DFS Depth First Search on Graph in DSA Typescript - Build from Scratch

DFS Depth First Search on Graph

📖 Scenario: Imagine you have a map of cities connected by roads. You want to explore all cities starting from one city by traveling along the roads. This is like exploring a graph using Depth First Search (DFS).

🎯 Goal: You will build a simple graph using an adjacency list and write a DFS function to visit all connected cities starting from a given city.

📋 What You'll Learn

Create a graph as an adjacency list with exact cities and connections

Create a visited set to keep track of visited cities

Write a DFS function that visits cities recursively

Print the order of cities visited starting from 'A'

💡 Why This Matters

🌍 Real World

Graph traversal like DFS is used in maps, social networks, and solving puzzles by exploring connected points.

💼 Career

Understanding DFS is essential for software engineers working on algorithms, network analysis, and game development.

1

Create the graph as an adjacency list

Create a variable called graph as an object with these exact entries: 'A': ['B', 'C'], 'B': ['D'], 'C': ['E'], 'D': [], 'E': []

DSA Typescript

# Your code here

Hint

Use an object where keys are city names and values are arrays of connected cities.

2

Create a visited set to track visited cities

Create a variable called visited as a new empty Set<string>()

DSA Typescript

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

// Your code here

Hint

Use new Set<string>() to create an empty set for visited cities.

3

Write the DFS function to visit cities recursively

Write a function called dfs that takes a city: string. Inside, add city to visited. Then use for loop with neighbor over graph[city]. If neighbor is not in visited, call dfs(neighbor) recursively.

DSA Typescript

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

const visited: Set = new Set();

// Your code here

Hint

Use recursion to visit neighbors that are not yet visited.

4

Print the order of cities visited starting from 'A'

Call dfs('A') to start DFS from city 'A'. Then print the visited cities as an array using console.log(Array.from(visited))

DSA Typescript

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

const visited: Set = new Set();

function dfs(city: string): void {
  visited.add(city);
  for (const neighbor of graph[city]) {
    if (!visited.has(neighbor)) {
      dfs(neighbor);
    }
  }
}

// Your code here

Hint

Call dfs('A') and then print the visited cities as an array.

Practice

1. What is the main idea behind Depth First Search (DFS) on a graph?

easy

A. Explore as far as possible along each branch before backtracking

B. Visit all neighbors of a node before moving deeper

C. Visit nodes in order of their distance from the start node

D. Randomly visit nodes until all are visited

Solution

1. Step 1: Understand DFS traversal strategy

   DFS explores nodes by going deep into one branch before backtracking to explore other branches.

2. Step 2: Compare with other traversal methods

   BFS visits neighbors first, but DFS goes deep first, matching Explore as far as possible along each branch before backtracking.

3. Final Answer:

   Explore as far as possible along each branch before backtracking -> Option A

4. Quick Check:

   DFS = deep exploration first [OK]

Hint: DFS goes deep first, BFS goes wide first [OK]

Common Mistakes:

• Confusing DFS with BFS
• Thinking DFS visits neighbors first
• Assuming DFS visits nodes by distance

2. Which of the following is the correct TypeScript function signature for a DFS function on a graph represented as an adjacency list?

easy

A. function dfs(graph: Map, start: number): void

B. function dfs(graph: number[], start: number): void

C. function dfs(graph: number[][], start: number): void

D. function dfs(graph: string[][], start: string): void

Solution

1. Step 1: Identify graph representation type

   An adjacency list for a graph with numbered nodes is usually number[][], where each index holds neighbors.

2. Step 2: Check parameter types

   Start node is a number, so function signature with graph: number[][] and start: number is correct.

3. Final Answer:

   function dfs(graph: number[][], start: number): void -> Option C

4. Quick Check:

   Adjacency list = number[][], start node = number [OK]

Hint: Adjacency list uses array of arrays for neighbors [OK]

Common Mistakes:

• Using number[] instead of number[][] for adjacency list
• Using Map with incorrect value type
• Using string types for numeric graphs

3. What is the output of the following DFS traversal starting from node 0?

const graph = [[1, 2], [2], [0, 3], [3]];
const visited: boolean[] = [];
const result: number[] = [];
function dfs(node: number) {
  if (visited[node]) return;
  visited[node] = true;
  result.push(node);
  for (const neighbor of graph[node]) {
    dfs(neighbor);
  }
}
dfs(0);
console.log(result);

medium

A. [0, 2, 3, 1]

B. [0, 2, 1, 3]

C. [0, 1, 2]

D. [0, 1, 2, 3]

Solution

1. Step 1: Start DFS at node 0

   Visit 0, mark visited, add to result: [0]. Neighbors: 1, 2.

2. Step 2: Visit neighbor 1

   Visit 1, mark visited, add: [0,1]. Neighbor: 2.

3. Step 3: Visit neighbor 2 from 1

   Visit 2, mark visited, add: [0,1,2]. Neighbors: 0 (visited), 3.

4. Step 4: Visit neighbor 3 from 2

   Visit 3, mark visited, add: [0,1,2,3]. Neighbor: 3 (already visited).

5. Final Answer:

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

6. Quick Check:

   DFS order = [0,2,1,3] [OK]

Hint: Follow neighbors recursively, mark visited to avoid repeats [OK]

Common Mistakes:

• Not marking nodes visited before recursion
• Visiting neighbors in wrong order
• Ignoring already visited nodes

4. Identify the bug in this DFS implementation and choose the fix:

function dfs(node: number, graph: number[][], visited: boolean[]) {
  visited[node] = true;
  for (const neighbor of graph[node]) {
    if (!visited[neighbor]) {
      dfs(neighbor, graph, visited);
    }
  }
}

const graph = [[1], [2], [0]];
const visited = new Array(graph.length).fill(false);
dfs(0, graph, visited);
console.log(visited);

medium

A. Mark visited[node] = true after recursive calls

B. Initialize visited array with true instead of false

C. Add a base case to return if node is already visited at start

D. No bug, code works correctly

Solution

1. Step 1: Check visited marking timing

   Visited[node] is marked true before recursion, preventing revisits.

2. Step 2: Verify recursion and base case

   Recursion only happens if neighbor not visited, so no infinite loops.

3. Final Answer:

   No bug, code works correctly -> Option D

4. Quick Check:

   Visited marked before recursion = correct DFS [OK]

Hint: Mark visited before recursion to avoid cycles [OK]

Common Mistakes:

• Marking visited after recursion causing infinite loops
• Initializing visited array incorrectly
• Missing base case check

5. Given a graph with possible cycles, how can you modify DFS to detect if a cycle exists starting from a given node? Choose the best approach.

hard

A. Use a recursion stack array to track nodes in the current path and detect back edges

B. Only mark nodes visited after all neighbors are visited

C. Use BFS instead of DFS to detect cycles

D. Ignore visited nodes and continue traversal

Solution

1. Step 1: Understand cycle detection in DFS

   Detecting cycles requires knowing if a node is in the current recursion path (stack).

2. Step 2: Use recursion stack tracking

   Maintain a separate array to track nodes currently in recursion; if a neighbor is in this stack, a cycle exists.

3. Step 3: Evaluate other options

   Marking visited after neighbors or using BFS won't reliably detect cycles; ignoring visited nodes causes infinite loops.

4. Final Answer:

   Use a recursion stack array to track nodes in the current path and detect back edges -> Option A

5. Quick Check:

   Cycle detection = recursion stack tracking [OK]

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

Common Mistakes:

• Not tracking recursion stack causing missed cycles
• Using BFS which doesn't track recursion path
• Marking visited too late or ignoring visited nodes