One Pager Cheat Sheet

• Kruskal's Algorithm is a coding interview topic known for demonstrating mastery of computer science basics, as it calculates the minimum spanning tree (MST) of a connected, weighted graph, testing skills like understanding of graphs, greedy algorithms, union-find data structures, and time complexity; MSTs, which connect all vertices without cycles and minimize total cost, have applications in networks, circuit design, and facility location.
• In graph theory, a Minimum Spanning Tree (MST) is a subset of a graph's edges that connects all vertices without cycles and with the minimum total edge weight, accomplished by using a minimization principle and a greedy approach in algorithms like Kruskal's.
• Kruskal's Algorithm constructs a Minimum Spanning Tree (MST) without cycles by starting with an empty canvas, sorting edges by weight, adding edges that do not create a cycle, and terminating when the MST is complete (has V - 1 edges), with the process illustrated through ASCII diagrams and code snippets in multiple languages.
• The guide details the implementation of Kruskal's Algorithm using union-find and priority queue data structures to prevent cycles, ensure connectivity, and always select edges with the lowest weight, demonstrating the procedure in multiple programming languages. The algorithm's time complexity is O(E log E) due to sorting edges and checking for cycles, while its space complexity is O(V) for storing parent pointers, with an additional performance tweak option provided: union by rank which balances the tree and reduces time complexity. The pros include simplicity and optimality, while the cons suggest potential slowness, alongside an alternative: Prim's Algorithm.
• Implementing Kruskal's algorithm showcases essential computer science skills including working with graphs, using greedy algorithms and union-find structures, and analyzing time complexity, with the algorithm functioning by processing edges from lowest to highest weight to create the minimum spanning tree.