Union Find Disjoint Set Data Structure in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the parent array so each element is its own parent.

DSA Go

for i := 0; i < n; i++ {
    parent[i] = [1]
}

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

Ai

B0

C-1

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Setting all parents to 0 causes wrong unions.

Using -1 or n as parent leads to invalid references.

Each element starts as its own parent, so parent[i] = i.

2fill in blank

medium

Complete the code to find the root parent of element x with path compression.

DSA Go

func find(x int) int {
    if parent[x] != x {
        parent[x] = [1](parent[x])
    }
    return parent[x]
}

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

Afind

Bunion

Cparent

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Using union instead of find causes errors.

Assigning parent[x] to parent[x] does nothing.

We recursively call find to get the root and compress the path.

3fill in blank

hard

Fix the error in the union function to correctly merge two sets.

DSA Go

func union(x, y int) {
    rootX := find(x)
    rootY := find(y)
    if rootX != rootY {
        parent[[1]] = rootY
    }
}

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

ArootY

By

Cx

DrootX

Attempts:

3 left

💡 Hint

Common Mistakes

Updating parent[x] or parent[y] instead of root parents.

Assigning parent[rootY] = rootX reverses the union.

We set the parent of rootX to rootY to merge the sets.

4fill in blank

hard

Fill both blanks to check if two elements are in the same set.

DSA Go

func connected(x, y int) bool {
    return find([1]) == find([2])
}

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

Ax

By

CrootX

DrootY

Attempts:

3 left

💡 Hint

Common Mistakes

Using rootX or rootY which are undefined here.

Comparing x and y directly without find.

We check if the roots of x and y are the same to confirm connection.

5fill in blank

hard

Fill all three blanks to implement union by rank optimization.

DSA Go

func union(x, y int) {
    rootX := find(x)
    rootY := find(y)
    if rootX != rootY {
        if rank[[1]] < rank[[2]] {
            parent[rootX] = rootY
        } else if rank[rootX] > rank[rootY] {
            parent[rootY] = rootX
        } else {
            parent[rootY] = rootX
            rank[[3]]++
        }
    }
}

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

ArootX

BrootY

Cx

Dy

Attempts:

3 left

💡 Hint

Common Mistakes

Using original elements x or y instead of root parents.

Increasing rank of wrong element.

We compare ranks of rootX and rootY, update parents accordingly, and increase rank of rootX if equal.

Practice

1. What is the main purpose of the Union Find Disjoint Set data structure?

easy

A. To efficiently track and merge groups of connected elements

B. To sort elements in ascending order

C. To store key-value pairs for fast lookup

D. To implement a queue with fast enqueue and dequeue

Solution

1. Step 1: Understand the role of Union Find

   The Union Find data structure helps keep track of which elements belong to the same group or set.

2. Step 2: Identify its main operation

   It supports merging two groups and checking if two elements are in the same group efficiently.

3. Final Answer:

   To efficiently track and merge groups of connected elements -> Option A

4. Quick Check:

   Union Find = Track and merge groups [OK]

Hint: Union Find manages connected groups fast [OK]

Common Mistakes:

• Confusing Union Find with sorting algorithms
• Thinking it stores key-value pairs
• Mixing it up with queue or stack data structures

2. Which of the following is the correct way to declare a Union Find parent array in Go for 5 elements?

easy

A. parent := make([]int, 5)

B. parent := [5]int{0}

C. parent := []int{5}

D. parent := make(int, 5)

Solution

1. Step 1: Understand Go slice creation

   To create a slice of integers with length 5, use make([]int, 5).

2. Step 2: Check each option

   parent := make([]int, 5) correctly uses make with []int and size 5. parent := [5]int{0} is an array but initializes only first element. parent := []int{5} creates a slice with one element 5, not length 5. parent := make(int, 5) is invalid syntax.

3. Final Answer:

   parent := make([]int, 5) -> Option A

4. Quick Check:

   Go slice with make([]int, 5) = correct [OK]

Hint: Use make([]int, size) to create int slice [OK]

Common Mistakes:

• Using make(int, 5) instead of make([]int, 5)
• Confusing array and slice syntax
• Initializing slice with single element instead of length

3. Consider the following Go code using Union Find:

parent := []int{0, 1, 2, 3, 4}

func find(x int) int {
    if parent[x] != x {
        parent[x] = find(parent[x])
    }
    return parent[x]
}

func union(a, b int) {
    rootA := find(a)
    rootB := find(b)
    if rootA != rootB {
        parent[rootB] = rootA
    }
}

union(0, 1)
union(1, 2)
union(3, 4)

fmt.Println(find(2), find(4))

What is the output?

medium

A. 1 3

B. 2 4

C. 0 4

D. 0 3

Solution

1. Step 1: Trace union operations

   union(0,1) merges sets of 0 and 1, so parent[1] = 0. union(1,2) merges sets of 1 and 2, so parent[2] = 0 (since find(1) = 0). union(3,4) merges sets of 3 and 4, so parent[4] = 3.

2. Step 2: Find roots of 2 and 4

   find(2) follows parent[2] = 0, so root is 0. find(4) follows parent[4] = 3, so root is 3.

3. Final Answer:

   0 3 -> Option D

4. Quick Check:

   Roots after unions = 0 and 3 [OK]

Hint: Follow parent links to find root [OK]

Common Mistakes:

• Not applying path compression in find
• Mixing up which root belongs to which element
• Assuming union merges by value instead of root

4. The following Go code for Union Find has a bug. What is the error?

parent := []int{0, 1, 2, 3, 4}

func find(x int) int {
    if parent[x] == x {
        return x
    }
    return find(parent[x])
}

func union(a, b int) {
    rootA := find(a)
    rootB := find(b)
    if rootA != rootB {
        parent[rootA] = rootB
    }
}

union(0, 1)
union(1, 2)
fmt.Println(find(2))

medium

A. Incorrect union direction causing unbalanced tree

B. Missing path compression in find function

C. Parent array not initialized properly

D. Using recursion in find causes stack overflow

Solution

1. Step 1: Analyze find function

   The find function recursively finds the root but does not update parent[x] to root, so path compression is missing.

2. Step 2: Understand impact of missing path compression

   Without path compression, the tree can become deep, causing slower future finds. The union logic is correct, and parent array is initialized properly.

3. Final Answer:

   Missing path compression in find function -> Option B

4. Quick Check:

   Path compression missing = bug [OK]

Hint: Add parent[x] = find(parent[x]) in find [OK]

Common Mistakes:

• Thinking union direction is always wrong
• Assuming recursion causes stack overflow here
• Ignoring path compression benefits

5. You have 6 elements (0 to 5) initially separate. After these unions: union(0,1), union(2,3), union(4,5), union(1,2), which of the following pairs are in the same set?

hard

A. 2 and 4

B. 1 and 5

C. 0 and 3

D. 3 and 5

Solution

1. Step 1: Track unions step-by-step

   union(0,1) merges sets {0,1}, union(2,3) merges {2,3}, union(4,5) merges {4,5}, union(1,2) merges sets containing 1 and 2, so {0,1,2,3} become one set.

2. Step 2: Check pairs

   Pair 0 and 3 are in the same set {0,1,2,3}. Pairs 1 and 5, 2 and 4, 3 and 5 are in different sets.

3. Final Answer:

   0 and 3 -> Option C

4. Quick Check:

   Unions merge sets correctly = 0 and 3 same set [OK]

Hint: Merge sets stepwise, check membership [OK]

Common Mistakes:

• Assuming all unions merge all elements
• Mixing sets after union(1,2)
• Confusing pairs in different sets