Weighted graphs in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding weighted graph edges

In a weighted graph, what does the weight on an edge represent?

A The total number of edges in the graph

B The number of nodes connected by the edge

C The color assigned to the edge for visualization

D A value representing the cost, distance, or capacity between two nodes

💡 Hint

Think about what extra information a weighted graph provides compared to an unweighted graph.

The weight on an edge in a weighted graph usually represents a measurable value like cost, distance, or capacity between the two connected nodes.

📋 Factual

intermediate

Weighted graph representation

Which data structure is commonly used to represent a weighted graph efficiently?

A Adjacency matrix with weights stored in cells

B Simple list of nodes without edges

C Stack storing nodes in order of visitation

D Queue storing nodes for breadth-first traversal

💡 Hint

Consider how to store both connections and their weights compactly.

An adjacency matrix stores weights directly in the cells representing edges between nodes, making it a common choice for weighted graphs.

🔍 Analysis

advanced

Shortest path in weighted graphs

Given a weighted graph with positive edge weights, which algorithm is best suited to find the shortest path from one node to all others?

A Dijkstra's algorithm

B Topological sort

C Breadth-first search (BFS)

D Depth-first search (DFS)

💡 Hint

Think about an algorithm that considers edge weights and finds minimum distances efficiently.

Dijkstra's algorithm is designed to find the shortest path in weighted graphs with non-negative weights by exploring nodes with the smallest tentative distance first.

❓ Comparison

advanced

Difference between weighted and unweighted graphs

Which statement correctly distinguishes a weighted graph from an unweighted graph?

A Unweighted graphs cannot have cycles; weighted graphs can.

B Weighted graphs have edges with values representing costs; unweighted graphs treat all edges equally.

C Weighted graphs always have directed edges; unweighted graphs have undirected edges.

D Weighted graphs have more nodes than unweighted graphs.

💡 Hint

Focus on what extra information weighted graphs carry on edges.

Weighted graphs assign values to edges to represent costs or distances, while unweighted graphs consider all edges equal without weights.

❓ Reasoning

expert

Impact of negative weights in weighted graphs

What issue arises when using Dijkstra's algorithm on a weighted graph that contains negative edge weights?

A The algorithm will run faster because negative weights reduce distances.

B Dijkstra's algorithm will ignore negative edges and only consider positive ones.

C Dijkstra's algorithm may produce incorrect shortest path results because it assumes all weights are non-negative.

D There is no issue; Dijkstra's algorithm works correctly with negative weights.

💡 Hint

Consider the assumptions Dijkstra's algorithm makes about edge weights.

Dijkstra's algorithm assumes all edge weights are non-negative. Negative weights can cause it to miss shorter paths, leading to incorrect results.