Retranslate the complete English edition from Simplified Chinese (#2010)

* Retranslate the complete English edition from Simplified Chinese

* Polish three English explanations after reader-focused review

en/codes/java/chapter_graph/graph_adjacency_matrix.java

@@ -9,21 +9,21 @@ package chapter_graph;
 import utils.*;
 import java.util.*;
 
-/* Undirected graph class based on adjacency matrix */
+/* Undirected graph class implemented with an adjacency matrix */
 class GraphAdjMat {
-    List<Integer> vertices; // Vertex list, where the element represents the "vertex value" and the index represents the "vertex index"
-    List<List<Integer>> adjMat; // Adjacency matrix, where the row and column indices correspond to the "vertex index"
+    List<Integer> vertices; // Vertex list: elements are vertex values, and indices are vertex indices
+    List<List<Integer>> adjMat; // Adjacency matrix: row and column indices correspond to vertex indices
 
     /* Constructor */
     public GraphAdjMat(int[] vertices, int[][] edges) {
         this.vertices = new ArrayList<>();
         this.adjMat = new ArrayList<>();
-        // Add vertex
+        // Add a vertex
         for (int val : vertices) {
             addVertex(val);
         }
-        // Add edge
-        // Note that the edges elements represent vertex indices, i.e., corresponding to the vertices element indices
+        // Add an edge
+        // Note that the entries in edges are vertex indices, corresponding to element indices in vertices
         for (int[] e : edges) {
             addEdge(e[0], e[1]);
         }
@@ -34,10 +34,10 @@ class GraphAdjMat {
         return vertices.size();
     }
 
-    /* Add vertex */
+    /* Add a vertex */
     public void addVertex(int val) {
         int n = size();
-        // Add the value of the new vertex to the vertex list
+        // Append the new vertex value to the vertex list
         vertices.add(val);
         // Add a row to the adjacency matrix
         List<Integer> newRow = new ArrayList<>(n);
@@ -51,42 +51,42 @@ class GraphAdjMat {
         }
     }
 
-    /* Remove vertex */
+    /* Remove a vertex */
     public void removeVertex(int index) {
         if (index >= size())
             throw new IndexOutOfBoundsException();
-        // Remove the vertex at index from the vertex list
+        // Remove the vertex at index `index` from the vertex list
         vertices.remove(index);
-        // Remove the row at index from the adjacency matrix
+        // Remove row `index` from the adjacency matrix
         adjMat.remove(index);
-        // Remove the column at index from the adjacency matrix
+        // Remove column `index` from the adjacency matrix
         for (List<Integer> row : adjMat) {
             row.remove(index);
         }
     }
 
-    /* Add edge */
-    // Parameters i, j correspond to the vertices element indices
+    /* Add an edge */
+    // Parameters i and j are element indices in vertices
     public void addEdge(int i, int j) {
-        // Handle index out of bounds and equality
+        // Handle out-of-bounds or equal indices
         if (i < 0 || j < 0 || i >= size() || j >= size() || i == j)
             throw new IndexOutOfBoundsException();
-        // In an undirected graph, the adjacency matrix is symmetric about the main diagonal, i.e., (i, j) == (j, i)
+        // For an undirected graph, the adjacency matrix is symmetric about its main diagonal: entries (i, j) and (j, i) are equal
         adjMat.get(i).set(j, 1);
         adjMat.get(j).set(i, 1);
     }
 
-    /* Remove edge */
-    // Parameters i, j correspond to the vertices element indices
+    /* Remove an edge */
+    // Parameters i and j are element indices in vertices
     public void removeEdge(int i, int j) {
-        // Handle index out of bounds and equality
+        // Handle out-of-bounds or equal indices
         if (i < 0 || j < 0 || i >= size() || j >= size() || i == j)
             throw new IndexOutOfBoundsException();
         adjMat.get(i).set(j, 0);
         adjMat.get(j).set(i, 0);
     }
 
-    /* Print adjacency matrix */
+    /* Print the adjacency matrix */
     public void print() {
         System.out.print("Vertex list = ");
         System.out.println(vertices);
@@ -97,35 +97,35 @@ class GraphAdjMat {
 
 public class graph_adjacency_matrix {
     public static void main(String[] args) {
-        /* Add edge */
-        // Note that the edges elements represent vertex indices, i.e., corresponding to the vertices element indices
+        /* Initialize the undirected graph */
+        // Note that the entries in edges are vertex indices, corresponding to element indices in vertices
         int[] vertices = { 1, 3, 2, 5, 4 };
         int[][] edges = { { 0, 1 }, { 0, 3 }, { 1, 2 }, { 2, 3 }, { 2, 4 }, { 3, 4 } };
         GraphAdjMat graph = new GraphAdjMat(vertices, edges);
-        System.out.println("\nAfter initialization, graph is");
+        System.out.println("\nGraph after initialization:");
         graph.print();
 
-        /* Add edge */
-        // Add vertex
+        /* Add an edge */
+        // Vertices 1 and 2 have indices 0 and 2, respectively
         graph.addEdge(0, 2);
-        System.out.println("\nAfter adding edge 1-2, graph is");
+        System.out.println("\nGraph after adding edge 1-2:");
         graph.print();
 
-        /* Remove edge */
-        // Vertices 1, 3 have indices 0, 1 respectively
+        /* Remove an edge */
+        // Vertices 1 and 3 have indices 0 and 1, respectively
         graph.removeEdge(0, 1);
-        System.out.println("\nAfter removing edge 1-3, graph is");
+        System.out.println("\nGraph after removing edge 1-3:");
         graph.print();
 
-        /* Add vertex */
+        /* Add a vertex */
         graph.addVertex(6);
-        System.out.println("\nAfter adding vertex 6, graph is");
+        System.out.println("\nGraph after adding vertex 6:");
         graph.print();
 
-        /* Remove vertex */
+        /* Remove a vertex */
         // Vertex 3 has index 1
         graph.removeVertex(1);
-        System.out.println("\nAfter removing vertex 3, graph is");
+        System.out.println("\nGraph after removing vertex 3:");
         graph.print();
     }
 }