Connected Components Using BFS in DSA C - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare the queue size for BFS traversal.

DSA C

int queue[[1]];

Drag options to blanks, or click blank then click option'

A-1

B10

C0

D1000

Attempts:

3 left

💡 Hint

Common Mistakes

Using too small queue size causing overflow.

The queue size should be large enough to hold all nodes. Using 1000 ensures enough space for BFS.

2fill in blank

medium

Complete the code to mark a node as visited inside BFS.

DSA C

visited[[1]] = 1;

Drag options to blanks, or click blank then click option'

Anode

Bqueue[rear]

Ci

Dqueue[front]

Attempts:

3 left

💡 Hint

Common Mistakes

Marking wrong node as visited.

We mark the node at the front of the queue as visited after dequeuing it.

3fill in blank

hard

Fix the error in the BFS enqueue operation to add neighbors.

DSA C

if(adj[node][i] == 1 && visited[i] == 0) {
    queue[[1]] = i;
    rear++;
    visited[i] = 1;
}

Drag options to blanks, or click blank then click option'

Ai

Bnode

Crear

Dfront

Attempts:

3 left

💡 Hint

Common Mistakes

Adding at front index causing overwrite.

We add the neighbor at the rear of the queue before incrementing rear.

4fill in blank

hard

Fill both blanks to correctly initialize BFS queue pointers.

DSA C

int front = [1];
int rear = [2];

Drag options to blanks, or click blank then click option'

A0

B-1

C1

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Setting rear to 0 causes off-by-one errors.

Front starts at 0 and rear starts at -1 before any elements are enqueued.

5fill in blank

hard

Fill all three blanks to complete the BFS loop condition and dequeue operation.

DSA C

while([1] <= [2]) {
    int node = queue[[3]];
    front++;
    // process node
}

Drag options to blanks, or click blank then click option'

Arear

Bfront

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using rear as dequeue index.

The BFS loop runs while front <= rear. We dequeue from queue[front].

Practice

1. What does the BFS algorithm help find in an undirected graph when used to find connected components?

easy

A. All nodes reachable from a starting node forming one connected component

B. The shortest path between two nodes only

C. The number of edges in the graph

D. The degree of each node

Solution

1. Step 1: Understand BFS traversal in undirected graphs

   BFS explores all nodes reachable from a given start node by visiting neighbors level by level.

2. Step 2: Connect BFS to connected components

   By running BFS from an unvisited node, we find all nodes in that node's connected component.

3. Final Answer:

   All nodes reachable from a starting node forming one connected component -> Option A

4. Quick Check:

   BFS finds connected components by exploring reachable nodes [OK]

Hint: BFS visits all nodes in one connected component [OK]

Common Mistakes:

• Thinking BFS only finds shortest paths
• Confusing connected components with edge counts
• Assuming BFS finds node degrees

2. Which of the following is the correct way to mark a node as visited in BFS when using an array named visited and current node u?

easy

A. visited[u] = 0;

B. visited[u] = true;

C. visited[u] == true;

D. visited[u] = null;

Solution

1. Step 1: Understand marking visited nodes

   To mark a node visited, assign true to visited[u], indicating it is visited.

2. Step 2: Check syntax correctness

   Using visited[u] = true; correctly assigns the boolean true. Using == is a comparison, not assignment.

3. Final Answer:

   visited[u] = true; -> Option B

4. Quick Check:

   Assign true to mark visited[u] [OK]

Hint: Use assignment (=), not comparison (==), to mark visited [OK]

Common Mistakes:

• Using == instead of = for assignment
• Assigning 0 instead of true to visited
• Assigning null which is invalid in C

3. Given the following graph adjacency list and BFS code snippet, what is the output number of connected components?

int n = 5;
int adj[5][5] = {
  {0,1,0,0,0},
  {1,0,0,0,0},
  {0,0,0,1,1},
  {0,0,1,0,0},
  {0,0,1,0,0}
};
bool visited[5] = {false};

int count = 0;
for (int i = 0; i < n; i++) {
  if (!visited[i]) {
    bfs(i, adj, visited, n);
    count++;
  }
}
printf("%d\n", count);

medium

A. 2

B. 1

C. 3

D. 4

Solution

1. Step 1: Analyze adjacency matrix for connected components

   Nodes 0 and 1 are connected; nodes 2, 3, 4 form another connected group.

2. Step 2: Count connected components using BFS

   BFS from node 0 visits nodes 0 and 1; BFS from node 2 visits nodes 2, 3, 4. Total components = 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Two groups found by BFS = 2 [OK]

Hint: Count BFS runs on unvisited nodes for components [OK]

Common Mistakes:

• Counting edges instead of components
• Misreading adjacency matrix connections
• Forgetting to mark visited nodes

4. Identify the bug in this BFS function for counting connected components:

void bfs(int start, int adj[][5], bool visited[], int n) {
  queue<int> q;
  q.push(start);
  visited[start] = true;
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int v = 0; v < n; v++) {
      if (adj[u][v] == 1 && visited[v] == false) {
        q.push(v);
      }
    }
  }
}

medium

A. Loop condition should be while(q.size() > 1)

B. Queue is not initialized properly

C. Start node is not marked visited

D. Missing visited[v] = true; inside the loop

Solution

1. Step 1: Check BFS neighbor processing

   When a neighbor v is found unvisited, it must be marked visited immediately to avoid re-adding.

2. Step 2: Identify missing visited mark

   The code pushes v to queue but does not mark visited[v] = true; causing repeated visits.

3. Final Answer:

   Missing visited[v] = true; inside the loop -> Option D

4. Quick Check:

   Mark visited when enqueueing neighbors [OK]

Hint: Mark visited when pushing to queue, not after popping [OK]

Common Mistakes:

• Marking visited only after popping from queue
• Incorrect queue initialization
• Wrong loop condition for BFS

5. You have a graph with 7 nodes and edges: (0-1), (1-2), (3-4), (5-6). Using BFS to find connected components, what is the minimum number of BFS calls needed to find all components?

hard

A. 1

B. 2

C. 3

D. 4

Solution

1. Step 1: Identify connected components from edges

   Edges connect nodes into groups: {0,1,2}, {3,4}, {5,6}. Since nodes are numbered 0 to 6, there are no other nodes.

2. Step 2: Count connected components

   Groups are: {0,1,2}, {3,4}, {5,6} -> 3 components total.

3. Step 3: BFS calls equal connected components

   Each BFS call finds one component, so minimum BFS calls = 3.

4. Final Answer:

   3 -> Option C

5. Quick Check:

   Number of BFS calls = number of connected components [OK]

Hint: Count connected groups; BFS calls = groups [OK]

Common Mistakes:

• Counting edges instead of components
• Miscounting isolated nodes
• Assuming BFS calls equal nodes