Graph();
private:
void DFS2(int currentNode, vector<int> &component, int currentComponent, vector<vector<int>> & solution); // used in stronglyConnComponents
};
Graph::Graph(int nrNodes, bool oriented) {
this->nrNodes = nrNodes;
this->oriented = oriented;
edges.resize(nrNodes + 1);
this->transposedGraph.resize(this->nrNodes+1);
}
void Graph::addEdge(int x, int y) {
this->edges[x].push_back(y);
if(!oriented) {
this->edges[y].push_back(x);
}
}
void Graph::BFS(int startingNode, ostream& g) {
vector<int> cost(this->nrNodes+1, -1);
vector<int> visited(this->nrNodes+1, 0);
queue<int> queue;
cost[startingNode] = 0;
visited[startingNode] = 1;
queue.push(startingNode);
while(!queue.empty()){
int currentNode = queue.front();
for(auto node : edges[currentNode]){
if(!visited[node]){
visited[node] = 1;
cost[node] = cost[currentNode] + 1;
queue.push(node);
}
}
queue.pop();
}
for(int i = 1; i<= nrNodes; i++ ){
g << cost[i] << " ";
}
}
void Graph::DFS(int currentNode, vector<int> &visited) {
for(auto node : this->edges[currentNode]) {
if(!visited[node]) {
visited[node] = 1;
DFS(node, visited);
}
}
}
int Graph::connectedComponents() {
int connectedComp = 0;
vector<int>visited(this->nrNodes + 1, 0);
for(int i = 1; i<= nrNodes; i++) {
if(!visited[i]) {
visited[i] = 1;
connectedComp++;
DFS(i, visited);
}
}
return connectedComp;
}
void Graph::topologicalSort(int currentNode, vector<int> &visited) {
visited[currentNode] = 1;
for(auto node: this->edges[currentNode]){
if(!visited[node])
topologicalSort(node, visited);
}
this->topoSort.push(currentNode);
}
stack<int> Graph::getTopologicalSortedGraph() {
return this->topoSort;
}
void Graph::DFS2(int currentNode, vector<int> &visited, int currentComponent, vector<vector<int>> & solution) { // dfs used for strongly conn comp
visited[currentNode] = 1;
solution[currentComponent].push_back(currentNode);
for(auto i: this->transposedGraph[currentNode]){
if(visited[i] == 0){
DFS2(i,visited,currentComponent,solution);
}
}
}
void Graph::stronglyConnectedComponents(ofstream &g) {
vector<vector<int>>solution(nrNodes+1);
this->transposedGraph.resize(this->nrNodes+1);
for(int i = 1; i<= this->nrNodes; i++){ // compute transposed graph
for(auto j : edges[i]){
transposedGraph[j].push_back(i);
}
}
vector<int>visited(this->nrNodes+1, 0);
for(int i = 1; i<= nrNodes; i++){
if(!visited[i])
topologicalSort(i, visited); // sort in topologcal order
}
vector<int>visited2(this->nrNodes+1, 0);
int currentComponent = 0;
while(!topoSort.empty()) {
int i = topoSort.top();
if(visited2[i] == 0) {
currentComponent++;
DFS2(i, visited2, currentComponent,solution);
}
topoSort.pop();
}
g << currentComponent << "\n";
for(int i = 1; i<=currentComponent; i++){
for(auto j : solution[i]){
g << j << " ";
}
g << "\n";
}
}
bool Graph::havelHakim(vector<int> grades) {
sort(grades.begin(), grades.end(), greater<>());
if(grades[0] > grades.size()-1)
return false;
while (true){
int gr = grades[0];
grades.erase(grades.begin());
for(int& i: grades){
gr--;
i--;
if(i < 0) return false;
if(gr == 0) break;
}
sort(grades.begin(), grades.end(), greater<>());
if(grades.size() == 0 || grades[0] == 0){
return true;
}
}
}
Graph::~Graph(){
edges.clear();
}
int main()
{
int nrNodes, nrEdges;
ifstream f("sortaret.in");
ofstream g("sortaret.out");
f >> nrNodes >> nrEdges;
Graph G(nrNodes);
int x,y;
for(int i = 0; i< nrEdges; i++ ){
f >> x >> y;
G.addEdge(x,y);
}
vector<int>visited(nrNodes+1, 0);
for(int i = 1; i<= nrNodes; i++ ){
if(!visited[i]){
G.topologicalSort(i,visited);
}
}
stack<int> topoSortedGraph = G.getTopologicalSortedGraph();
while(!topoSortedGraph.empty()){
int x = topoSortedGraph.top();
g << x << " ";
topoSortedGraph.pop();
}
return 0;
}