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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the queue with the start node.

DSA Javascript

const queue = [[1]];

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

Adistance

Bgraph

Cstart

Dvisited

Attempts:

3 left

💡 Hint

Common Mistakes

Adding the whole graph instead of the start node.

Starting with an empty queue.

We start BFS by adding the start node to the queue.

2fill in blank

medium

Complete the code to mark the start node as visited.

DSA Javascript

visited[[1]] = true;

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

Agraph

Bdistance

Cqueue

Dstart

Attempts:

3 left

💡 Hint

Common Mistakes

Marking the whole graph as visited.

Marking the queue or distance instead of the node.

We mark the start node as visited to avoid revisiting it.

3fill in blank

hard

Fix the error in the loop to get the current node from the queue.

DSA Javascript

const current = queue.[1]();

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

Ashift

Bpush

Cpop

Dunshift

Attempts:

3 left

💡 Hint

Common Mistakes

Using pop() which removes from the end, causing DFS behavior.

Using push() or unshift() which add elements instead of removing.

We use shift() to remove the first element from the queue in BFS.

4fill in blank

hard

Fill both blanks to check if a neighbor is unvisited and then mark it visited.

DSA Javascript

if (!visited[neighbor]) {
  visited[[1]] = true;
  queue.[2](neighbor);
}

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

Aneighbor

Bcurrent

Cpush

Dpop

Attempts:

3 left

💡 Hint

Common Mistakes

Marking the current node instead of the neighbor.

Using pop() which removes elements instead of adding.

We mark the neighbor as visited and add it to the queue using push().

5fill in blank

hard

Fill all three blanks to update the distance for neighbors correctly.

DSA Javascript

distance[neighbor] = distance[[1]] [2] 1;
queue.[3](neighbor);

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

Acurrent

B+

Cpush

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using '-' instead of '+' for distance update.

Adding neighbor with pop() instead of push().

The neighbor's distance is current node's distance plus one, then neighbor is added to the queue.

Practice

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

easy

A. The longest path between two nodes

B. The node with the highest degree

C. The total number of nodes in the graph

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

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 D

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 counts total nodes only

2. Which JavaScript data structure is best to implement the BFS queue for shortest path?

easy

A. Map to store node distances

B. Array with push and shift methods

C. Set to store unique nodes

D. Object with key-value pairs

Solution

1. Step 1: Identify BFS queue operations

   BFS requires adding nodes at the end and removing from the front, which is a queue behavior.

2. Step 2: Use Array methods for queue

   JavaScript arrays support push (add end) and shift (remove front), perfect for BFS queue.

3. Final Answer:

   Array with push and shift methods -> Option B

4. Quick Check:

   Queue = Array push/shift [OK]

Hint: Use array push/shift for BFS queue in JavaScript [OK]

Common Mistakes:

• Using Set as queue (no order guaranteed)
• Using Map for queue operations
• Using Object which has no order

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

const graph = {
  0: [1, 2],
  1: [0, 3],
  2: [0, 3],
  3: [1, 2, 4],
  4: [3]
};
// BFS from node 0

medium

A. [1, 0, 0, 1, 2]

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

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

D. [0, 2, 2, 3, 4]

Solution

1. Step 1: Initialize distances and start BFS

   Distance to start node 0 is 0. Neighbors 1 and 2 get distance 1.

2. Step 2: Visit neighbors of 1 and 2

   Node 3 is neighbor of 1 and 2, so distance is 2. Node 4 is neighbor of 3, distance 3.

3. Final Answer:

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

4. Quick Check:

   Distances = [0,1,1,2,3] [OK]

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

Common Mistakes:

• Assigning wrong distances to neighbors
• Mixing up node indices
• Forgetting to update distance only once

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

function bfs(graph, start) {
  const queue = [];
  const distances = {};
  queue.push(start);
  distances[start] = 0;
  while (queue.length > 0) {
    const node = queue.pop();
    for (const neighbor of graph[node]) {
      if (!(neighbor in distances)) {
        distances[neighbor] = distances[node] + 1;
        queue.push(neighbor);
      }
    }
  }
  return distances;
}

medium

A. Using pop() instead of shift() causes wrong BFS order

B. Distances should be initialized with -1

C. Neighbors should be checked before pushing start node

D. Queue should be a Set to avoid duplicates

Solution

1. Step 1: Check queue operations in BFS

   BFS requires FIFO order, so nodes must be removed from front using shift(), not pop() which removes from end.

2. Step 2: Effect of using pop()

   Using pop() makes it LIFO, turning BFS into DFS order, breaking shortest path logic.

3. Final Answer:

   Using pop() instead of shift() causes wrong BFS order -> Option A

4. Quick Check:

   Queue removal must be shift() for BFS [OK]

Hint: Use shift() to dequeue in BFS, not pop() [OK]

Common Mistakes:

• Using pop() instead of shift() for queue
• Initializing distances incorrectly
• Using Set for queue which loses order

5. Given a graph with nodes 0 to 5 and edges: 0-1, 0-2, 1-3, 2-3, 3-4, 4-5, what is the shortest path from node 0 to node 5 using BFS?

hard

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

B. [0, 2, 3, 4, 5]

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

D. [0, 2, 4, 5]

Solution

1. Step 1: Explore neighbors from node 0

   Neighbors are 1 and 2, both distance 1.

2. Step 2: From neighbors, explore node 3

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

3. Step 3: From node 3, go to 4 then 5

   Node 4 distance 3, node 5 distance 4. The path via 1 is [0,1,3,4,5].

4. Final Answer:

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

5. Quick Check:

   Shortest path = [0,1,3,4,5] [OK]

Hint: Trace BFS layers from start to target [OK]

Common Mistakes:

• Choosing longer paths ignoring BFS order
• Skipping nodes in path
• Confusing edges and neighbors