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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to add the starting node to the queue.

DSA Python

queue = []
queue.[1](start)

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

Aappend

Bpop

Cremove

Dinsert

Attempts:

3 left

💡 Hint

Common Mistakes

Using pop() instead of append() which removes an element.

Using remove() which deletes a specific element.

Using insert() without specifying the index.

We use append() to add the starting node to the end of the queue for BFS.

2fill in blank

medium

Complete the code to dequeue the first element from the queue.

DSA Python

current = queue.[1](0)

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

Ainsert

Bappend

Cpop

Dremove

Attempts:

3 left

💡 Hint

Common Mistakes

Using append() which adds instead of removes.

Using remove() which removes by value, not index.

Using insert() which adds elements.

pop(0) removes and returns the first element from the queue.

3fill in blank

hard

Fix the error in checking if a neighbor has been visited.

DSA Python

if neighbor not in [1]:

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

Avisited

Bgraph

Cqueue

Dcurrent

Attempts:

3 left

💡 Hint

Common Mistakes

Checking in queue instead of visited.

Checking in graph which contains all nodes.

Checking in current which is a single node.

We check if neighbor is not in visited to avoid revisiting nodes.

4fill in blank

hard

Fill both blanks to update the distance and add neighbor to the queue.

DSA Python

distance[neighbor] = distance[current] [1] 1
queue.[2](neighbor)

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

A+

B-

Cappend

Dpop

Attempts:

3 left

💡 Hint

Common Mistakes

Using '-' instead of '+' which decreases distance.

Using pop() instead of append() which removes elements.

We add 1 to the current node's distance and append the neighbor to the queue.

5fill in blank

hard

Fill all three blanks to initialize the BFS data structures.

DSA Python

visited = set()
distance = [1]()
queue = []
visited.[2](start)
distance[start] = [3]

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

Adict

Badd

C0

Dlist

Attempts:

3 left

💡 Hint

Common Mistakes

Using list() instead of dict() for distance.

Using append() instead of add() for set.

Setting start distance to 1 instead of 0.

We use dict() for distance, add() to mark visited, and 0 as start distance.

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 longest path in the graph

C. The node with the highest degree

D. The cycle in the graph

Solution

1. Step 1: Understand BFS traversal

   BFS explores nodes level by level starting from the source node.

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

   Because BFS visits nodes in order of distance, it finds the shortest path to each node.

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 explores neighbors level-wise 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 Python data structure is best to implement the queue needed for BFS?

easy

A. list with append() and pop(0)

B. collections.deque for efficient pops from front

C. set to store unique nodes

D. dictionary to map nodes to distances

Solution

1. Step 1: Identify queue operations in BFS

   BFS requires adding to the back and removing from the front efficiently.

2. Step 2: Choose data structure with O(1) pops from front

   collections.deque supports fast append and popleft operations, unlike list pop(0) which is slow.

3. Final Answer:

   collections.deque for efficient pops from front -> Option B

4. Quick Check:

   Use deque for BFS queue [OK]

Hint: Use deque for fast queue operations in BFS [OK]

Common Mistakes:

• Using list pop(0) causing slow performance
• Using set which is unordered
• Using dict which is not a queue

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

graph = {0: [1, 2], 1: [0, 3], 2: [0], 3: [1]}

medium

A. [0, 2, 2, 3]

B. [1, 0, 1, 2]

C. [0, 1, 1, 2]

D. [0, 1, 2, 3]

Solution

1. Step 1: Initialize distances and start BFS from node 0

   Distance to 0 is 0, others are infinity initially.

2. Step 2: Visit neighbors level-wise

   Neighbors of 0 are 1 and 2, distance 1 each. Then neighbor of 1 is 3, distance 2.

3. Final Answer:

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

4. Quick Check:

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

Hint: Distance increments by 1 per BFS level [OK]

Common Mistakes:

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

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

def bfs(graph, start):
    from collections import deque
    queue = deque([start])
    distances = {start: 0}
    while queue:
        node = queue.pop()
        for neighbor in graph[node]:
            if neighbor not in distances:
                distances[neighbor] = distances[node] + 1
                queue.append(neighbor)
    return distances

medium

A. Using queue.pop() instead of queue.popleft() causes wrong order

B. Distances dictionary should be a list

C. Neighbors should be checked before popping from queue

D. Start node distance should be -1

Solution

1. Step 1: Check queue operations in BFS

   BFS requires removing from front (FIFO), but pop() removes from end (LIFO).

2. Step 2: Identify correct method to remove front element

   queue.popleft() removes from front, preserving BFS order.

3. Final Answer:

   Using queue.pop() instead of queue.popleft() causes wrong order -> Option A

4. Quick Check:

   Use popleft() for BFS queue [OK]

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

Common Mistakes:

• Using pop() causing DFS-like behavior
• Confusing list and dict for distances
• Incorrect initialization of distances

5. Given a grid where 0 represents open cell and 1 represents blocked cell, how can BFS be used to find the shortest path from top-left to bottom-right?

grid = [
  [0, 0, 1],
  [1, 0, 1],
  [1, 0, 0]
]

hard

A. Use BFS only on rows, ignoring columns

B. Run DFS to explore all paths and pick shortest

C. Use BFS but ignore blocked cells as neighbors

D. Treat each cell as a node, edges connect adjacent open cells; run BFS from start to find shortest path

Solution

1. Step 1: Model grid as graph nodes and edges

   Each open cell is a node; edges connect up/down/left/right neighbors if open.

2. Step 2: Run BFS from top-left to bottom-right

   BFS finds shortest path in unweighted graph; blocked cells are excluded from edges.

3. Final Answer:

   Treat each cell as a node, edges connect adjacent open cells; run BFS from start to find shortest path -> Option D

4. Quick Check:

   Grid BFS = shortest path via open neighbors [OK]

Hint: Model grid as graph, BFS finds shortest path avoiding blocks [OK]

Common Mistakes:

• Using DFS which is not shortest path
• Ignoring blocked cells incorrectly
• Not connecting neighbors properly