Dijkstra's Algorithm Single Source Shortest Path in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the distance to the source node as zero.

DSA Python

distances = {node: float('inf') for node in graph}
distances[source] = [1]

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

ANone

B1

C-1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Setting the distance to 1 instead of 0

Using None which is not a number

Setting distance to -1 which is invalid

The distance from the source node to itself is always zero.

2fill in blank

medium

Complete the code to select the unvisited node with the smallest distance.

DSA Python

current_node = min(
    (node for node in unvisited),
    key=lambda node: distances[node]
) if unvisited else [1]

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

A0

BNone

Cfloat('inf')

Dsource

Attempts:

3 left

💡 Hint

Common Mistakes

Setting current_node to 0 which may not be a node

Using float('inf') which is not a node

Using source which may cause infinite loops

If there are no unvisited nodes left, current_node should be None to stop the algorithm.

3fill in blank

hard

Fix the error in updating the distance for neighbor nodes.

DSA Python

for neighbor, weight in graph[current_node].items():
    if neighbor in unvisited:
        new_distance = distances[current_node] + weight
        if new_distance [1] distances[neighbor]:
            distances[neighbor] = new_distance

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

A>=

B>

C<

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using greater than which updates with longer paths

Using greater or equal which may cause unnecessary updates

Using less or equal which is correct but less precise

We update the neighbor's distance only if the new distance is smaller than the current known distance.

4fill in blank

hard

Fill both blanks to correctly remove the current node from unvisited and add it to visited.

DSA Python

unvisited.[1](current_node)
visited.[2](current_node)

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

Aremove

Badd

Cdiscard

Dpop

Attempts:

3 left

💡 Hint

Common Mistakes

Using pop which removes an arbitrary element

Using discard for adding elements

Using add to remove elements

We remove the current node from unvisited and add it to visited sets.

5fill in blank

hard

Fill all three blanks to complete the dictionary comprehension that builds the graph from edges.

DSA Python

graph = {}
for u, v, w in edges:
    graph.setdefault([1], [2])[[3]] = w

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

Au

B{}

Cv

D[]

Attempts:

3 left

💡 Hint

Common Mistakes

Using list [] instead of dictionary {} for neighbors

Using v as the main key instead of u

Using [] instead of {} in setdefault

We use u as the key, setdefault with an empty dictionary, and v as the neighbor key to assign weight w.

Practice

1. What is the main purpose of Dijkstra's Algorithm in graph theory?

easy

A. To sort vertices in topological order

B. To find the maximum flow in a network

C. To detect cycles in a graph

D. To find the shortest path from a single source to all other vertices

Solution

1. Step 1: Understand the algorithm's goal

   Dijkstra's Algorithm is designed to find the shortest distance from one starting point (source) to every other point in a graph.

2. Step 2: Compare with other graph algorithms

   Other algorithms like max flow or cycle detection serve different purposes, so they do not match Dijkstra's goal.

3. Final Answer:

   To find the shortest path from a single source to all other vertices -> Option D

4. Quick Check:

   Shortest path = find minimum distances [OK]

Hint: Dijkstra finds shortest paths from one start point [OK]

Common Mistakes:

• Confusing with max flow algorithms
• Thinking it detects cycles
• Assuming it sorts vertices

2. Which Python data structure is commonly used to efficiently select the next vertex with the smallest tentative distance in Dijkstra's Algorithm?

easy

A. List

B. Heap (Priority Queue)

C. Queue

D. Set

Solution

1. Step 1: Identify the need for efficient minimum extraction

   Dijkstra's Algorithm repeatedly picks the vertex with the smallest tentative distance, so an efficient way to get the minimum is needed.

2. Step 2: Choose the right data structure

   A heap or priority queue allows quick extraction of the smallest element, unlike lists or queues which are slower for this task.

3. Final Answer:

   Heap (Priority Queue) -> Option B

4. Quick Check:

   Priority queue = efficient min extraction [OK]

Hint: Use a heap to get smallest distance vertex fast [OK]

Common Mistakes:

• Using a simple list which is slow
• Using a queue which is FIFO, not min-based
• Using a set which has no order

3. What will be the output distances array after running Dijkstra's Algorithm from source vertex 0 on this graph represented by adjacency list with weights?

graph = {
  0: [(1, 4), (2, 1)],
  1: [(3, 1)],
  2: [(1, 2), (3, 5)],
  3: []
}

medium

A. [0, 4, 1, 6]

B. [0, 2, 1, 3]

C. [0, 3, 1, 4]

D. [0, 1, 2, 5]

Solution

1. Step 1: Initialize distances and start from vertex 0

   Distances: 0 to 0 = 0, others infinity initially. Update neighbors: vertex 1 = 4, vertex 2 = 1.

2. Step 2: Pick vertex with smallest distance (2), update neighbors

   From vertex 2, update vertex 1: min(4, 1+2=3) = 3, vertex 3 = 1+5=6.

3. Step 3: Pick vertex with smallest distance (1), update neighbors

   From vertex 1, update vertex 3: min(6, 3+1=4) = 4.

4. Step 4: Final distances

   Distances array is [0, 3, 1, 4].

5. Final Answer:

   [0, 3, 1, 4] -> Option C

6. Quick Check:

   Distances updated stepwise = [0, 3, 1, 4] [OK]

Hint: Update neighbors with min distance each step [OK]

Common Mistakes:

• Not updating vertex 1 distance from vertex 2
• Ignoring better path to vertex 3
• Mixing up edge weights

4. Consider this Dijkstra's Algorithm snippet in Python:

def dijkstra(graph, source):
    dist = {v: float('inf') for v in graph}
    dist[source] = 0
    visited = set()
    while len(visited) < len(graph):
        u = min((v for v in graph if v not in visited), key=lambda x: dist[x])
        visited.add(u)
        for v, w in graph[u]:
            if dist[u] + w < dist[v]:
                dist[v] = dist[u] + w
    return dist

What is the main issue with it?

medium

A. The algorithm does not use a priority queue for efficiency

B. The visited set is not updated properly

C. The algorithm does not handle unreachable vertices

D. The algorithm does not update distances correctly

Solution

1. Step 1: Analyze the selection of next vertex

   The code uses min() over all unvisited vertices to find the smallest distance vertex, which is correct but inefficient.

2. Step 2: Identify efficiency problem

   Without a priority queue, each min() call takes O(V) time, making the algorithm slower but still correct logically.

3. Step 3: Check for correctness vs efficiency

   Though inefficient, the code updates distances and visited set correctly, so the main issue is lack of priority queue for efficiency.

4. Final Answer:

   The algorithm does not use a priority queue for efficiency -> Option A

5. Quick Check:

   Missing priority queue = inefficient but correct [OK]

Hint: Dijkstra needs priority queue for speed, else slow [OK]

Common Mistakes:

• Thinking visited set is not updated
• Assuming distance updates are wrong
• Confusing unreachable vertex handling

5. Given a weighted graph with negative edge weights but no negative cycles, why can't Dijkstra's Algorithm be used to find shortest paths from a source vertex?

hard

A. Because Dijkstra's Algorithm assumes all edge weights are non-negative

B. Because Dijkstra's Algorithm cannot handle graphs with cycles

C. Because Dijkstra's Algorithm requires the graph to be directed acyclic

D. Because Dijkstra's Algorithm only works on unweighted graphs

Solution

1. Step 1: Understand Dijkstra's assumption on edge weights

   Dijkstra's Algorithm assumes all edge weights are zero or positive to guarantee correctness.

2. Step 2: Explain why negative weights break the algorithm

   Negative weights can cause the algorithm to miss shorter paths found later, as it greedily picks the smallest tentative distance.

3. Step 3: Clarify other options

   The algorithm can handle cycles if no negative cycles exist, and it works on weighted graphs, not just unweighted.

4. Final Answer:

   Because Dijkstra's Algorithm assumes all edge weights are non-negative -> Option A

5. Quick Check:

   Negative weights break Dijkstra's assumptions [OK]

Hint: Dijkstra fails if any edge weight is negative [OK]

Common Mistakes:

• Thinking it can't handle cycles at all
• Believing it only works on unweighted graphs
• Confusing negative cycles with negative edges