#include <iostream>
#include <vector>
#include <queue>
#include <fstream>
#include <stack>
#include <unordered_map>
#include <algorithm>
#include <iterator>
using namespace std;
ifstream in("sortaret.in");
ofstream out("sortaret.out");
class Graph {
//private attributes
vector<vector<int>> edges;
int numberOfNodes;
//-------------------------------------
//private methods
void DFS(unordered_map<int, bool>&, int);
void tarjan(int, int&, vector<int>&, vector<int>&, stack<int>&,
unordered_map<int ,bool>&, unordered_map<int ,bool>&, vector<vector<int>>&);
// void bicomponentsDFS(int, int, unordered_map<int, bool>, stack<int>,
// vector<int>, vector<int>, int&, vector<vector<int>>& );
void topologicalSortingDFS(int, vector<bool>&, stack<int>&);
public:
Graph(int);
~Graph();
void setEdge(int, int);
vector<int> distance(int);
int numberOfComponents();
void displayEdges();
vector<vector<int>> SCC();
// void biconnectedComponents();
void topologicalSort();
bool havelHakimi(vector<int>);
};
int main() {
int numberOfNodes, numberOfEdges, from, to;
in >> numberOfNodes >> numberOfEdges;
auto* graph = new Graph(numberOfNodes);
for (int countEdge = 1; countEdge <= numberOfEdges; countEdge++) {
in >> from >> to;
graph->setEdge(from, to);
}
graph->topologicalSort();
return 0;
}
void Graph::displayEdges() {
for(int node = 1; node <= numberOfNodes; node ++) {
for (auto edge: edges[node])
cout << node << " " << edge << endl;
}
}
Graph::Graph(int numberOfNodes) {
this->numberOfNodes = numberOfNodes;
edges.resize(numberOfNodes + 1);
}
Graph::~Graph() = default;
void Graph::setEdge(int from, int to) {
edges[from].push_back(to);
}
vector<int> Graph::distance(int from) {
queue<int> queue;
vector<int> visited(numberOfNodes + 1, -1);
visited[from] = 0;
queue.push(from);
while (!queue.empty()) {
int node = queue.front();
for (auto edge : edges[node]) {
if (visited[edge] == -1) {
visited[edge] = visited[node] + 1;
queue.push(edge);
}
}
queue.pop();
}
return visited;
}
void Graph::DFS(unordered_map<int, bool> &visited, int start) {
visited[start] = true;
for(int &node : edges[start]) {
if(!visited[node]) {
DFS (visited ,node);
}
}
}
int Graph::numberOfComponents() {
unordered_map<int ,bool> visited;
int nrOfComp = 0;
for(int node = 1; node <= numberOfNodes; node ++) {
if(visited[node] == 0) {
nrOfComp ++;
DFS(visited, node);
}
}
return nrOfComp;
}
vector<vector<int>> Graph::SCC() {
stack<int> stack;
vector<int> ids(numberOfNodes + 1), low_link(numberOfNodes + 1);
vector<vector<int>> scc;
unordered_map<int ,bool> visited, onStack;
int id = 1;
for(int node = 1; node <= numberOfNodes; node++){
if(!visited[node])
tarjan(node, id, ids, low_link, stack, onStack, visited, scc);
}
return scc;
}
void Graph::tarjan(int start, int &id, vector<int> &ids, vector<int> &low_link,
stack<int>& stack, unordered_map<int ,bool> &onStack,
unordered_map<int, bool> &visited,vector<vector<int>> &scc) {
ids[start] = id;
low_link[start] = id;
stack.push(start);
visited[start] = true;
onStack[start] = true;
id++;
for(auto node : edges[start]) {
if(!visited[node]) {
tarjan(node, id, ids, low_link, stack, onStack, visited, scc);
low_link[start] = min(low_link[start], low_link[node]);
} else {
if (onStack[node]) {
low_link[start] = min(low_link[start], low_link[node]);
}
}
}
if(low_link[start] == ids[start]){
vector<int> cc;
int ccNode;
do {
ccNode = stack.top();
cc.push_back(ccNode);
stack.pop();
onStack[ccNode] = false;
} while(ccNode != start);
scc.push_back(cc);
}
}
//void Graph::bicomponentsDFS(int start, int parent, unordered_map<int, bool> visited,
// stack<int> stack, vector<int> low_link, vector<int> link,
// int& noOfBiconnectedComponents , vector<vector<int>>& biconnectedComponents) {
// link[start] = link[parent] + 1;
// low_link[start] = link[start];
// stack.push(start);
// visited[start] = true;
//
// for (auto node : edges[start]) {
// if (visited[node]) {
// cout << low_link[node] << " --- " << link[start] << endl;
// if(low_link[start] > link[node])
// low_link[start] = link[node];
// cout << low_link[node] << " ---- " << link[start] << endl;
// } else {
// bicomponentsDFS(node, start, visited, stack, low_link, link, noOfBiconnectedComponents, biconnectedComponents);
//
// cout << low_link[node] << " -- " << link[start] << endl;
// if(low_link[start] > low_link[node])
// low_link[start] = low_link[node];
//
// cout << low_link[node] << " - " << link[start] << endl;
// if(low_link[node] >= link[start]) {
// cout << " - ";
// noOfBiconnectedComponents ++;
// cout << noOfBiconnectedComponents << " - ";
//
// while(!stack.empty() && stack.top() != node) {
// biconnectedComponents[noOfBiconnectedComponents].push_back(stack.top());
// stack.pop();
// }
// biconnectedComponents[noOfBiconnectedComponents].push_back(stack.top());
// stack.pop();
// biconnectedComponents[noOfBiconnectedComponents].push_back(start);
// }
// }
// }
//}
//
//void Graph::biconnectedComponents() {
// int start = 1, parent = 0, noOfBiconnectedComponents = 0;
// unordered_map<int, bool> visited;
// stack<int> stack;
// vector<int> low_link(numberOfNodes + 1, 0), link(numberOfNodes + 1, 0);
// vector<vector<int>> biconnectedComponents;
//
// bicomponentsDFS(start , parent, visited, stack, low_link, link, noOfBiconnectedComponents, biconnectedComponents);
//
// cout << noOfBiconnectedComponents << "\n";
// for(int biconnectedComponent = 1; biconnectedComponent <= noOfBiconnectedComponents; biconnectedComponent++) {
// for(auto elements : biconnectedComponents[biconnectedComponent])
// cout << elements << " ";
// cout << "\n";
// }
//}
void Graph::topologicalSortingDFS(int start, vector<bool>& visited, stack<int>& stack)
{
visited[start] = true;
for (int node : edges[start]) {
if (!visited[node]) {
topologicalSortingDFS(node, visited, stack);
}
}
stack.push(start);
}
void Graph::topologicalSort()
{
stack<int> stack;
vector<bool> visited(numberOfNodes + 1, false);;
for (int node = 1; node < visited.size(); node++) {
if (!visited[node]) {
topologicalSortingDFS(node, visited, stack);
}
}
while (!stack.empty()) {
out << stack.top() << " ";
stack.pop();
}
}
bool Graph::havelHakimi(vector <int> degrees) {
int sum = 0;
for(int node = 1; node <= degrees.size(); node ++) {
sum += degrees[node];
}
//if sum of degrees is not even => graph cant be built
if(sum % 2 == 1){
return false;
}
while(true) {
std::sort(degrees.begin(), degrees.end(), greater<int>());
//if first elem = 0 => all elements are 0 => graph can be built
if(degrees[0] == 0) {
return true;
}
//if degree of the largest node is bigger than the no of nodes - 1 => graph cant be built
if(degrees[0] > degrees.size() - 1) {
return false;
}
int node = degrees[0];
degrees.erase(degrees.begin() + 0);
for(int i = 0; i < node; ++i) {
degrees[i] --;
if(degrees[i] < 0) {
return false;
}
}
}
}