Cycle Detection in Directed Graph in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the visited slice for all nodes.

DSA Go

visited := make([]bool, [1])

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Alen(graph)

Bcap(graph)

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using cap(graph) instead of len(graph)

Initializing visited with length 0 or 1

We need to create a visited slice with length equal to the number of nodes in the graph, which is len(graph).

2fill in blank

medium

Complete the code to mark the current node as being in the recursion stack.

DSA Go

recStack[[1]] = true

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Agraph

Bnode

Cvisited

Dindex

Attempts:

3 left

💡 Hint

Common Mistakes

Using graph or visited instead of node as index

Using an undefined variable like index

We mark the current node index as true in recStack to indicate it is in the recursion stack.

3fill in blank

hard

Fix the error in the DFS function to detect a cycle when a node is already in the recursion stack.

DSA Go

if recStack[neighbor] [1] true {
    return true
}

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A==

B>

C<

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '!=' instead of '=='

Using comparison operators like '<' or '>' on booleans

We check if recStack[neighbor] == true to detect a cycle in the recursion stack.

4fill in blank

hard

Fill both blanks to complete the DFS function that marks nodes visited and removes them from recursion stack.

DSA Go

visited[[1]] = true
recStack[[2]] = false

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Anode

Bneighbor

Ccurrent

Dindex

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variables for visited and recStack

Using neighbor or index instead of node

We mark the current node as visited and remove it from the recursion stack using the same node index.

5fill in blank

hard

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

DSA Go

for [1] := 0; [2] < len(graph); [3]++ {
    if !visited[i] {
        if dfs(i, graph, visited, recStack) {
            return true
        }
    }
}

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Ai

Dnode

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names in loop parts

Using 'node' instead of 'i' in the loop

The loop variable is 'i' used for initialization, condition, and increment to iterate over graph nodes.

Practice

1. What does cycle detection in a directed graph help us find?

easy

A. Whether there is a path that starts and ends at the same node following the direction of edges

B. The shortest path between two nodes

C. The total number of nodes in the graph

D. The maximum degree of any node

Solution

1. Step 1: Understand cycle in directed graph

   A cycle means a path that starts and ends at the same node, following edge directions.

2. Step 2: Identify what cycle detection finds

   Cycle detection checks if such a path exists in the graph.

3. Final Answer:

   Whether there is a path that starts and ends at the same node following the direction of edges -> Option A

4. Quick Check:

   Cycle detection = finding directed loops [OK]

Hint: Cycle means a loop following edge directions [OK]

Common Mistakes:

• Confusing cycle with shortest path
• Ignoring edge directions
• Thinking cycle means any repeated node

2. Which of the following Go code snippets correctly declares a graph as an adjacency list for cycle detection?

easy

A. graph := make(map[int][]int)

B. graph := []int{}

C. graph := map[int]int{}

D. graph := [][]int{}

Solution

1. Step 1: Understand adjacency list representation

   An adjacency list for a directed graph maps each node to a list of nodes it points to.

2. Step 2: Check Go syntax for adjacency list

   Using map[int][]int creates a map from int to slice of ints, perfect for adjacency list.

3. Final Answer:

   graph := make(map[int][]int) -> Option A

4. Quick Check:

   Adjacency list = map[int][]int [OK]

Hint: Adjacency list uses map of int to slice of int [OK]

Common Mistakes:

• Using slice of int only (no mapping)
• Using map[int]int which stores single int per node
• Using [][]int without map keys

3. What will be the output of the following Go code snippet detecting cycle in a directed graph?

package main
import "fmt"

func dfs(node int, graph map[int][]int, visited, recStack map[int]bool) bool {
    if recStack[node] {
        return true
    }
    if visited[node] {
        return false
    }
    visited[node] = true
    recStack[node] = true
    for _, neighbor := range graph[node] {
        if dfs(neighbor, graph, visited, recStack) {
            return true
        }
    }
    recStack[node] = false
    return false
}

func main() {
    graph := map[int][]int{
        1: {2},
        2: {3},
        3: {1},
    }
    visited := make(map[int]bool)
    recStack := make(map[int]bool)
    fmt.Println(dfs(1, graph, visited, recStack))
}

medium

A. false

B. true

C. Compilation error

D. Runtime panic

Solution

1. Step 1: Analyze graph structure

   Graph edges: 1->2, 2->3, 3->1 form a cycle.

2. Step 2: Trace DFS cycle detection

   DFS from node 1 visits 2, then 3, then back to 1 which is in recursion stack, so returns true.

3. Final Answer:

   true -> Option B

4. Quick Check:

   Cycle detected = true [OK]

Hint: Cycle if node revisited in recursion stack [OK]

Common Mistakes:

• Ignoring recursion stack for cycle detection
• Assuming visited alone detects cycle
• Confusing false with no cycle

4. Identify the bug in the following Go code snippet for cycle detection in a directed graph:

func dfs(node int, graph map[int][]int, visited map[int]bool) bool {
    if visited[node] {
        return true
    }
    visited[node] = true
    for _, neighbor := range graph[node] {
        if dfs(neighbor, graph, visited) {
            return true
        }
    }
    return false
}

medium

A. Return type should be int, not bool

B. Visited map should be a slice, not a map

C. Missing recursion stack to track nodes in current path

D. Graph should be a slice of slices, not a map

Solution

1. Step 1: Understand cycle detection logic

   Cycle detection in directed graph needs to track nodes in current recursion path (recursion stack).

2. Step 2: Identify missing recursion stack

   This code only uses visited to mark visited nodes, which cannot detect cycles correctly in directed graphs.

3. Final Answer:

   Missing recursion stack to track nodes in current path -> Option C

4. Quick Check:

   Recursion stack needed for directed cycle detection [OK]

Hint: Use recursion stack to detect back edges [OK]

Common Mistakes:

• Using only visited to detect cycles
• Confusing undirected and directed cycle detection
• Ignoring recursion stack leads to false negatives

5. Given a directed graph represented as adjacency list:

graph := map[int][]int{
    1: {2, 3},
    2: {4},
    3: {4, 5},
    4: {6},
    5: {6},
    6: {3},
}

Which nodes are part of a cycle in this graph?

hard

A. [1, 3, 5]

B. [1, 2, 5]

C. [2, 4, 5]

D. [3, 4, 6]

Solution

1. Step 1: Analyze edges for cycles

   Edges: 3->4, 4->6, 6->3 form a cycle involving nodes 3, 4, 6.

2. Step 2: Confirm cycle nodes

   Nodes 1, 2, 5 lead into cycle but are not part of cycle themselves.

3. Final Answer:

   [3, 4, 6] -> Option D

4. Quick Check:

   Cycle nodes = [3,4,6] [OK]

Hint: Trace back edges to find cycle nodes [OK]

Common Mistakes:

• Including nodes that only lead to cycle
• Missing nodes that form the cycle
• Confusing cycle membership with reachability