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Critical Connections in a Network in C++
Suppose there are n servers. And these are numbered from 0 to n-1 connected by an undirected server-to-server connections forming a network where connections[i] = [a,b] represents a connection between servers a and b. All servers are connected directly or through some other servers. Now, a critical connection is a connection that, if that is removed, it will make some server unable to reach some other server. We have to find all critical connections.
So, if the input is like n = 4 and connection = [[0,1],[1,2],[2,0],[1,3]],
then the output will be [[1,3]]
To solve this, we will follow these steps −
Define one set
Define an array disc
Define an array low
Define one 2D array ret
Define a function dfs(), this will take node, par, one 2D array graph,
if node is in of visited, then −
return
insert node into visited
disc[node] := time
low[node] := time
(increase time by 1)
for all elements x in graph[node]
if x is same as par, then −
Ignore following part, skip to the next iteration
if x is not in visited, then −
dfs(x, node, graph)
low[node] := minimum of low[node] and low[x]
if disc[node] < low[x], then −
insert { node, x } at the end of ret
Otherwise
low[node] := minimum of low[node] and disc[x]
From the main method, do the following −
set size of disc as n + 1
set size of low as n + 1
time := 0
Define an array of lists of size graph n + 1
for initialize i := 0, when i < size of v, update (increase i by 1), do −
u := v[i, 0]
w := v[i, 1]
insert w at the end of graph[u]
insert u at the end of graph[w]
dfs(0, -1, graph)
return ret
Let us see the following implementation to get better understanding −
Example
#include <bits/stdc++.h>
using namespace std;
void print_vector(vector<vector<auto> > v){
cout << "[";
for(int i = 0; i<v.size(); i++){
cout << "[";
for(int j = 0; j <v[i].size(); j++){
cout << v[i][j] << ", ";
}
cout << "],";
}
cout << "]"<<endl;
}
class Solution {
public:
set<int> visited;
vector<int> disc;
vector<int> low;
int time;
vector<vector<int> > ret;
void dfs(int node, int par, vector<int> graph[]) {
if (visited.count(node))
return;
visited.insert(node);
disc[node] = low[node] = time;
time++;
for (int x : graph[node]) {
if (x == par)
continue;
if (!visited.count(x)) {
dfs(x, node, graph);
low[node] = min(low[node], low[x]);
if (disc[node] < low[x]) {
ret.push_back({ node, x });
}
} else{
low[node] = min(low[node], disc[x]);
}
}
}
vector<vector<int> > criticalConnections(int n, vector<vector<int> >& v) {
disc.resize(n + 1);
low.resize(n + 1);
time = 0;
vector<int> graph[n + 1];
for (int i = 0; i < v.size(); i++) {
int u = v[i][0];
int w = v[i][1];
graph[u].push_back(w);
graph[w].push_back(u);
}
dfs(0, -1, graph);
return ret;
}
};
main(){
Solution ob;
vector<vector<int>> v = {{0,1},{1,2},{2,0},{1,3}};
print_vector(ob.criticalConnections(4,v));
}Input
4, {{0,1},{1,2},{2,0},{1,3}}Output
[[1, 3, ],]
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