Articulation Points And Bridges

The pseudocode algorithm provided calculates the total number of articulation points in a graph.

Example

# Here, we are writing down the algorithm to demonstrate the concept of 
# Articulation Points and Bridges with their edge cases, functions, and algorithmic
# loops included articulating the brute force approach 
function find_articulation_points(adj[][], V)
    count = 0
    for i = 0 to V
        visited[i] = false
    initial_val = 0 
    for i = 0 to V
        if visited[i] == false
            DFS(adj, V, visited, i)
            initial_val = initial_val+1
# the below for loop code snippet help us with looping over the entire graph
    for i=0 to V
        for j = 0 to V
            visited[j] = false
            copy[j] = adj[i][j]
            adj[i][j]=adj[j][i]=0
# for loop code snippet helping us with mapping the visited nodes in a graph
        nval = 0
        for j= 0 to V
            if visited[j] == false AND j != i
                nval = nval + 1
                DFS(adj, n, visited, j)
# edge case shielding for the visited nodes in a graph data structure algorithm
        if nval > initial_val
            count = count + 1
        for j= 0 to V
            adj[i][j] = adj[j][i] = copy[j]
            # after the traversal, it returns us the number of articulation points
            # of the given graph structure
    return count
    # end of the Pseudocode algorithm of articulation points 
    # in a graph data structure

Pseudo Code

Example

# Here, we are writing down the algorithm to demonstrate the concept of 
# Articulation Points and Bridges with their edge cases, functions, and algorithmic
# loops included articulating the brute force approach     
time = 0
function DFS(adj[][], disc[], low[], visited[], parent[], AP[], vertex, V)
        visited[vertex] = true
        disc[vertex] = low[vertex] = time+1
        child = 0
    # the below for loop code snippet help us with looping over the entire graph
        for i = 0 to V
                if adj[vertex][i] == true
                        if visited[i] == false
                                child = child + 1
# for loop code snippet helping us with mapping the visited nodes in a graph
                                parent[i] = vertex
                                DFS(adj, disc, low, visited, parent, AP, i, n, time+1)
                                low[vertex] = minimum(low[vertex], low[i])
                                if parent[vertex] == nil and child > 1
                                        AP[vertex] = true
                                if parent[vertex] != nil and low[i] >= disc[vertex]
                                        AP[vertex] = true
# edge case shielding for the visited nodes in a graph data structure algorithm
                        else if parent[vertex] != i
                                low[vertex] = minimum(low[vertex], disc[i])
# after the traversal, it returns us the number of articulation points
# of the given graph structure
# end of the Pseudocode algorithm of articulation points 
# in a graph data structure

Bridges

The link between two vertices, such as x and y, within a graph is known as an articulation point. Once this link is eliminated, there are no remaining traversal routes. This action can expose weaknesses in the network accessible to the device or system. Similar to an articulation point, a thorough examination of every vertex in the complete graph data structure is required through brute force to verify the existence of paths by removing connections and confirming vertex connectivity.

Pseudo Code

Example

# Here, we are writing down the algorithm to demonstrate the concept of 
# Articulation Points and Bridges with their edge cases, functions, and algorithmic
# loops included articulating the brute force approach     
function find_bridges(adj[][], V, Edge[], E, isBridge[])
    for i = 0 to E
        adj[Edge[i].u][Edge[i].v]=adj[Edge[i].v][Edge[i].u]=0
        for j = 0 to V
            visited[j] = false
        Queue.Insert(Edge[i].u])
        visited[Edge[i].u] = true
        check = false
        while Queue.isEmpty() == false
            x = Queue.top()
            if x == Edge[i].v
                check = true
                BREAK
            Queue.Delete()
# the below for loop code snippet help us with looping over the entire graph
            for j = 0 to V
                if adj[x][j] == true AND visited[j] == false
                    Queue.insert(j)
                    visited[j] = true
        adj[Edge[i].u][Edge[i].v]=adj[Edge[i].v][Edge[i].u]=1
        if check == false
            isBridge[i] = true
# end of the Pseudocode algorithm of articulation points, bridges
    # in a graph data structure

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