feat: Traditional Chinese version (#1163)

* First commit * Update mkdocs.yml * Translate all the docs to traditional Chinese * Translate the code files. * Translate the docker file * Fix mkdocs.yml * Translate all the figures from SC to TC * 二叉搜尋樹 -> 二元搜尋樹 * Update terminology. * Update terminology * 构造函数/构造方法 -> 建構子异或 -> 互斥或 * 擴充套件 -> 擴展 * constant - 常量 - 常數 * 類 -> 類別 * AVL -> AVL 樹 * 數組 -> 陣列 * 係統 -> 系統斐波那契數列 -> 費波那契數列運算元量 -> 運算量引數 -> 參數 * 聯絡 -> 關聯 * 麵試 -> 面試 * 面向物件 -> 物件導向歸併排序 -> 合併排序范式 -> 範式 * Fix 算法 -> 演算法 * 錶示 -> 表示反碼 -> 一補數補碼 -> 二補數列列尾部 -> 佇列尾部區域性性 -> 區域性一摞 -> 一疊 * Synchronize with main branch * 賬號 -> 帳號推匯 -> 推導 * Sync with main branch * First commit * Update mkdocs.yml * Translate all the docs to traditional Chinese * Translate the code files. * Translate the docker file * Fix mkdocs.yml * Translate all the figures from SC to TC * 二叉搜尋樹 -> 二元搜尋樹 * Update terminology * 构造函数/构造方法 -> 建構子异或 -> 互斥或 * 擴充套件 -> 擴展 * constant - 常量 - 常數 * 類 -> 類別 * AVL -> AVL 樹 * 數組 -> 陣列 * 係統 -> 系統斐波那契數列 -> 費波那契數列運算元量 -> 運算量引數 -> 參數 * 聯絡 -> 關聯 * 麵試 -> 面試 * 面向物件 -> 物件導向歸併排序 -> 合併排序范式 -> 範式 * Fix 算法 -> 演算法 * 錶示 -> 表示反碼 -> 一補數補碼 -> 二補數列列尾部 -> 佇列尾部區域性性 -> 區域性一摞 -> 一疊 * Synchronize with main branch * 賬號 -> 帳號推匯 -> 推導 * Sync with main branch * Update terminology.md * 操作数量（num. of operations）-> 操作數量 * 字首和->前綴和 * Update figures * 歸 -> 迴記憶體洩漏 -> 記憶體流失 * Fix the bug of the file filter * 支援 -> 支持 Add zh-Hant/README.md * Add the zh-Hant chapter covers. Bug fixes. * 外掛 -> 擴充功能 * Add the landing page for zh-Hant version * Unify the font of the chapter covers for the zh, en, and zh-Hant version * Move zh-Hant/ to zh-hant/ * Translate terminology.md to traditional Chinese
2026-09-04 14:17:14 +00:00 · 2024-04-06 02:30:11 +08:00
parent 33d7f8a2e5
commit 5f7385c8a3
1875 changed files with 102923 additions and 18 deletions
@@ -0,0 +1,4 @@
+add_executable(graph_adjacency_matrix graph_adjacency_matrix.c)
+add_executable(graph_adjacency_list_test graph_adjacency_list_test.c)
+add_executable(graph_bfs graph_bfs.c)
+add_executable(graph_dfs graph_dfs.c)
@@ -0,0 +1,171 @@
+/**
+ * File: graph_adjacency_list.c
+ * Created Time: 2023-07-07
+ * Author: NI-SW (947743645@qq.com)
+ */
+
+#include "../utils/common.h"
+
+// 假設節點最大數量為 100
+#define MAX_SIZE 100
+
+/* 節點結構體 */
+typedef struct AdjListNode {
+    Vertex *vertex;           // 頂點
+    struct AdjListNode *next; // 後繼節點
+} AdjListNode;
+
+/* 基於鄰接表實現的無向圖類別 */
+typedef struct {
+    AdjListNode *heads[MAX_SIZE]; // 節點陣列
+    int size;                     // 節點數量
+} GraphAdjList;
+
+/* 建構子 */
+GraphAdjList *newGraphAdjList() {
+    GraphAdjList *graph = (GraphAdjList *)malloc(sizeof(GraphAdjList));
+    if (!graph) {
+        return NULL;
+    }
+    graph->size = 0;
+    for (int i = 0; i < MAX_SIZE; i++) {
+        graph->heads[i] = NULL;
+    }
+    return graph;
+}
+
+/* 析構函式 */
+void delGraphAdjList(GraphAdjList *graph) {
+    for (int i = 0; i < graph->size; i++) {
+        AdjListNode *cur = graph->heads[i];
+        while (cur != NULL) {
+            AdjListNode *next = cur->next;
+            if (cur != graph->heads[i]) {
+                free(cur);
+            }
+            cur = next;
+        }
+        free(graph->heads[i]->vertex);
+        free(graph->heads[i]);
+    }
+    free(graph);
+}
+
+/* 查詢頂點對應的節點 */
+AdjListNode *findNode(GraphAdjList *graph, Vertex *vet) {
+    for (int i = 0; i < graph->size; i++) {
+        if (graph->heads[i]->vertex == vet) {
+            return graph->heads[i];
+        }
+    }
+    return NULL;
+}
+
+/* 新增邊輔助函式 */
+void addEdgeHelper(AdjListNode *head, Vertex *vet) {
+    AdjListNode *node = (AdjListNode *)malloc(sizeof(AdjListNode));
+    node->vertex = vet;
+    // 頭插法
+    node->next = head->next;
+    head->next = node;
+}
+
+/* 新增邊 */
+void addEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {
+    AdjListNode *head1 = findNode(graph, vet1);
+    AdjListNode *head2 = findNode(graph, vet2);
+    assert(head1 != NULL && head2 != NULL && head1 != head2);
+    // 新增邊 vet1 - vet2
+    addEdgeHelper(head1, vet2);
+    addEdgeHelper(head2, vet1);
+}
+
+/* 刪除邊輔助函式 */
+void removeEdgeHelper(AdjListNode *head, Vertex *vet) {
+    AdjListNode *pre = head;
+    AdjListNode *cur = head->next;
+    // 在鏈結串列中搜索 vet 對應節點
+    while (cur != NULL && cur->vertex != vet) {
+        pre = cur;
+        cur = cur->next;
+    }
+    if (cur == NULL)
+        return;
+    // 將 vet 對應節點從鏈結串列中刪除
+    pre->next = cur->next;
+    // 釋放記憶體
+    free(cur);
+}
+
+/* 刪除邊 */
+void removeEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {
+    AdjListNode *head1 = findNode(graph, vet1);
+    AdjListNode *head2 = findNode(graph, vet2);
+    assert(head1 != NULL && head2 != NULL);
+    // 刪除邊 vet1 - vet2
+    removeEdgeHelper(head1, head2->vertex);
+    removeEdgeHelper(head2, head1->vertex);
+}
+
+/* 新增頂點 */
+void addVertex(GraphAdjList *graph, Vertex *vet) {
+    assert(graph != NULL && graph->size < MAX_SIZE);
+    AdjListNode *head = (AdjListNode *)malloc(sizeof(AdjListNode));
+    head->vertex = vet;
+    head->next = NULL;
+    // 在鄰接表中新增一個新鏈結串列
+    graph->heads[graph->size++] = head;
+}
+
+/* 刪除頂點 */
+void removeVertex(GraphAdjList *graph, Vertex *vet) {
+    AdjListNode *node = findNode(graph, vet);
+    assert(node != NULL);
+    // 在鄰接表中刪除頂點 vet 對應的鏈結串列
+    AdjListNode *cur = node, *pre = NULL;
+    while (cur) {
+        pre = cur;
+        cur = cur->next;
+        free(pre);
+    }
+    // 走訪其他頂點的鏈結串列，刪除所有包含 vet 的邊
+    for (int i = 0; i < graph->size; i++) {
+        cur = graph->heads[i];
+        pre = NULL;
+        while (cur) {
+            pre = cur;
+            cur = cur->next;
+            if (cur && cur->vertex == vet) {
+                pre->next = cur->next;
+                free(cur);
+                break;
+            }
+        }
+    }
+    // 將該頂點之後的頂點向前移動，以填補空缺
+    int i;
+    for (i = 0; i < graph->size; i++) {
+        if (graph->heads[i] == node)
+            break;
+    }
+    for (int j = i; j < graph->size - 1; j++) {
+        graph->heads[j] = graph->heads[j + 1];
+    }
+    graph->size--;
+    free(vet);
+}
+
+/* 列印鄰接表 */
+void printGraph(const GraphAdjList *graph) {
+    printf("鄰接表 =\n");
+    for (int i = 0; i < graph->size; ++i) {
+        AdjListNode *node = graph->heads[i];
+        printf("%d: [", node->vertex->val);
+        node = node->next;
+        while (node) {
+            printf("%d, ", node->vertex->val);
+            node = node->next;
+        }
+        printf("]\n");
+    }
+}
@@ -0,0 +1,55 @@
+/**
+ * File: graph_adjacency_list_test.c
+ * Created Time: 2023-07-11
+ * Author: NI-SW (947743645@qq.com)
+ */
+
+#include "graph_adjacency_list.c"
+
+/* Driver Code */
+int main() {
+    int vals[] = {1, 3, 2, 5, 4};
+    int size = sizeof(vals) / sizeof(vals[0]);
+    Vertex **v = valsToVets(vals, size);
+    Vertex *edges[][2] = {{v[0], v[1]}, {v[0], v[3]}, {v[1], v[2]}, {v[2], v[3]}, {v[2], v[4]}, {v[3], v[4]}};
+    int egdeSize = sizeof(edges) / sizeof(edges[0]);
+    GraphAdjList *graph = newGraphAdjList();
+    // 新增所有頂點和邊
+    for (int i = 0; i < size; i++) {
+        addVertex(graph, v[i]);
+    }
+    for (int i = 0; i < egdeSize; i++) {
+        addEdge(graph, edges[i][0], edges[i][1]);
+    }
+    printf("\n初始化後，圖為\n");
+    printGraph(graph);
+
+    /* 新增邊 */
+    // 頂點 1, 2 即 v[0], v[2]
+    addEdge(graph, v[0], v[2]);
+    printf("\n新增邊 1-2 後，圖為\n");
+    printGraph(graph);
+
+    /* 刪除邊 */
+    // 頂點 1, 3 即 v[0], v[1]
+    removeEdge(graph, v[0], v[1]);
+    printf("\n刪除邊 1-3 後，圖為\n");
+    printGraph(graph);
+
+    /* 新增頂點 */
+    Vertex *v5 = newVertex(6);
+    addVertex(graph, v5);
+    printf("\n新增頂點 6 後，圖為\n");
+    printGraph(graph);
+
+    /* 刪除頂點 */
+    // 頂點 3 即 v[1]
+    removeVertex(graph, v[1]);
+    printf("\n刪除頂點 3 後，圖為:\n");
+    printGraph(graph);
+
+    // 釋放記憶體
+    delGraphAdjList(graph);
+    free(v);
+    return 0;
+}
@@ -0,0 +1,150 @@
+/**
+ * File: graph_adjacency_matrix.c
+ * Created Time: 2023-07-06
+ * Author: NI-SW (947743645@qq.com)
+ */
+
+#include "../utils/common.h"
+
+// 假設頂點數量最大為 100
+#define MAX_SIZE 100
+
+/* 基於鄰接矩陣實現的無向圖結構體 */
+typedef struct {
+    int vertices[MAX_SIZE];
+    int adjMat[MAX_SIZE][MAX_SIZE];
+    int size;
+} GraphAdjMat;
+
+/* 建構子 */
+GraphAdjMat *newGraphAdjMat() {
+    GraphAdjMat *graph = (GraphAdjMat *)malloc(sizeof(GraphAdjMat));
+    graph->size = 0;
+    for (int i = 0; i < MAX_SIZE; i++) {
+        for (int j = 0; j < MAX_SIZE; j++) {
+            graph->adjMat[i][j] = 0;
+        }
+    }
+    return graph;
+}
+
+/* 析構函式 */
+void delGraphAdjMat(GraphAdjMat *graph) {
+    free(graph);
+}
+
+/* 新增頂點 */
+void addVertex(GraphAdjMat *graph, int val) {
+    if (graph->size == MAX_SIZE) {
+        fprintf(stderr, "圖的頂點數量已達最大值\n");
+        return;
+    }
+    // 新增第 n 個頂點，並將第 n 行和列置零
+    int n = graph->size;
+    graph->vertices[n] = val;
+    for (int i = 0; i <= n; i++) {
+        graph->adjMat[n][i] = graph->adjMat[i][n] = 0;
+    }
+    graph->size++;
+}
+
+/* 刪除頂點 */
+void removeVertex(GraphAdjMat *graph, int index) {
+    if (index < 0 || index >= graph->size) {
+        fprintf(stderr, "頂點索引越界\n");
+        return;
+    }
+    // 在頂點串列中移除索引 index 的頂點
+    for (int i = index; i < graph->size - 1; i++) {
+        graph->vertices[i] = graph->vertices[i + 1];
+    }
+    // 在鄰接矩陣中刪除索引 index 的行
+    for (int i = index; i < graph->size - 1; i++) {
+        for (int j = 0; j < graph->size; j++) {
+            graph->adjMat[i][j] = graph->adjMat[i + 1][j];
+        }
+    }
+    // 在鄰接矩陣中刪除索引 index 的列
+    for (int i = 0; i < graph->size; i++) {
+        for (int j = index; j < graph->size - 1; j++) {
+            graph->adjMat[i][j] = graph->adjMat[i][j + 1];
+        }
+    }
+    graph->size--;
+}
+
+/* 新增邊 */
+// 參數 i, j 對應 vertices 元素索引
+void addEdge(GraphAdjMat *graph, int i, int j) {
+    if (i < 0 || j < 0 || i >= graph->size || j >= graph->size || i == j) {
+        fprintf(stderr, "邊索引越界或相等\n");
+        return;
+    }
+    graph->adjMat[i][j] = 1;
+    graph->adjMat[j][i] = 1;
+}
+
+/* 刪除邊 */
+// 參數 i, j 對應 vertices 元素索引
+void removeEdge(GraphAdjMat *graph, int i, int j) {
+    if (i < 0 || j < 0 || i >= graph->size || j >= graph->size || i == j) {
+        fprintf(stderr, "邊索引越界或相等\n");
+        return;
+    }
+    graph->adjMat[i][j] = 0;
+    graph->adjMat[j][i] = 0;
+}
+
+/* 列印鄰接矩陣 */
+void printGraphAdjMat(GraphAdjMat *graph) {
+    printf("頂點串列 = ");
+    printArray(graph->vertices, graph->size);
+    printf("鄰接矩陣 =\n");
+    for (int i = 0; i < graph->size; i++) {
+        printArray(graph->adjMat[i], graph->size);
+    }
+}
+
+/* Driver Code */
+int main() {
+    // 初始化無向圖
+    GraphAdjMat *graph = newGraphAdjMat();
+    int vertices[] = {1, 3, 2, 5, 4};
+    for (int i = 0; i < 5; i++) {
+        addVertex(graph, vertices[i]);
+    }
+    int edges[][2] = {{0, 1}, {0, 3}, {1, 2}, {2, 3}, {2, 4}, {3, 4}};
+    for (int i = 0; i < 6; i++) {
+        addEdge(graph, edges[i][0], edges[i][1]);
+    }
+    printf("\n初始化後，圖為\n");
+    printGraphAdjMat(graph);
+
+    /* 新增邊 */
+    // 頂點 1, 2 的索引分別為 0, 2
+    addEdge(graph, 0, 2);
+    printf("\n新增邊 1-2 後，圖為\n");
+    printGraphAdjMat(graph);
+
+    /* 刪除邊 */
+    // 頂點 1, 3 的索引分別為 0, 1
+    removeEdge(graph, 0, 1);
+    printf("\n刪除邊 1-3 後，圖為\n");
+    printGraphAdjMat(graph);
+
+    /* 新增頂點 */
+    addVertex(graph, 6);
+    printf("\n新增頂點 6 後，圖為\n");
+    printGraphAdjMat(graph);
+
+    /* 刪除頂點 */
+    // 頂點 3 的索引為 1
+    removeVertex(graph, 1);
+    printf("\n刪除頂點 3 後，圖為\n");
+    printGraphAdjMat(graph);
+
+    // 釋放記憶體
+    delGraphAdjMat(graph);
+
+    return 0;
+}
@@ -0,0 +1,116 @@
+/**
+ * File: graph_bfs.c
+ * Created Time: 2023-07-11
+ * Author: NI-SW (947743645@qq.com)
+ */
+
+#include "graph_adjacency_list.c"
+
+// 假設節點最大數量為 100
+#define MAX_SIZE 100
+
+/* 節點佇列結構體 */
+typedef struct {
+    Vertex *vertices[MAX_SIZE];
+    int front, rear, size;
+} Queue;
+
+/* 建構子 */
+Queue *newQueue() {
+    Queue *q = (Queue *)malloc(sizeof(Queue));
+    q->front = q->rear = q->size = 0;
+    return q;
+}
+
+/* 判斷佇列是否為空 */
+int isEmpty(Queue *q) {
+    return q->size == 0;
+}
+
+/* 入列操作 */
+void enqueue(Queue *q, Vertex *vet) {
+    q->vertices[q->rear] = vet;
+    q->rear = (q->rear + 1) % MAX_SIZE;
+    q->size++;
+}
+
+/* 出列操作 */
+Vertex *dequeue(Queue *q) {
+    Vertex *vet = q->vertices[q->front];
+    q->front = (q->front + 1) % MAX_SIZE;
+    q->size--;
+    return vet;
+}
+
+/* 檢查頂點是否已被訪問 */
+int isVisited(Vertex **visited, int size, Vertex *vet) {
+    // 走訪查詢節點，使用 O(n) 時間
+    for (int i = 0; i < size; i++) {
+        if (visited[i] == vet)
+            return 1;
+    }
+    return 0;
+}
+
+/* 廣度優先走訪 */
+// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點
+void graphBFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize, Vertex **visited, int *visitedSize) {
+    // 佇列用於實現 BFS
+    Queue *queue = newQueue();
+    enqueue(queue, startVet);
+    visited[(*visitedSize)++] = startVet;
+    // 以頂點 vet 為起點，迴圈直至訪問完所有頂點
+    while (!isEmpty(queue)) {
+        Vertex *vet = dequeue(queue); // 佇列首頂點出隊
+        res[(*resSize)++] = vet;      // 記錄訪問頂點
+        // 走訪該頂點的所有鄰接頂點
+        AdjListNode *node = findNode(graph, vet);
+        while (node != NULL) {
+            // 跳過已被訪問的頂點
+            if (!isVisited(visited, *visitedSize, node->vertex)) {
+                enqueue(queue, node->vertex);             // 只入列未訪問的頂點
+                visited[(*visitedSize)++] = node->vertex; // 標記該頂點已被訪問
+            }
+            node = node->next;
+        }
+    }
+    // 釋放記憶體
+    free(queue);
+}
+
+/* Driver Code */
+int main() {
+    // 初始化無向圖
+    int vals[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
+    int size = sizeof(vals) / sizeof(vals[0]);
+    Vertex **v = valsToVets(vals, size);
+    Vertex *edges[][2] = {{v[0], v[1]}, {v[0], v[3]}, {v[1], v[2]}, {v[1], v[4]}, {v[2], v[5]}, {v[3], v[4]},
+                          {v[3], v[6]}, {v[4], v[5]}, {v[4], v[7]}, {v[5], v[8]}, {v[6], v[7]}, {v[7], v[8]}};
+    int egdeSize = sizeof(edges) / sizeof(edges[0]);
+    GraphAdjList *graph = newGraphAdjList();
+    // 新增所有頂點和邊
+    for (int i = 0; i < size; i++) {
+        addVertex(graph, v[i]);
+    }
+    for (int i = 0; i < egdeSize; i++) {
+        addEdge(graph, edges[i][0], edges[i][1]);
+    }
+    printf("\n初始化後，圖為\n");
+    printGraph(graph);
+
+    // 廣度優先走訪
+    // 頂點走訪序列
+    Vertex *res[MAX_SIZE];
+    int resSize = 0;
+    // 用於記錄已被訪問過的頂點
+    Vertex *visited[MAX_SIZE];
+    int visitedSize = 0;
+    graphBFS(graph, v[0], res, &resSize, visited, &visitedSize);
+    printf("\n廣度優先走訪（BFS）頂點序列為\n");
+    printArray(vetsToVals(res, resSize), resSize);
+
+    // 釋放記憶體
+    delGraphAdjList(graph);
+    free(v);
+    return 0;
+}
@@ -0,0 +1,75 @@
+/**
+ * File: graph_dfs.c
+ * Created Time: 2023-07-13
+ * Author: NI-SW (947743645@qq.com)
+ */
+
+#include "graph_adjacency_list.c"
+
+// 假設節點最大數量為 100
+#define MAX_SIZE 100
+
+/* 檢查頂點是否已被訪問 */
+int isVisited(Vertex **res, int size, Vertex *vet) {
+    // 走訪查詢節點，使用 O(n) 時間
+    for (int i = 0; i < size; i++) {
+        if (res[i] == vet) {
+            return 1;
+        }
+    }
+    return 0;
+}
+
+/* 深度優先走訪輔助函式 */
+void dfs(GraphAdjList *graph, Vertex **res, int *resSize, Vertex *vet) {
+    // 記錄訪問頂點
+    res[(*resSize)++] = vet;
+    // 走訪該頂點的所有鄰接頂點
+    AdjListNode *node = findNode(graph, vet);
+    while (node != NULL) {
+        // 跳過已被訪問的頂點
+        if (!isVisited(res, *resSize, node->vertex)) {
+            // 遞迴訪問鄰接頂點
+            dfs(graph, res, resSize, node->vertex);
+        }
+        node = node->next;
+    }
+}
+
+/* 深度優先走訪 */
+// 使用鄰接表來表示圖，以便獲取指定頂點的所有鄰接頂點
+void graphDFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize) {
+    dfs(graph, res, resSize, startVet);
+}
+
+/* Driver Code */
+int main() {
+    // 初始化無向圖
+    int vals[] = {0, 1, 2, 3, 4, 5, 6};
+    int size = sizeof(vals) / sizeof(vals[0]);
+    Vertex **v = valsToVets(vals, size);
+    Vertex *edges[][2] = {{v[0], v[1]}, {v[0], v[3]}, {v[1], v[2]}, {v[2], v[5]}, {v[4], v[5]}, {v[5], v[6]}};
+    int egdeSize = sizeof(edges) / sizeof(edges[0]);
+    GraphAdjList *graph = newGraphAdjList();
+    // 新增所有頂點和邊
+    for (int i = 0; i < size; i++) {
+        addVertex(graph, v[i]);
+    }
+    for (int i = 0; i < egdeSize; i++) {
+        addEdge(graph, edges[i][0], edges[i][1]);
+    }
+    printf("\n初始化後，圖為\n");
+    printGraph(graph);
+
+    // 深度優先走訪
+    Vertex *res[MAX_SIZE];
+    int resSize = 0;
+    graphDFS(graph, v[0], res, &resSize);
+    printf("\n深度優先走訪（DFS）頂點序列為\n");
+    printArray(vetsToVals(res, resSize), resSize);
+
+    // 釋放記憶體
+    delGraphAdjList(graph);
+    free(v);
+    return 0;
+}