Hello! Today, we will learn about the Minimum Spanning Tree<\/strong> problem that frequently appears in algorithm exams. In particular, we will delve deeply into how to solve this problem using Java.<\/p>\n Let’s assume there is a weighted connected graph as follows. All vertices of this graph are connected, and the weights are different from each other. Your goal is to find the minimum spanning tree of this graph.<\/p>\n Print the list of edges that make up the minimum spanning tree and the total weight.<\/p>\n The representative algorithms used to find the minimum spanning tree are Kruskal’s Algorithm<\/strong> and Prim’s Algorithm<\/strong>. Here, we will use Kruskal’s Algorithm to solve this problem.<\/p>\n Now, let’s implement Kruskal’s Algorithm through Java code.<\/p>\n The above code implements the following key functionalities:<\/p>\n When you compile and execute this code, the following results will be printed:<\/p>\n Minimum spanning trees can be applied in various fields. For example:<\/p>\nProblem Description<\/h2>\n
Input Format<\/h3>\n
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V<\/code> and the number of edges E<\/code>.<\/li>\nE<\/code> lines contain the two vertices and the weight of each edge u<\/code>, v<\/code>, w<\/code>.<\/li>\n<\/ul>\nOutput Format<\/h3>\n
Example Input\/Output<\/h2>\n
Example Input<\/h4>\n
\n 3 3\n 1 2 1\n 2 3 2\n 1 3 3\n <\/pre>\n
Example Output<\/h4>\n
\n 1 - 2\n 2 - 3\n Total Weight: 3\n <\/pre>\n<\/div>\n
Approach to Problem Solving<\/h2>\n
Overview of Kruskal’s Algorithm<\/h3>\n
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Java Code Implementation<\/h2>\n
\nimport java.util.Arrays;\n\npublic class Kruskal {\n static class Edge implements ComparableCode Explanation<\/h2>\n
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Testing and Execution<\/h2>\n
\nEdges of the minimum spanning tree:\n1 - 2\n2 - 3\nTotal Weight: 3\n <\/pre>\n
Applications of Minimum Spanning Trees<\/h2>\n