#include <iostream>
#include <algorithm>
#include <stack>
#include <vector>
#include <queue>
#include <fstream>
#include <list>
#include <climits>
#include <unordered_set>
//Probleme
//BFS https://www.infoarena.ro/job_detail/2788173?action=view-source
//DFS https://www.infoarena.ro/job_detail/2788178?action=view-source
//Biconex https://www.infoarena.ro/job_detail/2788743?action=view-source
//CTC https://www.infoarena.ro/job_detail/2795579?action=view-source
//sortaret https://www.infoarena.ro/job_detail/2789749?action=view-source
//RJ https://www.infoarena.ro/job_detail/2791322?action=view-source
//Graf https://www.infoarena.ro/job_detail/2791468?action=view-source
//Critical connections in a network https://leetcode.com/submissions/detail/578227255/
//Disjoint https://www.infoarena.ro/job_detail/2799580?action=view-source
//APM (Kruskall) https://www.infoarena.ro/job_detail/2799355?action=view-source
//Dijkstra https://www.infoarena.ro/job_detail/2799949?action=view-source
//Bellman-Ford https://www.infoarena.ro/job_detail/2800728?action=view-source
using namespace std;
ifstream fin("royfloyd.in");
ofstream fout("royfloyd.out");
struct Edge
{
int source;
int destination;
int cost;
Edge(int source = 0,int destination = 0,int cost = 0):
source(source),
destination(destination),
cost(cost) { }
friend ostream& operator<<(ostream& out, const Edge& e);
};
struct compareCost{
bool operator()(Edge& e1, Edge& e2){ return e1.cost > e2.cost; }
};
ostream& operator<<(ostream& out, const Edge& e)
{
out<<e.source<<' '<<e.destination<<' '<<e.cost<<'\n';
return out;
}
class Graph{
private:
//private variables
int vertices, edges;
bool oriented, weighted;
vector<vector<Edge>> adjacency_list;
vector<Edge> edges_list;
//To compute:
vector<unordered_set<int>> biconnected_components;
vector<vector<int>> strongly_connected_components;
vector<int> topological;
vector<pair<int,int>> bridges;
vector<vector<int>> matrix_of_weights;
//private functions
//homework 1;
void BFS(int starting_vertex,vector<int>& distances);
void DFS(int vertex, vector<int>& visited);
void BCC(int vertex, vector<int>& parent,stack<int>& vertices_stack,vector<int>& discovery_time, vector<int>& lowest_reachable,int& timer);
void SCCTJ(int vertex, stack<int>& vertices_stack, vector<int>& discovery_time, vector<int>& lowest_reachable, vector<bool>& has_component,int& timer);
void SCCKJ(int vertex,vector<bool>& visited, vector<int>& component);
void CCN(int vertex, vector<int> &discovery_time, vector<int> &lowest_reachable,vector<bool>& visited,vector<int>& parent, int &timer);
void TOPOLOGICAL_SORT(int vertex, vector<int>& visited);
vector<int> BFSMD(int starting_vertex);
//homework 2;
void KRUSKAL(vector<int>& parent, vector<int>& dimension,int& total_cost, vector<Edge>& mst);
void DIJKSTRA(int vertex, vector<int>& dist, priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>& heap);
void BELLMANFORD(int vertex, vector<int>& dist, queue<int>& que);
//homework 3;
void ROYFLOYD(vector<vector<int>>& matrix_of_weights);
public:
Graph(int vertices = 0,int edges = 0,bool oriented = false,bool weighted = false);
Graph transpose();
vector<int> get_topological(){return topological;}
vector<unordered_set<int>> get_biconnected() {return biconnected_components;}
vector<vector<int>> get_strongly_connected() {return strongly_connected_components;}
vector<pair<int,int>> get_bridges() {return bridges;}
void add_edge(int v1,int v2,int c = 0);
void infoarena_graph();
void show_my_graph();
vector<int> solve_distances(int starting_vertex);
int solve_connected_components();
void solve_biconnected();
void solve_strongly_connected_tarjan();
void solve_strongly_connected_kosaraju();
void solve_topological();
void solve_critical_connections();
void solve_starting_ending_distance(int starting_vertex,int ending_vertex);
//homework 2;
int find(int v,vector<int>& parent);
bool unite(int v1,int v2,vector<int>& parent, vector<int>& dimension);
void update(int v1,int v2, int cost, vector<int>& dist);
pair<vector<Edge>,int> solve_apm();
vector<int> solve_dijkstra();
vector<int> solve_bellman_ford();
//homework 3;
int solve_tree_diameter();
void solve_roy_floyd();
};
template <class T>
void printv(vector<T> xs){
for(T i : xs) cout<<i<<' ';
cout<<'\n';
}
int main()
{
int N;
fin>>N;
Graph g(N);
g.solve_roy_floyd();
}
#pragma region utilities
Graph::Graph(int vertices, int edges, bool oriented, bool weighted) :
vertices(vertices),
edges(edges),
oriented(oriented),
weighted(weighted)
{
adjacency_list.resize(vertices + 1);
}
Graph Graph::transpose()
{
Graph gt(vertices,edges,oriented,weighted);
for(int i = 1;i<vertices+1;i++)
for(auto path : adjacency_list[i])
gt.adjacency_list[path.destination].push_back(Edge(path.destination,i,path.cost));
return gt;
}
void Graph::add_edge(int v1,int v2,int c)
{
adjacency_list[v1].push_back(Edge(v1,v2,c));
edges++;
}
void Graph::infoarena_graph() {
int x,y;
int c = 0;
for(int i = 1;i<=edges;i++)
{
fin>>x>>y;
if(weighted)
fin>>c;
Edge e(x,y,c);
adjacency_list[x].push_back(e);
edges_list.push_back(e);
if(!oriented)
adjacency_list[y].push_back(Edge(y,x,c));
}
}
void Graph::show_my_graph() {
for(int i = 1;i<=vertices;i++){
cout<<i<<"=>";
for(auto path : adjacency_list[i])
cout<<path.destination<<' ';
cout<<'\n';
}
}
#pragma endregion
//homework 1;
#pragma region Homework1_private
void Graph::BFS(int starting_vertex,vector<int>& distances)
{
distances.resize(vertices+1,-1);
queue<int> que;
que.push(starting_vertex);
distances[starting_vertex] = 0;
while(!que.empty()){
int vert = que.front();
que.pop();
for(auto path : adjacency_list[vert])
if(distances[path.destination] == -1){
que.push(path.destination);
distances[path.destination] = distances[vert] + 1;
}
}
}
void Graph::DFS(int vertex, vector<int>& visited)
{
visited[vertex] = 1;
for(auto path : adjacency_list[vertex])
if(!visited[path.destination])
DFS(path.destination,visited);
}
void Graph::BCC(int vertex, vector<int>& parent,stack<int>& vertices_stack,vector<int>& discovery_time, vector<int>& lowest_reachable,int& timer)
{
discovery_time[vertex] = lowest_reachable[vertex] = ++timer;
for(auto path : adjacency_list[vertex])
{
vertices_stack.push(vertex);
if(parent[path.destination] == -1){
parent[path.destination] = vertex;
//will DFS till it reaches a leaf in dfs tree pushing nodes into the stack
BCC(path.destination,parent,vertices_stack,discovery_time,lowest_reachable,timer);
//will recurr till it meet an articulation point
//updating lowest reachable value to the min of all its neighbors
lowest_reachable[vertex] = min(lowest_reachable[vertex],lowest_reachable[path.destination]);
//articulation point is found when its discovery time is less than or equal to the lowest_reachable value of the neighbor
if(discovery_time[vertex] <= lowest_reachable[path.destination])
{
int aux;
biconnected_components.push_back(unordered_set<int>());
int n = biconnected_components.size();
aux = vertices_stack.top();
while(aux!=vertex)
{
if(biconnected_components[n-1].find(aux) == biconnected_components[n-1].end()){
biconnected_components[n-1].insert(aux);
}
aux = vertices_stack.top();
vertices_stack.pop();
}
biconnected_components[n-1].insert(aux);
}
}
//the leaf will check all cross edges of the dfs tree and update lowest_reachable to the first discovered
else{
lowest_reachable[vertex] = min(lowest_reachable[vertex],discovery_time[path.destination]);
}
}
}
void Graph::SCCTJ(int vertex,stack<int>& vertices_stack, vector<int>& discovery_time,vector<int>& lowest_reachable, vector<bool>& has_component, int& timer)
{
discovery_time[vertex] = lowest_reachable[vertex] = ++timer;
vertices_stack.push(vertex);
for(auto path : adjacency_list[vertex])
{
if(discovery_time[path.destination]==-1)
{
//will DFS till it reaches a leaf
SCCTJ(path.destination,vertices_stack,discovery_time,lowest_reachable,has_component,timer);
//continue updating values of lowest reachable ancestor till we found an articulation point
lowest_reachable[vertex] = min(lowest_reachable[vertex],lowest_reachable[path.destination]);
}
//if the leaf is not a part(because we need a max component) of a connected component, update value of its lowest reachable ancestor
else if (!has_component[path.destination])
lowest_reachable[vertex] = min(lowest_reachable[vertex],discovery_time[path.destination]);
}
// oriented !!
// neither descendants nor vertex itself has no cross edges to vertex ancestors, means it is an articulation point
if(lowest_reachable[vertex] == discovery_time[vertex])
{
vector<int> component;
int temp;
do{
temp = vertices_stack.top();
vertices_stack.pop();
has_component[temp] = true;
component.push_back(temp);
}while(temp!=vertex);
strongly_connected_components.push_back(component);
}
}
//Kosaraju util strongly_connected;
void Graph::SCCKJ(int vertex,vector<bool>& visited, vector<int>& component)
{
visited[vertex] = true;
component.push_back(vertex);
for(auto path : adjacency_list[vertex])
if(!visited[path.destination])
SCCKJ(path.destination,visited,component);
}
void Graph::CCN(int vertex, vector<int> &discovery_time, vector<int> &lowest_reachable,vector<bool>& visited,vector<int>& parent, int &timer)
{
discovery_time[vertex] = lowest_reachable[vertex] = ++timer;
visited[vertex] = true;
for(auto path : adjacency_list[vertex])
{
if(!visited[path.destination])
{
parent[path.destination] = vertex;
CCN(path.destination,discovery_time,lowest_reachable,visited,parent,timer);
lowest_reachable[vertex] = min(lowest_reachable[vertex],lowest_reachable[path.destination]);
if(discovery_time[vertex] < lowest_reachable[path.destination])
bridges.push_back({vertex,path.destination});
}
else if(parent[vertex] != path.destination)
lowest_reachable[vertex] = min(lowest_reachable[vertex],discovery_time[path.destination]);
}
}
//topological sort (helps solving scc based on kosaraju algorithm)
void Graph::TOPOLOGICAL_SORT(int vertex, vector<int>& visited){
visited[vertex] = 1;
for(auto path : adjacency_list[vertex])
if(!visited[path.destination])
TOPOLOGICAL_SORT(path.destination,visited);
topological.push_back(vertex);
}
#pragma endregion
#pragma region Homework1_solutions
vector<int> Graph::solve_distances(int starting_vertex)
{
vector<int> distances;
BFS(starting_vertex,distances);
for(int i = 1;i<vertices+1;i++)
fout<<distances[i]<<' ';
return distances;
}
int Graph::solve_connected_components()
{
vector<int> visited(vertices+1,0);
int cnt = 0;
for(int i = 1;i<=vertices;i++)
if(!visited[i])
DFS(i,visited),cnt++;
return cnt;
}
void Graph::solve_biconnected(){
stack<int> vertices_stack;
vector<int> parent(vertices+1,-1);
vector<int> discovery_time(vertices+1,0);
vector<int> lowest_reachable(vertices+1,0);
int timer = 0;
BCC(1,parent,vertices_stack,discovery_time,lowest_reachable,timer);
fout<<biconnected_components.size()<<'\n';
for(auto components : biconnected_components){
for(auto i : components){
fout<<i<<' ';
}
fout<<'\n';
}
}
void Graph::solve_strongly_connected_tarjan()
{
stack<int> vertices_stack;
vector<int> discovery_time(vertices+1,-1);
vector<int> lowest_reachable(vertices+1,-1);
vector<bool> has_component(vertices+1,false);
int timer = 0;
for(int i = 1;i<vertices+1;i++)
if(discovery_time[i] == -1)
SCCTJ(i,vertices_stack,discovery_time,lowest_reachable,has_component,timer);
fout<<strongly_connected_components.size()<<'\n';
for(auto component : strongly_connected_components){
for(auto i : component) fout<<i<<' ';
fout<<'\n';
}
}
void Graph::solve_strongly_connected_kosaraju()
{
vector<bool> visited(vertices+1,false);
solve_topological();
printv(topological);
Graph gt = transpose();
//will iterate through topologically sorted vector and will do dfs from all unvisited vertices
//all the dfs will form strongly conected components
for(int i = topological.size()-1;i>=0;i--)
{
if(!visited[topological[i]])
{
vector<int> component;
gt.SCCKJ(topological[i],visited,component);
strongly_connected_components.push_back(component);
}
}
fout<<strongly_connected_components.size()<<'\n';
for(auto component : strongly_connected_components)
{
for(auto i : component)
fout<<i<<' ';
fout<<'\n';
}
}
void Graph::solve_topological()
{
vector<int> visited(vertices+1,0);
for(int i = 1;i<=vertices;i++)
if(!visited[i])
TOPOLOGICAL_SORT(i,visited);
}
#pragma endregion
//homework 2;
#pragma region Homework2
int Graph::find(int v,vector<int>& parent)
{
while(v!=parent[v])
v = parent[v];
return v;
}
bool Graph::unite(int v1, int v2,vector<int>& parent, vector<int>& dimension)
{
int v1_parent = find(v1,parent);
int v2_parent = find(v2,parent);
if(v1_parent == v2_parent) return false;
if(dimension[v1_parent] <= dimension[v2_parent])
{
parent[v1_parent] = v2_parent;
dimension[v2_parent] += dimension[v1_parent];
}
else
{
parent[v2_parent] = v1_parent;
dimension[v1_parent] += dimension[v2_parent];
}
return true;
}
void Graph::KRUSKAL(vector<int>& parent, vector<int>& dimension,int& total_cost,vector<Edge>& mst)
{
//sort edges by cost
sort(edges_list.begin(),edges_list.end(),[](Edge e1,Edge e2){ return e1.cost < e2.cost;});
//select each optimal edge
for(auto e : edges_list)
if(unite(e.source,e.destination,parent,dimension))
{
total_cost+=e.cost;
mst.push_back(e);
}
}
void Graph::DIJKSTRA(int vertex, vector<int>& dist, priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>& heap)
{
dist[vertex] = 0;
heap.push({0,vertex});
vector<int> vis(vertices+1,0);
//basically a BFS
//we always select to add a edge from a vertex with minimal distance
while(!heap.empty())
{
int node = heap.top().second;
heap.pop();
if(!vis[node])
for(auto path : adjacency_list[node])
{
if(!vis[path.destination])
if(dist[path.destination] == -1 || dist[path.destination] > path.cost + dist[node]){
dist[path.destination] = path.cost + dist[node];
heap.push({dist[path.destination],path.destination});
}
}
vis[node] = 1;
}
}
void Graph::BELLMANFORD(int vertex,vector<int>& dist,queue<int>& que)
{
que.push(vertex);
dist[vertex] = 0;
vector<int> check_count(vertices+1,0); //will check if a node has been checked n times
//if so quit
while(!que.empty())
{
int node = que.front();
que.pop();
check_count[node] += 1;
if(check_count[node] > vertices){
return;
}
for(auto path : adjacency_list[node])
{
int v2 = path.destination;
int cost = path.cost;
if(dist[v2] > dist[node] + cost)
{
dist[v2] = dist[node] + cost;
que.push(v2);
}
}
}
}
#pragma endregion
#pragma region Homework2_solve
pair<vector<Edge>, int> Graph::solve_apm()
{
vector<int> parent(vertices+1);
vector<int> dimension(vertices+1,1);
vector<Edge> mst;
for(int i = 1;i<vertices+1;i++)
parent[i] = i;
int total_cost = 0;
KRUSKAL(parent,dimension,total_cost,mst);
return make_pair(mst,total_cost);
}
vector<int> Graph::solve_dijkstra()
{
vector<int> dist(vertices+1,-1);
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>> heap;
DIJKSTRA(1,dist,heap);
return dist;
}
vector<int> Graph::solve_bellman_ford()
{
vector<int> dist(vertices+1,INT_MAX);
queue<int> que;
BELLMANFORD(1,dist,que);
for(int i = 0;i<edges;i++)
{
int v1 = edges_list[i].source;
int v2 = edges_list[i].destination;
int cost = edges_list[i].cost;
if(dist[v1] != INT_MAX && dist[v1] + cost < dist[v2])
{
cout<<"Ciclu negativ!";
vector<int> fs(1,0);
return fs;
}
}
return dist;
}
#pragma endregion
//homework 3;
int Graph::solve_tree_diameter()
{
vector<int> distances1;
BFS(1,distances1);
pair<int,int> id_val = {0,distances1[0]};
for(int i = 0;i<distances1.size();i++)
if(id_val.second < distances1[i])
id_val = {i,distances1[i]};
vector<int> distances2;
BFS(id_val.first,distances2);
for(int i = 0;i<distances2.size();i++)
if(id_val.second < distances2[i])
id_val = {i,distances2[i]};
return id_val.second;
}
void Graph::ROYFLOYD(vector<vector<int>>& matrix_of_weights)
{
for(int k = 1;k<=vertices;k++)
for(int i = 1;i<=vertices;i++)
for(int j = 1;j<=vertices;j++)
matrix_of_weights[i][j] = min(matrix_of_weights[i][j],matrix_of_weights[i][k]+matrix_of_weights[k][j]);
}
void Graph::solve_roy_floyd()
{
matrix_of_weights.resize(vertices+1,vector<int>(vertices,0));
int tmp;
for(int i = 1;i<=vertices;i++)
for(int j = 1;j<=vertices;j++)
{
fin>>tmp;
matrix_of_weights[i][j] = (tmp == 0) ? 1005 : tmp;
}
ROYFLOYD(matrix_of_weights);
for(int i = 1;i<=vertices;i++){
for(int j = 1;j<=vertices;j++){
if((matrix_of_weights[i][j] == 1005) || (i == j))
matrix_of_weights[i][j] = 0;
fout<<matrix_of_weights[i][j]<<' ';
}
fout<<'\n';
}
}