DATA STRUCTURES PROGRAM • GRAPHS
Find Articulation Points with Tarjan's DFS
Learn how to find articulation points with tarjan's dfs using a clear C program.
PROBLEM UNDERSTANDING
Input and expected output
Sample input
No input required
Sample output
Articulation points: 0 3
COMPLETE C PROGRAM
Complete C implementation
#include <stdio.h>
void ap_dfs(int vertex, int graph[5][5], int visited[5], int discovery[5],
int low[5], int parent[5], int articulation[5], int *time)
{
visited[vertex] = 1; discovery[vertex] = low[vertex] = ++(*time);
int children = 0;
for (int neighbour = 0; neighbour < 5; neighbour++) if (graph[vertex][neighbour]) {
if (!visited[neighbour]) {
children++; parent[neighbour] = vertex;
ap_dfs(neighbour, graph, visited, discovery, low, parent, articulation, time);
if (low[neighbour] < low[vertex]) low[vertex] = low[neighbour];
if (parent[vertex] == -1 && children > 1) articulation[vertex] = 1;
if (parent[vertex] != -1 && low[neighbour] >= discovery[vertex]) articulation[vertex] = 1;
} else if (neighbour != parent[vertex] && discovery[neighbour] < low[vertex])
low[vertex] = discovery[neighbour];
}
}
int main(void)
{
int graph[5][5] = {
{0,1,1,1,0}, {1,0,1,0,0}, {1,1,0,0,0}, {1,0,0,0,1}, {0,0,0,1,0}
};
int visited[5] = {0}, discovery[5], low[5], parent[5] = {-1,-1,-1,-1,-1};
int articulation[5] = {0}, time = 0;
ap_dfs(0, graph, visited, discovery, low, parent, articulation, &time);
printf("Articulation points: ");
for (int vertex = 0; vertex < 5; vertex++) if (articulation[vertex]) printf("%d ", vertex);
putchar('\n');
return 0;
}CURRENT STEP
SELECTED LINE
EXPECTED OUTPUT FOR THE SAMPLE
Articulation points: 0 3
Step 0 of 0
PROGRAM EXPLANATION
Algorithm and explanation
- Read the required input values.
- Use low-link values to detect vertices whose DFS child cannot reach an ancestor.
- Display the computed result.
Use low-link values to detect vertices whose DFS child cannot reach an ancestor.
EFFICIENCY
Time and space complexity
Time complexity
O(V²) with matrix
Auxiliary space
O(V)
DEBUGGING CHECKLIST
Common mistakes
Check this
Use the correct format specifier for every variable.
Check this
Initialize variables before using their values.
Check this
Check braces, semicolons and input order carefully.
Try it yourself
Practice: Run the program with the sample input, predict its output, and then test one boundary case of your own.
