Why Graphs Exist and What Trees Cannot Model in DSA Javascript - Test Your Knowledge

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a graph node with a value and an empty list of neighbors.

DSA Javascript

class GraphNode {
  constructor(value) {
    this.value = value;
    this.neighbors = [1];
  }
}

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

A[]

Bnull

C{}

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using an object {} instead of an array for neighbors.

The neighbors of a graph node are stored in an array to hold multiple connected nodes.

2fill in blank

medium

Complete the code to add an edge from one node to another in an undirected graph.

DSA Javascript

function addEdge(node1, node2) {
  node1.neighbors.push([1]);
  node2.neighbors.push(node1);
}

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

Anode2

Bnode1

Cnull

Dundefined

Attempts:

3 left

💡 Hint

Common Mistakes

Adding node1 to its own neighbors list.

To add an edge, node2 is added to node1's neighbors list.

3fill in blank

hard

Fix the error in the code to check if a graph has a cycle using a visited set.

DSA Javascript

function hasCycle(node, visited = new Set()) {
  if (visited.has(node)) {
    return [1];
  }
  visited.add(node);
  for (const neighbor of node.neighbors) {
    if (hasCycle(neighbor, visited)) {
      return true;
    }
  }
  return false;
}

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

Anull

Bfalse

Ctrue

Dundefined

Attempts:

3 left

💡 Hint

Common Mistakes

Returning false when a cycle is detected.

If the node is already visited, it means a cycle exists, so return true.

4fill in blank

hard

Fill both blanks to create a function that counts the total edges in an undirected graph.

DSA Javascript

function countEdges(graph) {
  let count = 0;
  for (const node of graph) {
    count += node.[1].length;
  }
  return count [2] 2;
}

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

Aneighbors

B*

C/

Dlength

Attempts:

3 left

💡 Hint

Common Mistakes

Multiplying by 2 instead of dividing.

Using wrong property instead of neighbors.

Count all neighbors for each node, then divide by 2 because edges are counted twice in an undirected graph.

5fill in blank

hard

Fill all three blanks to create a function that finds if a path exists between two nodes using DFS.

DSA Javascript

function pathExists(start, target, visited = new Set()) {
  if (start.value === [1]) return true;
  visited.add(start);
  for (const neighbor of start.[2]) {
    if (!visited.has(neighbor) && pathExists(neighbor, [3], visited)) {
      return true;
    }
  }
  return false;
}

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

Atarget.value

Bneighbors

Ctarget

Dstart.value

Attempts:

3 left

💡 Hint

Common Mistakes

Comparing start.value with start.value instead of target.value.

Using wrong variable for recursion.

Check if start node's value equals target's value, iterate over neighbors, and recursively check path existence.

Practice

1. Why do we need graphs when we already have trees in data structures?

easy

A. Because graphs can represent connections between nodes in any direction, including cycles.

B. Because trees are faster to search than graphs.

C. Because trees can only store numbers, not other data types.

D. Because graphs use less memory than trees.

Solution

1. Step 1: Understand tree limitations

   Trees are hierarchical and cannot represent cycles or multiple parent connections.

2. Step 2: Understand graph capabilities

   Graphs allow nodes to connect in any way, including cycles and multiple parents.

3. Final Answer:

   Because graphs can represent connections between nodes in any direction, including cycles. -> Option A

4. Quick Check:

   Graphs model cycles and complex connections = C [OK]

Hint: Graphs allow cycles; trees do not [OK]

Common Mistakes:

• Thinking trees can have cycles
• Confusing memory use between trees and graphs
• Assuming trees only store numbers

2. Which of the following is the correct way to represent an undirected graph using adjacency lists in JavaScript?

easy

A. const graph = [ [1, 2], [2, 3], [3, 1] ];

B. const graph = { 1: [2, 3], 2: [1], 3: [1] };

C. const graph = { 1: 2, 2: 3, 3: 1 };

D. const graph = [[1, 2], [2, 3], [3, 1]];

Solution

1. Step 1: Understand adjacency list format

   An adjacency list uses an object with keys as nodes and values as arrays of connected nodes.

2. Step 2: Check each option

   const graph = { 1: [2, 3], 2: [1], 3: [1] }; correctly uses an object with arrays for neighbors; others use incorrect formats.

3. Final Answer:

   const graph = { 1: [2, 3], 2: [1], 3: [1] }; -> Option B

4. Quick Check:

   Adjacency list = object with arrays [OK]

Hint: Adjacency lists use objects with arrays of neighbors [OK]

Common Mistakes:

• Using arrays of pairs instead of adjacency lists
• Assigning single values instead of arrays
• Confusing syntax for objects and arrays

3. What will be the output of the following JavaScript code that models a graph with cycles?

const graph = {
  A: ['B'],
  B: ['C', 'D'],
  C: ['A'],
  D: []
};

function hasCycle(node, visited, stack) {
  if (!visited[node]) {
    visited[node] = true;
    stack[node] = true;
    for (const neighbor of graph[node]) {
      if (!visited[neighbor] && hasCycle(neighbor, visited, stack)) {
        return true;
      } else if (stack[neighbor]) {
        return true;
      }
    }
  }
  stack[node] = false;
  return false;
}

console.log(hasCycle('A', {}, {}));

medium

A. TypeError

B. false

C. undefined

D. true

Solution

1. Step 1: Analyze graph structure

   Graph has nodes A->B, B->C,D, C->A forming a cycle A->B->C->A.

2. Step 2: Trace hasCycle function

   Function detects cycles using recursion and stack tracking; it returns true when cycle found.

3. Final Answer:

   true -> Option D

4. Quick Check:

   Cycle detected in graph = true [OK]

Hint: Cycle detection returns true if back edge found [OK]

Common Mistakes:

• Ignoring the cycle from C back to A
• Assuming no cycles in directed graphs
• Confusing visited and stack usage

4. The following code attempts to check if a graph has cycles but has a bug. What is the bug?

const graph = {
  1: [2],
  2: [3],
  3: [1]
};

function detectCycle(node, visited) {
  if (visited[node]) return true;
  visited[node] = true;
  for (const neighbor of graph[node]) {
    if (detectCycle(neighbor, visited)) return true;
  }
  return false;
}

console.log(detectCycle(1, {}));

medium

A. The graph object keys should be strings, not numbers.

B. The visited object is not initialized properly.

C. The function does not track recursion stack to detect back edges.

D. The function should return false immediately after visiting a node.

Solution

1. Step 1: Understand cycle detection logic

   Detecting cycles in directed graphs requires tracking recursion stack to find back edges.

2. Step 2: Identify missing recursion stack tracking

   Code only uses visited set, so it cannot distinguish between visited nodes in current path and others.

3. Final Answer:

   The function does not track recursion stack to detect back edges. -> Option C

4. Quick Check:

   Missing recursion stack tracking = bug [OK]

Hint: Track recursion stack to detect cycles in directed graphs [OK]

Common Mistakes:

• Assuming visited alone detects cycles
• Confusing graph keys types
• Returning false too early

5. You want to model a social network where users can follow each other, including mutual follows and cycles. Which data structure best models this, and why can't a tree be used here?

hard

A. Use a graph because it supports cycles and multiple connections; trees cannot model cycles or multiple parents.

B. Use a tree because it is simpler and supports mutual connections.

C. Use an array because it can store all users linearly.

D. Use a linked list because it supports cycles naturally.

Solution

1. Step 1: Understand social network connections

   Users can follow each other mutually, creating cycles and multiple parent connections.

2. Step 2: Compare data structures

   Trees are hierarchical and cannot represent cycles or multiple parents; graphs can model these complex relationships.

3. Final Answer:

   Use a graph because it supports cycles and multiple connections; trees cannot model cycles or multiple parents. -> Option A

4. Quick Check:

   Social network needs graph for cycles = A [OK]

Hint: Social networks need graphs for cycles and mutual links [OK]

Common Mistakes:

• Choosing trees for mutual connections
• Using arrays or lists for complex relations
• Ignoring cycles in social networks