Shortest Path in Unweighted Graph Using BFS in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does BFS stand for and what is its main use in graphs?

BFS stands for Breadth-First Search. It is used to explore all nodes in a graph level by level, which helps find the shortest path in an unweighted graph.

beginner

Why is BFS suitable for finding the shortest path in an unweighted graph?

Because BFS explores nodes in order of their distance from the start node, the first time it reaches a node, it has found the shortest path to that node.

beginner

In BFS for shortest path, what data structure is commonly used to keep track of nodes to visit next?

A queue is used to keep track of nodes to visit next, ensuring nodes are processed in the order they are discovered.

intermediate

What additional information do we store during BFS to reconstruct the shortest path?

We store the parent (or predecessor) of each node, so after BFS finishes, we can trace back from the target node to the start node to get the path.

intermediate

What is the time complexity of BFS when finding the shortest path in an unweighted graph?

The time complexity is O(V + E), where V is the number of vertices and E is the number of edges, because each node and edge is visited at most once.

What data structure does BFS use to explore nodes in the correct order?

A Hash Map

B Queue

C Priority Queue

D Stack

BFS uses a queue to explore nodes level by level.

In an unweighted graph, BFS finds the shortest path because it:

A Explores nodes in order of increasing distance from the start

B Explores nodes randomly

C Uses weights to calculate distances

D Only visits each node once

BFS explores nodes by their distance from the start, ensuring shortest paths.

Which of these is NOT needed to reconstruct the shortest path after BFS?

A Parent of each node

B Distance from start node

C Visited nodes list

D Stack of all nodes

A stack of all nodes is not needed; parent info is enough to reconstruct the path.

What is the initial step in BFS for shortest path?

A Mark all nodes as visited

B Enqueue all nodes

C Mark the start node as visited and enqueue it

D Dequeue the target node

BFS starts by marking the start node visited and adding it to the queue.

If BFS cannot reach the target node, what does that mean?

A There is no path from start to target

B The graph is weighted

C The graph is directed

D The BFS algorithm failed

If BFS can't reach the target, no path exists between start and target.

Explain step-by-step how BFS finds the shortest path in an unweighted graph.

Think about how BFS explores nodes and how to remember the path.

Describe how to reconstruct the shortest path after BFS completes.

Parents tell you where you came from for each node.

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