Topological Sort Using DFS in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to add the current node to the stack after visiting all its neighbors.

DSA Javascript

function dfs(node, visited, stack, graph) {
  visited.add(node);
  for (const neighbor of graph[node]) {
    if (!visited.has(neighbor)) {
      dfs(neighbor, visited, stack, graph);
    }
  }
  stack.[1](node);
}

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

Apush

Bunshift

Cshift

Dpop

Attempts:

3 left

💡 Hint

Common Mistakes

Using pop instead of push removes elements instead of adding.

Using shift or unshift changes the order incorrectly.

We add the node to the stack after visiting all neighbors using push to maintain the correct order for topological sort.

2fill in blank

medium

Complete the code to mark a node as visited before exploring its neighbors.

DSA Javascript

function dfs(node, visited, stack, graph) {
  [1].add(node);
  for (const neighbor of graph[node]) {
    if (!visited.has(neighbor)) {
      dfs(neighbor, visited, stack, graph);
    }
  }
  stack.push(node);
}

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

Astack

Bgraph

Cvisited

Dnode

Attempts:

3 left

💡 Hint

Common Mistakes

Trying to add the node to the stack before visiting neighbors.

Adding the node to the graph object instead of visited set.

We mark the node as visited by adding it to the visited set before exploring neighbors.

3fill in blank

hard

Fix the error in the loop that iterates over all nodes to start DFS if not visited.

DSA Javascript

function topologicalSort(graph) {
  const visited = new Set();
  const stack = [];
  for (const node [1] Object.keys(graph)) {
    if (!visited.has(node)) {
      dfs(node, visited, stack, graph);
    }
  }
  return stack.reverse();
}

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

Aof

Bin

C=

Dto

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'in' which iterates over keys of an object, not array elements.

Using '=' which is assignment, not iteration.

Use 'of' to iterate over the array returned by Object.keys(graph) in a for...of loop.

4fill in blank

hard

Fill both blanks to correctly initialize the graph and call topologicalSort.

DSA Javascript

const graph = [1];
const result = topologicalSort([2]);
console.log(result);

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

A{'A': ['C'], 'B': ['C', 'D'], 'C': ['E'], 'D': ['F'], 'E': [], 'F': []}

Bgraph

D{'A': ['B'], 'B': ['C'], 'C': []}

Attempts:

3 left

💡 Hint

Common Mistakes

Passing a string instead of the graph object to the function.

Using an undefined variable instead of graph.

Initialize graph with the correct adjacency list and pass it to topologicalSort function.

5fill in blank

hard

Fill all three blanks to complete the DFS function with cycle detection.

DSA Javascript

function dfs(node, visited, stack, graph, temp) {
  if (temp.has(node)) throw new Error('Cycle detected');
  if (!visited.has(node)) {
    temp.add(node);
    for (const neighbor of graph[[1]]) {
      dfs(neighbor, visited, stack, graph, temp);
    }
    temp.[2](node);
    visited.[3](node);
    stack.push(node);
  }
}

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

Anode

Bdelete

Cadd

Dremove

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong method names like 'remove' which does not exist on Set.

Accessing neighbors with wrong variable.

Use 'node' to access neighbors, remove node from temp set with 'delete', and add node to visited set with 'add'.

Practice

1. What is the main purpose of using DFS in Topological Sort on a directed graph?

easy

A. To count the number of connected components

B. To find the shortest path between two nodes

C. To detect cycles in an undirected graph

D. To visit nodes in a way that ensures dependencies come before dependents

Solution

1. Step 1: Understand DFS role in Topological Sort

   DFS visits nodes deeply, ensuring all nodes reachable from a node are visited before it is processed.

2. Step 2: Relate DFS order to dependencies

   In Topological Sort, nodes are added after visiting all their dependencies, so dependencies come before dependents.

3. Final Answer:

   To visit nodes in a way that ensures dependencies come before dependents -> Option D

4. Quick Check:

   DFS ensures dependency order = A [OK]

Hint: DFS post-order gives correct dependency order [OK]

Common Mistakes:

• Confusing DFS with BFS for topological sorting
• Thinking DFS finds shortest paths
• Mixing cycle detection with topological order

2. Which of the following is the correct way to mark a node as visited in a DFS-based topological sort in JavaScript?

easy

A. visited = node;

B. visited.push(node);

C. visited[node] = true;

D. visited[node] == true;

Solution

1. Step 1: Understand visited marking in DFS

   Visited is usually an array or object where each node's visited status is stored as a boolean.

2. Step 2: Correct syntax for marking visited

   Assigning true to visited[node] marks that node visited; using '==' is comparison, not assignment.

3. Final Answer:

   visited[node] = true; -> Option C

4. Quick Check:

   Assign true to visited[node] = A [OK]

Hint: Use assignment (=), not comparison (==), to mark visited [OK]

Common Mistakes:

• Using '==' instead of '=' for assignment
• Using push on visited array instead of index assignment
• Overwriting visited variable instead of marking node

3. What will be the output of the following code snippet performing topological sort using DFS on the graph with edges: 5->2, 5->0, 4->0, 4->1, 2->3, 3->1?

const graph = {
  5: [2, 0],
  4: [0, 1],
  2: [3],
  3: [1],
  0: [],
  1: []
};

const visited = {};
const stack = [];

function dfs(node) {
  visited[node] = true;
  for (const neighbor of graph[node]) {
    if (!visited[neighbor]) dfs(neighbor);
  }
  stack.push(node);
}

for (const node in graph) {
  if (!visited[node]) dfs(node);
}

console.log(stack.reverse());

medium

A. [5, 4, 2, 3, 1, 0]

B. [4, 5, 0, 2, 3, 1]

C. [5, 4, 0, 2, 3, 1]

D. [4, 5, 2, 3, 1, 0]

Solution

1. Step 1: Perform DFS and track stack push order

   DFS visits nodes deeply, pushing nodes after visiting neighbors. For node 5: visits 2, then 3, then 1, then 0; for node 4: visits 0 and 1. Stack push order is [1,3,2,0,5,4] reversed to [4,5,0,2,3,1].

2. Step 2: Reverse stack to get topological order

   Reversing stack gives [4, 5, 0, 2, 3, 1], which respects dependencies.

3. Final Answer:

   [4, 5, 0, 2, 3, 1] -> Option B

4. Quick Check:

   DFS post-order reversed = [4,5,0,2,3,1] [OK]

Hint: Reverse DFS finishing order for topological sort output [OK]

Common Mistakes:

• Not reversing the stack before output
• Visiting nodes in wrong order due to object key iteration
• Confusing push order with final topological order

4. Identify the bug in this DFS-based topological sort code snippet:

function dfs(node, graph, visited, stack) {
  if (visited[node]) return;
  visited[node] = true;
  for (const neighbor of graph[node]) {
    dfs(neighbor, graph, visited, stack);
  }
  stack.push(node);
}

const graph = {0: [1], 1: [2], 2: []};
const visited = {};
const stack = [];
for (const node in graph) {
  dfs(node, graph, visited, stack);
}
console.log(stack.reverse());

medium

A. No bug; code works correctly

B. Visited check missing before recursive call

C. Stack should be cleared before DFS

D. Visited should be reset inside DFS function

Solution

1. Step 1: Analyze visited check and recursion

   The code checks if node is visited before recursion, preventing repeated visits.

2. Step 2: Confirm stack usage and output

   Nodes are pushed after visiting neighbors, and stack is reversed for correct order.

3. Final Answer:

   No bug; code works correctly -> Option A

4. Quick Check:

   No bug; code works correctly = C [OK]

Hint: Check visited before recursion to avoid repeats [OK]

Common Mistakes:

• Calling dfs without visited check causing infinite recursion
• Not reversing stack before output
• Resetting visited inside DFS causing wrong results

5. Given a directed graph with nodes and edges, how can you modify the DFS-based topological sort to detect if the graph has a cycle?

hard

A. Use an extra recursion stack to track nodes in the current DFS path and detect back edges

B. Count the number of nodes visited and compare with total nodes

C. Sort nodes by their degree before DFS

D. Run BFS instead of DFS to detect cycles

Solution

1. Step 1: Understand cycle detection in DFS

   Cycle exists if a node is visited again in the current DFS path (back edge).

2. Step 2: Use recursion stack to track current path

   Maintain a recursion stack array marking nodes currently in DFS call; if a neighbor is in recursion stack, cycle detected.

3. Final Answer:

   Use an extra recursion stack to track nodes in the current DFS path and detect back edges -> Option A

4. Quick Check:

   Recursion stack detects cycles = D [OK]

Hint: Track recursion stack to find back edges indicating cycles [OK]

Common Mistakes:

• Only using visited array without recursion stack
• Trying to detect cycles by node count mismatch
• Using BFS without proper cycle detection logic