Weighted graphs in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a weighted graph?

A weighted graph is a type of graph where each edge has a number called a weight. This weight often represents cost, distance, or time between two points.

beginner

How do weights in a graph help in real life?

Weights help show how much it costs or how far it is to move from one point to another, like distances on a map or prices in a network.

beginner

What is the difference between a weighted graph and an unweighted graph?

A weighted graph has numbers (weights) on edges, while an unweighted graph treats all edges as equal with no weights.

intermediate

What is a common use of weighted graphs in computer science?

Weighted graphs are used to find the shortest path between points, like GPS navigation or network routing.

advanced

Can weights in a weighted graph be negative? What does it mean?

Yes, weights can be negative in some cases. Negative weights might represent things like profit or gain, but they can make finding paths more complex.

What does the weight on an edge in a weighted graph usually represent?

A The cost or distance between two points

B The color of the edge

C The number of nodes in the graph

D The shape of the graph

Weights typically show cost, distance, or time between connected points.

Which of these is NOT true about weighted graphs?

A Edges have numbers called weights

B Weights can help find shortest paths

C Weights can represent time or cost

D All edges are considered equal

In weighted graphs, edges are not all equal because they have weights.

What is a common algorithm used with weighted graphs to find the shortest path?

A Dijkstra's algorithm

B Bubble sort

C Binary search

D Depth-first search

Dijkstra's algorithm is widely used to find shortest paths in weighted graphs.

Can weights in a weighted graph be negative?

A Only if the graph is unweighted

B Yes, sometimes

C No, never

D Only if the graph is directed

Weights can be negative in some graphs, but this requires special handling.

In a weighted graph, what does a higher weight on an edge usually mean?

A The edge is more important

B It is easier to travel

C It is more costly or longer to travel

D The edge connects more nodes

Higher weights usually mean higher cost or longer distance.

Explain what a weighted graph is and give a real-life example.

Think about how roads between cities have distances.

Describe why weights are important in graphs and how they affect finding paths.

Consider how GPS finds the fastest route.