Articulation Point - I

Problem Statement

Given an undirected connected graph with V vertices and adjacency list adj. You are required to find all the vertices removing which (and edges through it) disconnects the graph into 2 or more components. Note: Indexing is zero-based i.e nodes numbering from (0 to V-1). There might be loops present in the graph.

Example 1:

Input:

Output:{1,4}
Explanation: Removing the vertex 1 will
discconect the graph as-

Removing the vertex 4 will disconnect the
graph as-

Your Task: You don't need to read or print anything. Your task is to complete the function articulationPoints() which takes V and adj as input parameters and returns a list containing all the vertices removing which turn the graph into two or more disconnected components in sorted order. If there are no such vertices then returns a list containing -1.

Intuition

Approach:

Similar to find bridges, just update low to start,

intuition is if adjacent cannot reach node, at earlier time than node
Then articulation point

Links

https://practice.geeksforgeeks.org/problems/articulation-point-1/1

Video Links

https://www.youtube.com/watch?v=j1QDfU21iZk

Approach 1:

C++

class Solution {
private:
    int timer = 1;
    void dfs(int node, int parent, vector<int> &vis, int tin[], int low[],
             vector<int> &mark, vector<int>adj[]) {
        vis[node] = 1;
        tin[node] = low[node] = timer;
        timer++;
        int child = 0;
        for (auto it : adj[node]) {
            if (it == parent) continue;
            if (!vis[it]) {
                dfs(it, node, vis, tin, low, mark, adj);
                low[node] = min(low[node], low[it]);
                if (low[it] >= tin[node] && parent != -1) {
                    mark[node] = 1;
                }
                child++;
            }
            else {
                low[node] = min(low[node], tin[it]);
            }
        }
        if (child > 1 && parent == -1) {
            mark[node] = 1;
        }
    }
public:
    vector<int> articulationPoints(int n, vector<int>adj[]) {
        vector<int> vis(n, 0);
        int tin[n];
        int low[n];
        vector<int> mark(n, 0);
        for (int i = 0; i < n; i++) {
            if (!vis[i]) {
                dfs(i, -1, vis, tin, low, mark, adj);
            }
        }
        vector<int> ans;
        for (int i = 0; i < n; i++) {
            if (mark[i] == 1) {
                ans.push_back(i);
            }
        }
        if (ans.size() == 0) return { -1};
        return ans;
    }
};

Approach 2:

C++

Approach 3:

C++

Approach 4:

C++