Minimum Spanning Tree Kruskal's Algorithm in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Minimum Spanning Tree (MST)?

A Minimum Spanning Tree is a subset of edges in a connected, weighted graph that connects all vertices together without any cycles and with the minimum possible total edge weight.

beginner

What is the main idea behind Kruskal's Algorithm?

Kruskal's Algorithm builds the MST by sorting all edges by weight and adding the smallest edge to the MST if it does not form a cycle, repeating until all vertices are connected.

intermediate

Why do we use a Disjoint Set (Union-Find) data structure in Kruskal's Algorithm?

The Disjoint Set helps efficiently check if adding an edge will create a cycle by tracking which vertices are in the same connected component.

intermediate

What is the time complexity of Kruskal's Algorithm?

The time complexity is O(E log E), where E is the number of edges, mainly due to sorting the edges. Union-Find operations are almost constant time.

beginner

In Kruskal's Algorithm, what happens if an edge connects two vertices already in the same set?

The edge is skipped to avoid creating a cycle in the MST.

What is the first step in Kruskal's Algorithm?

A Remove all cycles

B Pick any vertex as starting point

C Create adjacency matrix

D Sort all edges by weight

Kruskal's Algorithm starts by sorting all edges from smallest to largest weight.

Which data structure is commonly used to detect cycles in Kruskal's Algorithm?

A Disjoint Set (Union-Find)

B Queue

C Stack

D Binary Search Tree

Disjoint Set (Union-Find) efficiently tracks connected components to detect cycles.

What does Kruskal's Algorithm guarantee about the resulting tree?

A It contains all edges of the graph

B It has the maximum total edge weight

C It connects all vertices with minimum total edge weight

D It is a directed tree

Kruskal's Algorithm finds a tree connecting all vertices with the smallest total edge weight.

If adding an edge creates a cycle, what does Kruskal's Algorithm do?

A Skips the edge

B Adds the edge anyway

C Removes the cycle edges

D Restarts the algorithm

To keep the MST cycle-free, edges that create cycles are skipped.

What is the main factor affecting Kruskal's Algorithm's running time?

A Number of vertices

B Number of edges and sorting them

C Depth of recursion

D Size of adjacency list

Sorting edges by weight dominates the running time, which is O(E log E).

Explain step-by-step how Kruskal's Algorithm builds a Minimum Spanning Tree.

Think about sorting edges and using sets to avoid cycles.

Describe how the Disjoint Set (Union-Find) data structure helps in Kruskal's Algorithm.

Focus on cycle detection and set merging.