Path Compression in Union Find in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to find the root parent of a node in Union Find.

DSA Go

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

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

Ax

Bfind(parent, parent[x])

Cx + 1

Dparent[x]

Attempts:

3 left

💡 Hint

Common Mistakes

Returning parent[x] directly without recursion.

Returning x without checking if parent[x] == x.

The find function recursively finds the root parent of x by calling find on parent[x].

2fill in blank

medium

Complete the code to perform path compression during find operation.

DSA Go

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

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

Afind(parent, parent[x])

Bx

Cfind(parent, x)

Dparent[x]

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning parent[x] to x directly.

Calling find with x instead of parent[x].

Path compression sets parent[x] to the root parent found by recursively calling find on parent[x].

3fill in blank

hard

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

DSA Go

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

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

Aparent[rootY]

Bparent[x]

Cparent[y]

DrootY

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning parent[x] or parent[y] instead of parent[rootY].

Assigning rootY directly without using parent array.

To merge sets, set parent of rootY to rootX, linking rootY's tree under rootX.

4fill in blank

hard

Fill both blanks to implement union by rank optimization.

DSA Go

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

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

Aparent[rootX]

Bparent[x]

Cparent[rootY]

Dparent[y]

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping rootX and rootY in assignments.

Assigning parent[x] or parent[y] instead of parent[rootX] or parent[rootY].

If rank[rootX] < rank[rootY], set parent[rootX] = rootY; if rank[rootX] > rank[rootY], set parent[rootY] = rootX.

5fill in blank

hard

Fill all three blanks to implement find with path compression and union by rank.

DSA Go

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

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

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

Afind(parent, parent[x])

Bparent[rootX]

Cparent[rootY]

Dparent[x]

Attempts:

3 left

💡 Hint

Common Mistakes

Not using recursion in find for path compression.

Swapping parent assignments in union.

In find, assign parent[x] = find(parent, parent[x]) for path compression. In union, assign parent[rootX] = rootY if rank[rootX] < rank[rootY], else parent[rootY] = rootX.

Practice

1. What is the main purpose of path compression in the Union Find data structure?

easy

A. To speed up the find operation by making nodes point directly to the root

B. To merge two sets by size

C. To initialize the parent array

D. To count the number of connected components

Solution

1. Step 1: Understand the role of path compression

   Path compression is used during the find operation to flatten the tree structure by making nodes point directly to the root.

2. Step 2: Compare with other operations

   Merging sets by size is done in union by size/rank, not path compression. Initialization and counting components are unrelated to path compression.

3. Final Answer:

   To speed up the find operation by making nodes point directly to the root -> Option A

4. Quick Check:

   Path compression optimizes find = To speed up the find operation by making nodes point directly to the root [OK]

Hint: Path compression flattens trees to speed up find [OK]

Common Mistakes:

• Confusing path compression with union by size/rank
• Thinking it initializes the data structure
• Believing it counts components

2. Which of the following is the correct Go syntax for the find function with path compression in Union Find?

easy

A. func find(parent []int, x int) int { for parent[x] != x { x = parent[x] } return x }

B. func find(parent []int, x int) int { parent[x] = x; return x }

C. func find(parent []int, x int) int { if parent[x] == x { return x } else { return find(parent, x) } }

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

Solution

1. Step 1: Identify path compression in the code

   func find(parent []int, x int) int { if parent[x] != x { parent[x] = find(parent, parent[x]) } return parent[x] } recursively updates parent[x] to the root, which is path compression.

2. Step 2: Check other options for correctness

   func find(parent []int, x int) int { for parent[x] != x { x = parent[x] } return x } uses a loop but no path compression. func find(parent []int, x int) int { if parent[x] == x { return x } else { return find(parent, x) } } calls find without updating parent[x]. func find(parent []int, x int) int { parent[x] = x; return x } wrongly resets parent[x] to itself always.

3. Final Answer:

   func find(parent []int, x int) int { if parent[x] != x { parent[x] = find(parent, parent[x]) } return parent[x] } -> Option D

4. Quick Check:

   Recursive update of parent[x] = find(...) = func find(parent []int, x int) int { if parent[x] != x { parent[x] = find(parent, parent[x]) } return parent[x] } [OK]

Hint: Look for recursive parent update for path compression [OK]

Common Mistakes:

• Missing parent update in recursion
• Using loop without compression
• Resetting parent incorrectly

3. What will be the output of the following Go code snippet using Union Find with path compression?

package main
import "fmt"

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

func main() {
    parent := []int{0, 1, 2, 3, 4}
    parent[1] = 0
    parent[2] = 1
    fmt.Println(find(parent, 2))
    fmt.Println(parent)
}

medium

A. 1
[0 0 1 3 4]

B. 0
[0 0 0 3 4]

C. 2
[0 1 2 3 4]

D. 0
[0 1 0 3 4]

Solution

1. Step 1: Trace the find call for element 2

   find(2) calls find(1), which calls find(0). Since parent[0] = 0, root is 0.

2. Step 2: Apply path compression updates

   parent[2] is updated to 0, parent[1] is updated to 0. Final parent array is [0 0 0 3 4].

3. Final Answer:

   0 [0 0 0 3 4] -> Option B

4. Quick Check:

   Root of 2 is 0 and parent array updated = 0 [0 0 0 3 4] [OK]

Hint: Follow recursion and update parents on return [OK]

Common Mistakes:

• Not updating parent array after find
• Returning intermediate parent instead of root
• Confusing indices in parent array

4. Identify the bug in the following Go code implementing find with path compression:

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

medium

A. The function should not update parent[x] during recursion

B. The base case should check parent[x] != x instead of parent[x] == x

C. The recursive call should be find(parent, parent[x]) instead of find(parent, x)

D. The function should return x always

Solution

1. Step 1: Analyze the recursive call argument

   The recursive call uses find(parent, x), which causes infinite recursion because x does not change.

2. Step 2: Correct the recursive call

   It should call find(parent, parent[x]) to move up the tree towards the root.

3. Final Answer:

   The recursive call should be find(parent, parent[x]) instead of find(parent, x) -> Option C

4. Quick Check:

   Recursive call must move up tree = The recursive call should be find(parent, parent[x]) instead of find(parent, x) [OK]

Hint: Recursive find must use parent[x], not x [OK]

Common Mistakes:

• Calling find with same x causing infinite recursion
• Wrong base case condition
• Not updating parent[x] for compression

5. Given a Union Find structure with parent = [0, 0, 1, 2, 3], what will be the parent array after calling find(parent, 4) with path compression?

hard

A. [0, 0, 0, 0, 0]

B. [0, 0, 1, 2, 0]

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

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

Solution

1. Step 1: Trace the find call for element 4

   find(4) calls find(3), find(3) calls find(2), find(2) calls find(1), find(1) calls find(0). Root is 0.

2. Step 2: Apply path compression updates

   During recursion unwind: parent[1] = 0 (already), parent[2] = 0, parent[3] = 0, parent[4] = 0. Final parent array is [0, 0, 0, 0, 0].

3. Final Answer:

   [0, 0, 0, 0, 0] -> Option A

4. Quick Check:

   All nodes on path updated to root 0 = [0, 0, 0, 0, 0] [OK]

Hint: Update only nodes on path to root during find [OK]

Common Mistakes:

• Only updating parent[4] to root
• Failing to compress the full path
• Confusing parent indices