Graph Terminology Vertices Edges Directed Undirected Weighted in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare a graph vertex as an integer variable named 'vertex'.

DSA Java

int [1] = 5;

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

Aedge

Bvertex

Cweight

Dnode

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'edge' or 'weight' as variable name for a vertex.

The variable representing a graph vertex is commonly named vertex.

2fill in blank

medium

Complete the code to add an edge from vertex 1 to vertex 2 in a directed graph using adjacency list.

DSA Java

graph[1].[1](2);

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Aadd

Bget

Cclear

Dremove

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'remove' or 'get' instead of 'add'.

To add an edge in adjacency list, we use the add method to insert the destination vertex.

3fill in blank

hard

Fix the error in the code to correctly check if an edge exists from vertex u to vertex v in an undirected graph adjacency list.

DSA Java

if(graph[u].contains([1])) {
    System.out.println("Edge exists");
}

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

Av

Bgraph

Cu

Dedge

Attempts:

3 left

💡 Hint

Common Mistakes

Checking for u in u's adjacency list instead of v.

To check if an edge exists from u to v, we check if the adjacency list of u contains v.

4fill in blank

hard

Fill both blanks to create a weighted edge from vertex u to vertex v with weight w using an Edge class.

DSA Java

Edge e = new Edge([1], [2], w);

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

Au

Bv

Cw

Dweight

Attempts:

3 left

💡 Hint

Common Mistakes

Using weight or w as vertex parameters.

The Edge constructor takes source vertex u, destination vertex v, and weight w. Here, we fill u and v.

5fill in blank

hard

Fill all three blanks to create a map of vertices to their weights using Java streams.

DSA Java

Map<Integer, Integer> map = list.stream().filter(edge -> edge.getWeight() > [3]).collect(Collectors.toMap([1], [2]));

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AEdge::getVertex

BEdge::getWeight

C10

DEdge::getSource

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing vertex and weight methods or wrong filter value.

We map source vertices to weights and filter weights greater than 10.

Practice

1. Which of the following best describes a vertex in a graph?

easy

A. A point or node where edges meet

B. A line connecting two vertices

C. A graph with no edges

D. A graph that has weights on edges

Solution

1. Step 1: Understand the definition of vertex

   A vertex is a fundamental unit in a graph representing a point or node.

2. Step 2: Differentiate vertex from edges and graph types

   Edges connect vertices; weights and graph types describe edges or the whole graph, not vertices.

3. Final Answer:

   A point or node where edges meet -> Option A

4. Quick Check:

   Vertex = point/node [OK]

Hint: Vertices are points/nodes, edges are connections [OK]

Common Mistakes:

• Confusing edges with vertices
• Thinking weights define vertices
• Mixing graph types with vertex definition

2. Which of the following is the correct way to declare an undirected weighted graph using adjacency list in Java?

easy

A. Map graph = new HashMap<>();

B. Map graph = new TreeMap<>();

C. Map>> graph = new TreeSet<>();

D. Map>> graph = new HashMap<>();

Solution

1. Step 1: Identify data structure for weighted edges

   Weighted edges need to store both neighbor and weight, so Pair is used.

2. Step 2: Choose correct map and list types

   HashMap with List of pairs is standard for adjacency list of weighted graphs.

3. Final Answer:

   Map>> graph = new HashMap<>(); -> Option D

4. Quick Check:

   Weighted graph uses Pair for edges [OK]

Hint: Weighted edges need pairs: neighbor and weight [OK]

Common Mistakes:

• Using List<Integer> for weighted edges
• Using TreeSet instead of List for adjacency
• Confusing Map types for graph

3. Consider the following Java code snippet for a directed graph:

Map graph = new HashMap<>();
graph.put(1, Arrays.asList(2, 3));
graph.put(2, Arrays.asList(3));
graph.put(3, Arrays.asList());
System.out.println(graph.get(1));

What will be the output?

medium

A. null

B. [1, 2, 3]

C. [2, 3]

D. []

Solution

1. Step 1: Check what is stored for key 1

   Key 1 maps to list containing 2 and 3.

2. Step 2: Print the list for key 1

   Printing graph.get(1) outputs the list [2, 3].

3. Final Answer:

   [2, 3] -> Option C

4. Quick Check:

   graph.get(1) = [2, 3] [OK]

Hint: Print adjacency list for key to see neighbors [OK]

Common Mistakes:

• Expecting all vertices in output
• Confusing keys and values
• Assuming empty list prints null

4. The following code attempts to add an edge to an undirected graph represented by adjacency list. What is the bug?

void addEdge(Map graph, int u, int v) {
    graph.get(u).add(v);
}

medium

A. It adds edge only from u to v, missing v to u

B. It uses get() instead of put() to add edge

C. It should use a Set instead of List for adjacency

D. It should clear the adjacency list before adding

Solution

1. Step 1: Understand undirected graph edge addition

   Undirected edges must be added both ways: u to v and v to u.

2. Step 2: Analyze given code

   Code adds edge only from u to v, missing the reverse edge.

3. Final Answer:

   It adds edge only from u to v, missing v to u -> Option A

4. Quick Check:

   Undirected edges need both directions [OK]

Hint: Undirected edges require adding both directions [OK]

Common Mistakes:

• Adding edge only one way in undirected graph
• Confusing get() and put() usage
• Clearing adjacency list mistakenly

5. You have a weighted directed graph represented as:

Map>> graph = new HashMap<>();
graph.put(1, Arrays.asList(new Pair<>(2, 5), new Pair<>(3, 10)));
graph.put(2, Arrays.asList(new Pair<>(3, 2)));
graph.put(3, Arrays.asList());

How would you find the total weight of edges going out from vertex 1?

hard

A. Sum weights 10 + 2 = 12

B. Sum weights 5 + 10 = 15

C. Sum weights 5 + 2 = 7

D. Count edges: 2

Solution

1. Step 1: Identify edges from vertex 1

   Edges from 1 go to 2 with weight 5, and to 3 with weight 10.

2. Step 2: Sum the weights of these edges

   Total weight = 5 + 10 = 15.

3. Final Answer:

   Sum weights 5 + 10 = 15 -> Option B

4. Quick Check:

   Total outgoing weight from 1 = 15 [OK]

Hint: Add weights of all edges from the vertex [OK]

Common Mistakes:

• Adding weights from wrong vertices
• Counting edges instead of summing weights
• Mixing weights of different edges