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438
docs/chapter_graph/graph_operations.md
View file

@ -40,14 +40,11 @@ comments: true
class GraphAdjMat:
"""基于邻接矩阵实现的无向图类"""
# 顶点列表，元素代表“顶点值”，索引代表“顶点索引”
vertices: list[int] = []
# 邻接矩阵，行列索引对应“顶点索引”
adj_mat: list[list[int]] = []
def __init__(self, vertices: list[int], edges: list[list[int]]):
"""构造方法"""
# 顶点列表，元素代表“顶点值”，索引代表“顶点索引”
self.vertices: list[int] = []
# 邻接矩阵，行列索引对应“顶点索引”
self.adj_mat: list[list[int]] = []
# 添加顶点
for val in vertices:
@ -945,24 +942,72 @@ comments: true
=== "C"
```c title="graph_adjacency_matrix.c"
/* 基于邻接矩阵实现的无向图类结构 */
/* 基于邻接矩阵实现的无向图结构体 */
typedef struct {
int *vertices; // 顶点列表
int **adjMat; // 邻接矩阵，元素代表“边”，索引代表“顶点索引”
int size; // 顶点数量
int capacity; // 图容量
int vertices[MAX_SIZE];
int adjMat[MAX_SIZE][MAX_SIZE];
int size;
} GraphAdjMat;
/* 构造函数 */
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;
}
/* 添加顶点 */
void addVertex(GraphAdjMat *graph, int val) {
if (graph->size == MAX_SIZE) {
fprintf(stderr, "图的顶点数量已达最大值\n");
return;
}
// 添加第 n 个顶点，并将第 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++;
}
/* 删除顶点 */
void removeVertex(GraphAdjMat *graph, int index) {
if (index < 0 || index >= graph->size) {
fprintf(stderr, "顶点索引越界\n");
return;
}
// 在顶点列表中移除索引 index 的顶点
for (int i = index; i < graph->size - 1; i++) {
graph->vertices[i] = graph->vertices[i + 1];
}
// 在邻接矩阵中删除索引 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];
}
}
// 在邻接矩阵中删除索引 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--;
}
/* 添加边 */
// 参数 i, j 对应 vertices 元素索引
void addEdge(GraphAdjMat *graph, int i, int j) {
// 越界检查
if (i < 0 || j < 0 || i >= graph->size || j >= graph->size || i == j) {
printf("Out of range in %s:%d\n", __FILE__, __LINE__);
exit(1);
fprintf(stderr, "边索引越界或相等\n");
return;
}
// 添加边
// 参数 i, j 对应 vertices 元素索引
graph->adjMat[i][j] = 1;
graph->adjMat[j][i] = 1;
}
@ -970,137 +1015,22 @@ comments: true
/* 删除边 */
// 参数 i, j 对应 vertices 元素索引
void removeEdge(GraphAdjMat *graph, int i, int j) {
// 越界检查
if (i < 0 || j < 0 || i >= graph->size || j >= graph->size || i == j) {
printf("Out of range in %s:%d\n", __FILE__, __LINE__);
exit(1);
fprintf(stderr, "边索引越界或相等\n");
return;
}
// 删除边
// 参数 i, j 对应 vertices 元素索引
graph->adjMat[i][j] = 0;
graph->adjMat[j][i] = 0;
}
/* 添加顶点 */
void addVertex(GraphAdjMat *graph, int val) {
// 如果实际使用不大于预设空间，则直接初始化新空间
if (graph->size < graph->capacity) {
graph->vertices[graph->size] = val; // 初始化新顶点值
for (int i = 0; i < graph->size; i++) {
graph->adjMat[i][graph->size] = 0; // 邻接矩新列阵置0
}
memset(graph->adjMat[graph->size], 0, sizeof(int) * (graph->size + 1)); // 将新增行置 0
graph->size++;
return;
}
// 扩容，申请新的顶点数组
int *temp = (int *)malloc(sizeof(int) * (graph->size * 2));
memcpy(temp, graph->vertices, sizeof(int) * graph->size);
temp[graph->size] = val;
// 释放原数组
free(graph->vertices);
graph->vertices = temp;
// 扩容，申请新的二维数组
int **tempMat = (int **)malloc(sizeof(int *) * graph->size * 2);
int *tempMatLine = (int *)malloc(sizeof(int) * (graph->size * 2) * (graph->size * 2));
memset(tempMatLine, 0, sizeof(int) * (graph->size * 2) * (graph->size * 2));
for (int k = 0; k < graph->size * 2; k++) {
tempMat[k] = tempMatLine + k * (graph->size * 2);
}
/* 打印邻接矩阵 */
void printGraphAdjMat(GraphAdjMat *graph) {
printf("顶点列表 = ");
printArray(graph->vertices, graph->size);
printf("邻接矩阵 =\n");
for (int i = 0; i < graph->size; i++) {
memcpy(tempMat[i], graph->adjMat[i], sizeof(int) * graph->size); // 原数据复制到新数组
printArray(graph->adjMat[i], graph->size);
}
for (int i = 0; i < graph->size; i++) {
tempMat[i][graph->size] = 0; // 将新增列置 0
}
memset(tempMat[graph->size], 0, sizeof(int) * (graph->size + 1)); // 将新增行置 0
// 释放原数组
free(graph->adjMat[0]);
free(graph->adjMat);
// 扩容后，指向新地址
graph->adjMat = tempMat; // 指向新的邻接矩阵地址
graph->capacity = graph->size * 2;
graph->size++;
}
/* 删除顶点 */
void removeVertex(GraphAdjMat *graph, int index) {
// 越界检查
if (index < 0 || index >= graph->size) {
printf("Out of range in %s:%d\n", __FILE__, __LINE__);
exit(1);
}
for (int i = index; i < graph->size - 1; i++) {
graph->vertices[i] = graph->vertices[i + 1]; // 清除删除的顶点，并将其后所有顶点前移
}
graph->vertices[graph->size - 1] = 0; // 将被前移的最后一个顶点置 0
// 清除邻接矩阵中删除的列
for (int i = 0; i < graph->size - 1; i++) {
if (i < index) {
for (int j = index; j < graph->size - 1; j++) {
graph->adjMat[i][j] = graph->adjMat[i][j + 1]; // 被删除列后的所有列前移
}
} else {
memcpy(graph->adjMat[i], graph->adjMat[i + 1], sizeof(int) * graph->size); // 被删除行的下方所有行上移
for (int j = index; j < graph->size; j++) {
graph->adjMat[i][j] = graph->adjMat[i][j + 1]; // 被删除列后的所有列前移
}
}
}
graph->size--;
}
/* 打印顶点与邻接矩阵 */
void printGraph(GraphAdjMat *graph) {
if (graph->size == 0) {
printf("graph is empty\n");
return;
}
printf("顶点列表 = [");
for (int i = 0; i < graph->size; i++) {
if (i != graph->size - 1) {
printf("%d, ", graph->vertices[i]);
} else {
printf("%d", graph->vertices[i]);
}
}
printf("]\n");
printf("邻接矩阵 =\n[\n");
for (int i = 0; i < graph->size; i++) {
printf(" [");
for (int j = 0; j < graph->size; j++) {
if (j != graph->size - 1) {
printf("%u, ", graph->adjMat[i][j]);
} else {
printf("%u", graph->adjMat[i][j]);
}
}
printf("],\n");
}
printf("]\n");
}
/* 构造函数 */
GraphAdjMat *newGraphAjdMat(int numberVertices, int *vertices, int **adjMat) {
// 申请内存
GraphAdjMat *newGraph = (GraphAdjMat *)malloc(sizeof(GraphAdjMat)); // 为图分配内存
newGraph->vertices = (int *)malloc(sizeof(int) * numberVertices * 2); // 为顶点列表分配内存
newGraph->adjMat = (int **)malloc(sizeof(int *) * numberVertices * 2); // 为邻接矩阵分配二维内存
int *temp = (int *)malloc(sizeof(int) * numberVertices * 2 * numberVertices * 2); // 为邻接矩阵分配一维内存
newGraph->size = numberVertices; // 初始化顶点数量
newGraph->capacity = numberVertices * 2; // 初始化图容量
// 配置二维数组
for (int i = 0; i < numberVertices * 2; i++) {
newGraph->adjMat[i] = temp + i * numberVertices * 2; // 将二维指针指向一维数组
}
// 赋值
memcpy(newGraph->vertices, vertices, sizeof(int) * numberVertices);
for (int i = 0; i < numberVertices; i++) {
memcpy(newGraph->adjMat[i], adjMat[i],
sizeof(int) * numberVertices); // 将传入的邻接矩阵赋值给结构体内邻接矩阵
}
// 返回结构体指针
return newGraph;
}
```
@ -1967,120 +1897,160 @@ comments: true
=== "C"
```c title="graph_adjacency_list.c"
/* 基于邻接链表实现的无向图类结构 */
/* 节点结构体 */
typedef struct AdjListNode {
Vertex *vertex; // 顶点
struct AdjListNode *next; // 后继节点
} AdjListNode;
/* 查找顶点对应的节点 */
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;
}
/* 添加边辅助函数 */
void addEdgeHelper(AdjListNode *head, Vertex *vet) {
AdjListNode *node = (AdjListNode *)malloc(sizeof(AdjListNode));
node->vertex = vet;
// 头插法
node->next = head->next;
head->next = node;
}
/* 删除边辅助函数 */
void removeEdgeHelper(AdjListNode *head, Vertex *vet) {
AdjListNode *pre = head;
AdjListNode *cur = head->next;
// 在链表中搜索 vet 对应节点
while (cur != NULL && cur->vertex != vet) {
pre = cur;
cur = cur->next;
}
if (cur == NULL)
return;
// 将 vet 对应节点从链表中删除
pre->next = cur->next;
// 释放内存
free(cur);
}
/* 基于邻接表实现的无向图类 */
typedef struct {
Vertex **vertices; // 邻接表
unsigned int size; // 顶点数量
unsigned int capacity; // 顶点容量
AdjListNode *heads[MAX_SIZE]; // 节点数组
int size; // 节点数量
} GraphAdjList;
/* 添加边 */
void addEdge(GraphAdjList *graph, int i, int j) {
// 越界检查
if (i < 0 || j < 0 || i == j || i >= graph->size || j >= graph->size) {
printf("Out of range in %s:%d\n", __FILE__, __LINE__);
return;
/* 构造函数 */
GraphAdjList *newGraphAdjList() {
GraphAdjList *graph = (GraphAdjList *)malloc(sizeof(GraphAdjList));
if (!graph) {
return NULL;
}
// 查找欲添加边的顶点 vet1 - vet2
Vertex *vet1 = graph->vertices[i];
Vertex *vet2 = graph->vertices[j];
// 连接顶点 vet1 - vet2
pushBack(vet1->list, vet2);
pushBack(vet2->list, vet1);
graph->size = 0;
for (int i = 0; i < MAX_SIZE; i++) {
graph->heads[i] = NULL;
}
return graph;
}
/* 析构函数 */
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);
}
/* 查找顶点对应的节点 */
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;
}
/* 添加边 */
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);
// 添加边 vet1 - vet2
addEdgeHelper(head1, vet2);
addEdgeHelper(head2, vet1);
}
/* 删除边 */
void removeEdge(GraphAdjList *graph, int i, int j) {
// 越界检查
if (i < 0 || j < 0 || i == j || i >= graph->size || j >= graph->size) {
printf("Out of range in %s:%d\n", __FILE__, __LINE__);
return;
}
// 查找欲删除边的顶点 vet1 - vet2
Vertex *vet1 = graph->vertices[i];
Vertex *vet2 = graph->vertices[j];
// 移除待删除边 vet1 - vet2
removeLink(vet1->list, vet2);
removeLink(vet2->list, vet1);
void removeEdge(GraphAdjList *graph, Vertex *vet1, Vertex *vet2) {
AdjListNode *head1 = findNode(graph, vet1);
AdjListNode *head2 = findNode(graph, vet2);
assert(head1 != NULL && head2 != NULL);
// 删除边 vet1 - vet2
removeEdgeHelper(head1, head2->vertex);
removeEdgeHelper(head2, head1->vertex);
}
/* 添加顶点 */
void addVertex(GraphAdjList *graph, int val) {
// 若大小超过容量，则扩容
if (graph->size >= graph->capacity) {
Vertex **tempList = (Vertex **)malloc(sizeof(Vertex *) * 2 * graph->capacity);
memcpy(tempList, graph->vertices, sizeof(Vertex *) * graph->size);
free(graph->vertices); // 释放原邻接表内存
graph->vertices = tempList; // 指向新邻接表
graph->capacity = graph->capacity * 2; // 容量扩大至2倍
}
// 申请新顶点内存并将新顶点地址存入顶点列表
Vertex *newV = newVertex(val); // 建立新顶点
newV->pos = graph->size; // 为新顶点标记下标
newV->list = newLinklist(newV); // 为新顶点建立链表
graph->vertices[graph->size] = newV; // 将新顶点加入邻接表
graph->size++;
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;
// 在邻接表中添加一个新链表
graph->heads[graph->size++] = head;
}
/* 删除顶点 */
void removeVertex(GraphAdjList *graph, unsigned int index) {
// 越界检查
if (index < 0 || index >= graph->size) {
printf("Out of range in %s:%d\n", __FILE__, __LINE__);
exit(1);
void removeVertex(GraphAdjList *graph, Vertex *vet) {
AdjListNode *node = findNode(graph, vet);
assert(node != NULL);
// 在邻接表中删除顶点 vet 对应的链表
AdjListNode *cur = node, *pre = NULL;
while (cur) {
pre = cur;
cur = cur->next;
free(pre);
}
Vertex *vet = graph->vertices[index]; // 查找待删节点
if (vet == 0) { // 若不存在该节点，则返回
printf("index is:%d\n", index);
printf("Out of range in %s:%d\n", __FILE__, __LINE__);
return;
}
// 遍历待删除顶点的链表，将所有与待删除节点有关的边删除
Node *temp = vet->list->head->next;
while (temp != 0) {
removeLink(temp->val->list, vet); // 删除与该顶点有关的边
temp = temp->next;
}
// 将顶点前移
for (int i = index; i < graph->size - 1; i++) {
graph->vertices[i] = graph->vertices[i + 1]; // 顶点前移
graph->vertices[i]->pos--; // 所有前移的顶点索引值减 1
}
graph->vertices[graph->size - 1] = 0;
graph->size--;
// 释放内存
freeVertex(vet);
}
/* 打印顶点与邻接矩阵 */
void printGraph(GraphAdjList *graph) {
printf("邻接表 =\n");
// 遍历其他顶点的链表，删除所有包含 vet 的边
for (int i = 0; i < graph->size; i++) {
Node *n = graph->vertices[i]->list->head->next;
printf("%d: [", graph->vertices[i]->val);
while (n != 0) {
if (n->next != 0) {
printf("%d, ", n->val->val);
} else {
printf("%d", n->val->val);
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;
}
n = n->next;
}
printf("]\n");
}
}
/* 构造函数 */
GraphAdjList *newGraphAdjList(unsigned int verticesCapacity) {
// 申请内存
GraphAdjList *newGraph = (GraphAdjList *)malloc(sizeof(GraphAdjList));
// 建立顶点表并分配内存
newGraph->vertices = (Vertex **)malloc(sizeof(Vertex *) * verticesCapacity); // 为顶点列表分配内存
memset(newGraph->vertices, 0, sizeof(Vertex *) * verticesCapacity); // 顶点列表置 0
newGraph->size = 0; // 初始化顶点数量
newGraph->capacity = verticesCapacity; // 初始化顶点容量
// 返回图指针
return newGraph;
// 将该顶点之后的顶点向前移动，以填补空缺
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);
}
```

142
docs/chapter_graph/graph_traversal.md
View file

@ -342,43 +342,73 @@ BFS 通常借助队列来实现。队列具有“先入先出”的性质，这
=== "C"
```c title="graph_bfs.c"
/* 广度优先遍历 */
/* 节点队列结构体 */
typedef struct {
Vertex *vertices[MAX_SIZE];
int front, rear, size;
} Queue;
/* 构造函数 */
Queue *newQueue() {
Queue *q = (Queue *)malloc(sizeof(Queue));
q->front = q->rear = q->size = 0;
return q;
}
/* 判断队列是否为空 */
int isEmpty(Queue *q) {
return q->size == 0;
}
/* 入队操作 */
void enqueue(Queue *q, Vertex *vet) {
q->vertices[q->rear] = vet;
q->rear = (q->rear + 1) % MAX_SIZE;
q->size++;
}
/* 出队操作 */
Vertex *dequeue(Queue *q) {
Vertex *vet = q->vertices[q->front];
q->front = (q->front + 1) % MAX_SIZE;
q->size--;
return vet;
}
/* 检查顶点是否已被访问 */
int isVisited(Vertex **visited, int size, Vertex *vet) {
// 遍历查找节点，使用 O(n) 时间
for (int i = 0; i < size; i++) {
if (visited[i] == vet)
return 1;
}
return 0;
}
/* 广度优先遍历 BFS */
// 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点
Vertex **graphBFS(GraphAdjList *t, Vertex *startVet) {
// 顶点遍历序列
Vertex **res = (Vertex **)malloc(sizeof(Vertex *) * t->size);
memset(res, 0, sizeof(Vertex *) * t->size);
void graphBFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize, Vertex **visited, int *visitedSize) {
// 队列用于实现 BFS
Queue *que = newQueue(t->size);
// 哈希表，用于记录已被访问过的顶点
HashTable *visited = newHash(t->size);
int resIndex = 0;
queuePush(que, startVet); // 将第一个元素入队
hashMark(visited, startVet->pos); // 标记第一个入队的顶点
Queue *queue = newQueue();
enqueue(queue, startVet);
visited[(*visitedSize)++] = startVet;
// 以顶点 vet 为起点，循环直至访问完所有顶点
while (que->head < que->tail) {
// 遍历该顶点的边链表，将所有与该顶点有连接的，并且未被标记的顶点入队
Node *n = queueTop(que)->list->head->next;
while (n != 0) {
// 查询哈希表，若该索引的顶点已入队，则跳过，否则入队并标记
if (hashQuery(visited, n->val->pos) == 1) {
n = n->next;
continue; // 跳过已被访问过的顶点
while (!isEmpty(queue)) {
Vertex *vet = dequeue(queue); // 队首顶点出队
res[(*resSize)++] = vet; // 记录访问顶点
// 遍历该顶点的所有邻接顶点
AdjListNode *node = findNode(graph, vet);
while (node != NULL) {
// 跳过已被访问过的顶点
if (!isVisited(visited, *visitedSize, node->vertex)) {
enqueue(queue, node->vertex); // 只入队未访问的顶点
visited[(*visitedSize)++] = node->vertex; // 标记该顶点已被访问
}
queuePush(que, n->val); // 只入队未访问的顶点
hashMark(visited, n->val->pos); // 标记该顶点已被访问
node = node->next;
}
// 队首元素存入数组
res[resIndex] = queueTop(que); // 队首顶点加入顶点遍历序列
resIndex++;
queuePop(que); // 队首元素出队
}
// 释放内存
freeQueue(que);
freeHash(visited);
resIndex = 0;
// 返回顶点遍历序列
return res;
free(queue);
}
```
@ -749,39 +779,37 @@ BFS 通常借助队列来实现。队列具有“先入先出”的性质，这
=== "C"
```c title="graph_dfs.c"
/* 检查顶点是否已被访问 */
int isVisited(Vertex **res, int size, Vertex *vet) {
// 遍历查找节点，使用 O(n) 时间
for (int i = 0; i < size; i++) {
if (res[i] == vet) {
return 1;
}
}
return 0;
}
/* 深度优先遍历 DFS 辅助函数 */
int resIndex = 0;
void dfs(GraphAdjList *graph, HashTable *visited, Vertex *vet, Vertex **res) {
if (hashQuery(visited, vet->pos) == 1) {
return; // 跳过已被访问过的顶点
void dfs(GraphAdjList *graph, Vertex **res, int *resSize, Vertex *vet) {
// 记录访问顶点
res[(*resSize)++] = vet;
// 遍历该顶点的所有邻接顶点
AdjListNode *node = findNode(graph, vet);
while (node != NULL) {
// 跳过已被访问过的顶点
if (!isVisited(res, *resSize, node->vertex)) {
// 递归访问邻接顶点
dfs(graph, res, resSize, node->vertex);
}
node = node->next;
}
hashMark(visited, vet->pos); // 标记顶点并将顶点存入数组
res[resIndex] = vet; // 将顶点存入数组
resIndex++;
// 遍历该顶点链表
Node *n = vet->list->head->next;
while (n != 0) {
// 递归访问邻接顶点
dfs(graph, visited, n->val, res);
n = n->next;
}
return;
}
/* 深度优先遍历 DFS */
// 使用邻接表来表示图，以便获取指定顶点的所有邻接顶点
Vertex **graphDFS(GraphAdjList *graph, Vertex *startVet) {
// 顶点遍历序列
Vertex **res = (Vertex **)malloc(sizeof(Vertex *) * graph->size);
memset(res, 0, sizeof(Vertex *) * graph->size);
// 哈希表，用于记录已被访问过的顶点
HashTable *visited = newHash(graph->size);
dfs(graph, visited, startVet, res);
// 释放哈希表内存并将数组索引归零
freeHash(visited);
resIndex = 0;
// 返回遍历数组
return res;
void graphDFS(GraphAdjList *graph, Vertex *startVet, Vertex **res, int *resSize) {
dfs(graph, res, resSize, startVet);
}
```

8
docs/chapter_hashing/hash_collision.md
View file

@ -1164,7 +1164,7 @@ comments: true
Node **buckets; // 桶数组
} HashMapChaining;
/* 构造方法 */
/* 构造函数 */
HashMapChaining *initHashMapChaining() {
HashMapChaining *hashMap = (HashMapChaining *)malloc(sizeof(HashMapChaining));
hashMap->size = 0;
@ -1178,7 +1178,7 @@ comments: true
return hashMap;
}
/* 析构方法 */
/* 析构函数 */
void freeHashMapChaining(HashMapChaining *hashMap) {
for (int i = 0; i < hashMap->capacity; i++) {
Node *cur = hashMap->buckets[i];
@ -2682,7 +2682,7 @@ comments: true
Pair *TOMBSTONE; // 删除标记
} HashMapOpenAddressing;
/* 构造方法 */
/* 构造函数 */
HashMapOpenAddressing *newHashMapOpenAddressing() {
HashMapOpenAddressing *hashMap = (HashMapOpenAddressing *)malloc(sizeof(HashMapOpenAddressing));
hashMap->size = 0;
@ -2697,7 +2697,7 @@ comments: true
return hashMap;
}
/* 析构方法 */
/* 析构函数 */
void delHashMapOpenAddressing(HashMapOpenAddressing *hashMap) {
for (int i = 0; i < hashMap->capacity; i++) {
Pair *pair = hashMap->buckets[i];

50
docs/chapter_heap/top_k.md
View file

@ -259,33 +259,49 @@ comments: true
=== "TS"
```typescript title="top_k.ts"
[class]{}-[func]{pushMinHeap}
/* 元素入堆 */
function pushMinHeap(maxHeap: MaxHeap, val: number): void {
// 元素取反
maxHeap.push(-val);
}
[class]{}-[func]{popMinHeap}
/* 元素出堆 */
function popMinHeap(maxHeap: MaxHeap): number {
// 元素取反
return -maxHeap.pop();
}
[class]{}-[func]{peekMinHeap}
/* 访问堆顶元素 */
function peekMinHeap(maxHeap: MaxHeap): number {
// 元素取反
return -maxHeap.peek();
}
[class]{}-[func]{getMinHeap}
/* 取出堆中元素 */
function getMinHeap(maxHeap: MaxHeap): number[] {
// 元素取反
return maxHeap.getMaxHeap().map((num: number) => -num);
}
/* 基于堆查找数组中最大的 k 个元素 */
function topKHeap(nums: number[], k: number): number[] {
// 将堆中所有元素取反，从而用大顶堆来模拟小顶堆
const invertedNums = nums.map((num) => -num);
// 初始化小顶堆
// 请注意：我们将堆中所有元素取反，从而用大顶堆来模拟小顶堆
const maxHeap = new MaxHeap([]);
// 将数组的前 k 个元素入堆
const heap = new MaxHeap(invertedNums.slice(0, k));
for (let i = 0; i < k; i++) {
pushMinHeap(maxHeap, nums[i]);
}
// 从第 k+1 个元素开始，保持堆的长度为 k
for (let i = k; i < invertedNums.length; i++) {
// 若当前元素小于堆顶元素，则将堆顶元素出堆、当前元素入堆
if (invertedNums[i] < heap.peek()) {
heap.pop();
heap.push(invertedNums[i]);
for (let i = k; i < nums.length; i++) {
// 若当前元素大于堆顶元素，则将堆顶元素出堆、当前元素入堆
if (nums[i] > peekMinHeap(maxHeap)) {
popMinHeap(maxHeap);
pushMinHeap(maxHeap, nums[i]);
}
}
// 取出堆中元素
const maxHeap = heap.getMaxHeap();
// 对堆中元素取相反数
const invertedMaxHeap = maxHeap.map((num) => -num);
return invertedMaxHeap;
// 返回堆中元素
return getMinHeap(maxHeap);
}
```