Minimum Spanning Tree Kruskal's Algorithm in DSA C - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the parent array for union-find.

DSA C

for (int i = 0; i < n; i++) {
    parent[i] = [1];
}

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

A-1

B0

Ci

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Setting all parents to 0 causes incorrect union-find behavior.

Using -1 or n as parent values breaks the find operation.

Each node is initially its own parent, so parent[i] = i.

2fill in blank

medium

Complete the code to find the root parent of a node with path compression.

DSA C

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

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

Aparent[parent[x]]

Bfind(parent, parent[x])

Cx

Dx + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning parent[x] to x causes infinite recursion.

Using parent[parent[x]] misses path compression.

Path compression sets parent[x] to the root found by recursive find call.

3fill in blank

hard

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

DSA C

void unionSets(int parent[], int x, int y) {
    int rootX = find(parent, x);
    int rootY = find(parent, 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

Using x or y instead of root parents causes incorrect unions.

Assigning parent[rootY] = rootX merges sets incorrectly.

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

4fill in blank

hard

Fill both blanks to correctly sort edges by weight using qsort.

DSA C

int compare(const void *a, const void *b) {
    struct Edge *edgeA = (struct Edge *)[1];
    struct Edge *edgeB = (struct Edge *)[2];
    return edgeA->weight - edgeB->weight;
}

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

Aa

Bb

C*a

D*b

Attempts:

3 left

💡 Hint

Common Mistakes

Dereferencing a or b before casting causes errors.

Swapping a and b changes sort order.

Cast void pointers a and b to Edge pointers to compare weights.

5fill in blank

hard

Fill all three blanks to add an edge to MST and update total weight.

DSA C

if (find(parent, edges[i].src) != find(parent, edges[i].dest)) {
    unionSets(parent, [1], [2]);
    mstEdges[[3]] = edges[i];
    totalWeight += edges[i].weight;
    count++;
}

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

Aedges[i].src

Bedges[i].dest

Ccount

Di

Attempts:

3 left

💡 Hint

Common Mistakes

Using i instead of count to index mstEdges overwrites edges.

Swapping src and dest in unionSets causes wrong unions.

Union the source and destination nodes, add edge at index count, then increment count.

Practice

1. What is the main goal of Kruskal's algorithm in graph theory?

easy

A. To sort the vertices of a graph

B. To find the shortest path between two nodes

C. To detect cycles in a graph

D. To find the minimum spanning tree of a graph

Solution

1. Step 1: Understand Kruskal's algorithm purpose

   Kruskal's algorithm is designed to find a subset of edges that connects all vertices with the minimum total edge weight and no cycles.

2. Step 2: Compare with other graph algorithms

   Unlike shortest path or cycle detection, Kruskal's focuses on building a minimum spanning tree.

3. Final Answer:

   To find the minimum spanning tree of a graph -> Option D

4. Quick Check:

   Kruskal's algorithm = Minimum Spanning Tree [OK]

Hint: Kruskal's always builds minimum spanning tree by edges [OK]

Common Mistakes:

• Confusing MST with shortest path
• Thinking it detects cycles only
• Assuming it sorts vertices

2. Which data structure is commonly used in Kruskal's algorithm to detect cycles efficiently?

easy

A. Disjoint Set (Union-Find)

B. Stack

C. Queue

D. Priority Queue

Solution

1. Step 1: Identify cycle detection method in Kruskal's

   Kruskal's algorithm uses a Disjoint Set (Union-Find) data structure to check if adding an edge creates a cycle by checking if two vertices belong to the same set.

2. Step 2: Compare other data structures

   Queue and stack do not help detect cycles efficiently here; priority queue is used for sorting edges but not cycle detection.

3. Final Answer:

   Disjoint Set (Union-Find) -> Option A

4. Quick Check:

   Cycle detection in Kruskal's = Union-Find [OK]

Hint: Use Union-Find to quickly check cycles in Kruskal's [OK]

Common Mistakes:

• Confusing priority queue with cycle detection
• Using stack or queue for cycle detection
• Not knowing Union-Find purpose

3. Consider the following edges of a graph with weights:
Edges = [(A-B, 1), (B-C, 4), (A-C, 3), (C-D, 2)]
What is the total weight of the minimum spanning tree found by Kruskal's algorithm?

medium

A. 7

B. 6

C. 8

D. 10

Solution

1. Step 1: Sort edges by weight

   Sorted edges: (A-B,1), (C-D,2), (A-C,3), (B-C,4)

2. Step 2: Pick edges without cycles

   Pick (A-B,1), then (C-D,2), then (A-C,3). Adding (B-C,4) creates a cycle, so skip it.

3. Step 3: Calculate total weight

   Total weight = 1 + 2 + 3 = 6

4. Final Answer:

   6 -> Option B

5. Quick Check:

   Sum of MST edges = 6 [OK]

Hint: Sort edges, pick smallest without cycle until all connected [OK]

Common Mistakes:

• Adding all edges without checking cycles
• Choosing edges in wrong order
• Miscounting total weight

4. The following C code snippet is part of Kruskal's algorithm. What is the error?

int findParent(int parent[], int i) {
    if (parent[i] == i)
        return i;
    return findParent(parent, parent[i]);
}

void unionSet(int parent[], int x, int y) {
    int xset = findParent(parent, x);
    int yset = findParent(parent, y);
    parent[xset] = yset;
}

medium

A. unionSet should swap xset and yset

B. unionSet should not change parent array

C. Missing path compression in findParent

D. findParent should return void

Solution

1. Step 1: Analyze findParent function

   findParent recursively finds the root parent but does not update parent[i] to root, missing path compression optimization.

2. Step 2: Understand unionSet function

   unionSet correctly merges sets by updating parent of one root to another; no swap needed.

3. Final Answer:

   Missing path compression in findParent -> Option C

4. Quick Check:

   Path compression missing = findParent optimization [OK]

Hint: Add path compression to speed up findParent [OK]

Common Mistakes:

• Thinking unionSet must swap parents
• Believing findParent should return void
• Ignoring path compression importance

5. Given a graph with vertices {1, 2, 3, 4} and edges with weights:
(1-2, 5), (1-3, 3), (2-3, 4), (2-4, 2), (3-4, 7)
Using Kruskal's algorithm, which edges will be included in the minimum spanning tree?

hard

A. (2-4), (1-3), (2-3)

B. (1-3), (2-4), (1-2)

C. (2-4), (1-3), (1-2)

D. (1-2), (2-3), (3-4)

Solution

1. Step 1: Sort edges by weight

   Sorted edges: (2-4,2), (1-3,3), (2-3,4), (1-2,5), (3-4,7)

2. Step 2: Pick edges without cycles

   Pick (2-4,2), then (1-3,3). Next (2-3,4) connects 2 and 3 which are in different sets, so pick it. After these three edges, all vertices are connected and MST is complete.

3. Step 3: Verify options

   (2-4), (1-3), (2-3) matches edges (2-4), (1-3), (2-3). (2-4), (1-3), (1-2) includes (1-2) which is heavier than (2-3), so incorrect.

4. Final Answer:

   (2-4), (1-3), (2-3) -> Option A

5. Quick Check:

   Pick smallest edges connecting all vertices without cycle [OK]

Hint: Sort edges, pick smallest connecting new vertices until all connected [OK]

Common Mistakes:

• Choosing heavier edges over lighter ones
• Adding edges that create cycles
• Not stopping after n-1 edges