Shortest Path in Unweighted Graph Using BFS in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the queue for BFS traversal.

DSA Java

Queue<Integer> queue = new LinkedList<>();
queue.[1](start);

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

Aremove

Badd

Cpeek

Dpoll

Attempts:

3 left

💡 Hint

Common Mistakes

Using remove() instead of add() to insert elements.

Using poll() which removes elements instead of adding.

We use queue.add(start) to add the starting node to the BFS queue.

2fill in blank

medium

Complete the code to mark the starting node as visited.

DSA Java

boolean[] visited = new boolean[n];
visited[[1]] = true;

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A1

B0

Cn

Dstart

Attempts:

3 left

💡 Hint

Common Mistakes

Using a fixed index like 0 or 1 instead of the variable 'start'.

Using 'n' which is the size, not an index.

We mark the starting node as visited by setting visited[start] = true.

3fill in blank

hard

Fix the error in the BFS loop condition to continue while the queue is not empty.

DSA Java

while (!queue.[1]()) {
    int current = queue.poll();
    // process current
}

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

Acontains

BisFull

CisEmpty

Dempty

Attempts:

3 left

💡 Hint

Common Mistakes

Using isFull() which does not exist for queues.

Using empty() which is not a Java Queue method.

The method isEmpty() checks if the queue is empty. We continue while it is NOT empty.

4fill in blank

hard

Fill both blanks to check neighbors and update their distance if unvisited.

DSA Java

for (int neighbor : graph.get(current)) {
    if (!visited[neighbor]) {
        visited[neighbor] = [1];
        distance[neighbor] = distance[current] [2] 1;
        queue.add(neighbor);
    }
}

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

Atrue

B+

C-

Dfalse

Attempts:

3 left

💡 Hint

Common Mistakes

Setting visited to false instead of true.

Subtracting 1 from distance instead of adding.

We mark neighbors as visited by setting visited[neighbor] = true and update distance by adding 1.

5fill in blank

hard

Fill all three blanks to return the shortest path distance or -1 if unreachable.

DSA Java

return distance[[1]] != [2] ? distance[[3]] : -1;

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

Aend

BInteger.MAX_VALUE

Dstart

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'start' instead of 'end' for distance checks.

Comparing with 0 instead of Integer.MAX_VALUE.

We check if distance[end] is not Integer.MAX_VALUE (meaning reachable), then return distance[end], else -1.

Practice

1. What does BFS (Breadth-First Search) help find in an unweighted graph?

easy

A. The shortest path from a start node to all other nodes

B. The node with the highest degree

C. The longest path between two nodes

D. The total number of edges in the graph

Solution

1. Step 1: Understand BFS traversal

   BFS explores nodes level by level starting from the source node, visiting all neighbors before moving deeper.

2. Step 2: BFS finds shortest paths in unweighted graphs

   Because BFS visits nodes in order of increasing distance, the first time it reaches a node is via the shortest path.

3. Final Answer:

   The shortest path from a start node to all other nodes -> Option A

4. Quick Check:

   BFS = shortest path in unweighted graph [OK]

Hint: BFS visits nodes by distance layers to find shortest paths [OK]

Common Mistakes:

• Confusing BFS with DFS for shortest path
• Thinking BFS finds longest path
• Assuming BFS works only for weighted graphs

2. Which Java data structure is commonly used to implement BFS for shortest path in an unweighted graph?

easy

A. Queue

B. PriorityQueue

C. HashMap

D. Stack

Solution

1. Step 1: Recall BFS traversal order

   BFS explores nodes in a first-in, first-out order to visit neighbors level by level.

2. Step 2: Identify the correct data structure

   A Queue supports FIFO order, making it ideal for BFS traversal.

3. Final Answer:

   Queue -> Option A

4. Quick Check:

   BFS uses Queue for level order traversal [OK]

Hint: Use Queue for FIFO order in BFS traversal [OK]

Common Mistakes:

• Using Stack which is LIFO and suits DFS
• Confusing PriorityQueue with Queue
• Using HashMap which stores key-value pairs, not order

3. What is the output distance array after running BFS from node 0 on this graph?

Graph edges:
0 - 1
0 - 2
1 - 3
2 - 3
3 - 4

Assume nodes are 0 to 4 and distance to start node is 0.

medium

A. [0, 0, 0, 0, 0]

B. [0, 1, 2, 3, 4]

C. [0, 1, 1, 1, 2]

D. [0, 1, 1, 2, 3]

Solution

1. Step 1: Start BFS from node 0 and set distance 0

   Distance[0] = 0. Neighbors 1 and 2 get distance 1.

2. Step 2: Visit neighbors of 1 and 2

   Node 3 is neighbor of both 1 and 2, first reached at distance 2.

3. Step 3: Visit neighbor of 3

   Node 4 is neighbor of 3, distance is 3.

4. Final Answer:

   [0, 1, 1, 2, 3] -> Option D

5. Quick Check:

   Distances increase by 1 per BFS level [OK]

Hint: Distance increments by 1 each BFS layer from start [OK]

Common Mistakes:

• Assigning wrong distances to node 3
• Confusing BFS with DFS distances
• Setting all distances to zero

4. Identify the error in this BFS code snippet for shortest path:

int[] dist = new int[n];
Arrays.fill(dist, Integer.MAX_VALUE);
Queue<Integer> q = new LinkedList<>();
q.add(start);
dist[start] = 0;
while(!q.isEmpty()) {
  int u = q.poll();
  for(int v : graph.get(u)) {
    if(dist[v] == 0) {
      dist[v] = dist[u] + 1;
      q.add(v);
    }
  }
}

medium

A. The queue should be a Stack for BFS

B. Distance array should be initialized with zeros

C. The condition 'dist[v] == 0' should check for Integer.MAX_VALUE instead

D. The start node distance should be Integer.MAX_VALUE

Solution

1. Step 1: Understand distance initialization

   Distances are set to Integer.MAX_VALUE to mark unvisited nodes.

2. Step 2: Check visitation condition

   Condition 'dist[v] == 0' wrongly checks for zero, but unvisited nodes have Integer.MAX_VALUE.

3. Step 3: Correct condition

   Change condition to 'dist[v] == Integer.MAX_VALUE' to detect unvisited nodes properly.

4. Final Answer:

   The condition 'dist[v] == 0' should check for Integer.MAX_VALUE instead -> Option C

5. Quick Check:

   Check unvisited nodes by Integer.MAX_VALUE [OK]

Hint: Check unvisited nodes by initial max distance, not zero [OK]

Common Mistakes:

• Using zero to check unvisited nodes when distances initialized to max
• Using Stack instead of Queue for BFS
• Incorrect distance initialization

5. Given an unweighted graph with nodes 0 to 5 and edges:

0-1, 0-2, 1-3, 2-3, 3-4, 4-5

If BFS starts at node 0, what is the shortest path from node 0 to node 5?

hard

A. [0, 1, 2, 3, 4, 5]

B. [0, 1, 3, 4, 5]

C. [0, 2, 3, 5]

D. [0, 2, 4, 5]

Solution

1. Step 1: Run BFS to find shortest distances

   Distances: 0->0, 1->1, 2->1, 3->2, 4->3, 5->4.

2. Step 2: Trace shortest path from 5 back to 0

   From 5 to 4, 4 to 3, 3 to 1 or 2, choose 1 for shortest path: 0->1->3->4->5.

3. Final Answer:

   [0, 1, 3, 4, 5] -> Option B

4. Quick Check:

   Shortest path follows BFS layers [OK]

Hint: Trace path backward from target using distances [OK]

Common Mistakes:

• Choosing longer paths ignoring BFS distances
• Skipping nodes in path
• Confusing BFS with DFS path