1. What is a Minimum Spanning Tree?<\/h2>\n
A Minimum Spanning Tree (MST) is a subgraph in a weighted graph that includes all vertices while minimizing the sum of the weights. In other words, it means a tree where all vertices are connected and the sum of the weights of the given edges is the smallest. Minimum spanning trees are used in various fields such as network design, road construction, and telecommunications.<\/p>\n<\/section>\n The following is a problem to find the minimum spanning tree:<\/p>\n Given a graph with a specified number of vertices Output the sum of the weights of the minimum spanning tree.<\/p>\n<\/blockquote>\n<\/section>\n There are methods to find the minimum spanning tree, namely Prim’s algorithm and Kruskal’s algorithm. In this tutorial, we will use Prim’s algorithm to solve the problem. The Prim’s algorithm proceeds as follows:<\/p>\n The time complexity of Prim’s algorithm is O(E log V), where E is the number of edges and V is the number of vertices. On the other hand, Kruskal’s algorithm is O(E log E) and can be more efficient in different scenarios.<\/p>\n<\/section>\n Below is the Kotlin code to find the sum of the weights of the minimum spanning tree using Prim\u2019s algorithm:<\/p>\n The main function and input handling part to use the above `findMinimumSpanningTree` function is as follows:<\/p>\n There are several precautions to keep in mind when finding the minimum spanning tree:<\/p>\n Below are example cases to test the minimum spanning tree problem:<\/p>\n2. Problem Statement<\/h2>\n
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Problem Description<\/h3>\n
V<\/code> and edges E<\/code>, write a program in Kotlin to find the sum of weights of the minimum spanning tree. The edges are given with weights.<\/p>\nInput Format<\/h3>\n
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V<\/code> and the number of edges E<\/code>.<\/li>\nE<\/code> lines provide the information for each edge u, v, w<\/code> (the weight w<\/code> of the edge connecting vertices u<\/code> and v<\/code>).<\/li>\n<\/ul>\nOutput Format<\/h3>\n
3. Problem Solving Methodology<\/h2>\n
3.1. Algorithm Selection<\/h3>\n
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3.2. Time Complexity<\/h3>\n
4. Kotlin Code Implementation<\/h2>\n
\nfun findMinimumSpanningTree(V: Int, edges: List4.1. Main Function and Input Section<\/h3>\n
\nfun main() {\n val (V, E) = readLine()!!.split(\" \").map { it.toInt() }\n val edges = mutableListOf5. Precautions During Problem Solving Process<\/h2>\n
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6. Example Test Cases<\/h2>\n
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Example Input<\/h3>\n
4 5\n0 1 1\n0 2 3\n1 2 1\n1 3 4\n2 3 1<\/code><\/pre>\nExample Output<\/h3>\n
3<\/code><\/pre>\n<\/blockquote>\n