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/cpp/chapter_graph/graph_adjacency_matrix.cpp

@@ -6,20 +6,20 @@
 
 #include "../utils/common.hpp"
 
-/* Undirected graph class based on adjacency matrix */
+/* Undirected graph class implemented with an adjacency matrix */
 class GraphAdjMat {
-    vector<int> vertices;       // Vertex list, where the element represents the "vertex value" and the index represents the "vertex index"
-    vector<vector<int>> adjMat; // Adjacency matrix, where the row and column indices correspond to the "vertex index"
+    vector<int> vertices;       // Vertex list: elements are vertex values, and indices are vertex indices
+    vector<vector<int>> adjMat; // Adjacency matrix: row and column indices correspond to vertex indices
 
   public:
     /* Constructor */
     GraphAdjMat(const vector<int> &vertices, const vector<vector<int>> &edges) {
-        // 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 (const vector<int> &edge : edges) {
             addEdge(edge[0], edge[1]);
         }
@@ -30,10 +30,10 @@ class GraphAdjMat {
         return vertices.size();
     }
 
-    /* Add vertex */
+    /* Add a vertex */
     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.push_back(val);
         // Add a row to the adjacency matrix
         adjMat.emplace_back(vector<int>(n, 0));
@@ -43,45 +43,45 @@ class GraphAdjMat {
         }
     }
 
-    /* Remove vertex */
+    /* Remove a vertex */
     void removeVertex(int index) {
         if (index >= size()) {
-            throw out_of_range("Vertex does not exist");
+            throw out_of_range("Invalid vertex");
         }
-        // Remove the vertex at index from the vertex list
+        // Remove the vertex at index `index` from the vertex list
         vertices.erase(vertices.begin() + index);
-        // Remove the row at index from the adjacency matrix
+        // Remove row `index` from the adjacency matrix
         adjMat.erase(adjMat.begin() + index);
-        // Remove the column at index from the adjacency matrix
+        // Remove column `index` from the adjacency matrix
         for (vector<int> &row : adjMat) {
             row.erase(row.begin() + index);
         }
     }
 
-    /* Add edge */
-    // Parameters i, j correspond to the vertices element indices
+    /* Add an edge */
+    // Parameters i and j are element indices in vertices
     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 out_of_range("Vertex does not exist");
+            throw out_of_range("Invalid vertex");
         }
-        // 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[i][j] = 1;
         adjMat[j][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
     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 out_of_range("Vertex does not exist");
+            throw out_of_range("Invalid vertex");
         }
         adjMat[i][j] = 0;
         adjMat[j][i] = 0;
     }
 
-    /* Print adjacency matrix */
+    /* Print the adjacency matrix */
     void print() {
         cout << "Vertex list = ";
         printVector(vertices);
@@ -90,37 +90,37 @@ class GraphAdjMat {
     }
 };
 
-/* Driver Code */
+/* Driver code */
 int main() {
-    /* 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
     vector<int> vertices = {1, 3, 2, 5, 4};
     vector<vector<int>> edges = {{0, 1}, {0, 3}, {1, 2}, {2, 3}, {2, 4}, {3, 4}};
     GraphAdjMat graph(vertices, edges);
-    cout << "\nAfter initialization, graph is" << endl;
+    cout << "\nGraph after initialization:" << endl;
     graph.print();
 
-    /* Add edge */
-    // Add vertex
+    /* Add an edge */
+    // Vertices 1 and 2 have indices 0 and 2, respectively
     graph.addEdge(0, 2);
-    cout << "\nAfter adding edge 1-2, graph is" << endl;
+    cout << "\nGraph after adding edge 1-2:" << endl;
     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);
-    cout << "\nAfter removing edge 1-3, graph is" << endl;
+    cout << "\nGraph after removing edge 1-3:" << endl;
     graph.print();
 
-    /* Add vertex */
+    /* Add a vertex */
     graph.addVertex(6);
-    cout << "\nAfter adding vertex 6, graph is" << endl;
+    cout << "\nGraph after adding vertex 6:" << endl;
     graph.print();
 
-    /* Remove vertex */
+    /* Remove a vertex */
     // Vertex 3 has index 1
     graph.removeVertex(1);
-    cout << "\nAfter removing vertex 3, graph is" << endl;
+    cout << "\nGraph after removing vertex 3:" << endl;
     graph.print();
 
     return 0;