diff --git a/.prettierrc b/.prettierrc deleted file mode 100644 index 5a938ce18..000000000 --- a/.prettierrc +++ /dev/null @@ -1,4 +0,0 @@ -{ - "tabWidth": 4, - "useTabs": false -} diff --git a/Dockerfile b/Dockerfile new file mode 100644 index 000000000..f699e33ea --- /dev/null +++ b/Dockerfile @@ -0,0 +1,16 @@ +FROM python:3.9.0-alpine + +RUN pip install -i https://pypi.tuna.tsinghua.edu.cn/simple --upgrade pip +RUN pip install -i https://pypi.tuna.tsinghua.edu.cn/simple mkdocs-material==9.0.2 + +WORKDIR /app + +COPY codes /app/codes +COPY docs /app/docs +COPY mkdocs.yml /app/mkdocs.yml + +RUN mkdir ./docs/overrides && mkdocs build + +EXPOSE 8000 + +CMD ["mkdocs", "serve", "-a", "0.0.0.0:8000"] diff --git a/codes/c/chapter_array_and_linkedlist/CMakeLists.txt b/codes/c/chapter_array_and_linkedlist/CMakeLists.txt index 24658b301..dfa3322fb 100644 --- a/codes/c/chapter_array_and_linkedlist/CMakeLists.txt +++ b/codes/c/chapter_array_and_linkedlist/CMakeLists.txt @@ -1 +1,2 @@ -add_executable(array array.c) \ No newline at end of file +add_executable(array array.c) +add_executable(linked_list linked_list.c) \ No newline at end of file diff --git a/codes/c/chapter_array_and_linkedlist/array.c b/codes/c/chapter_array_and_linkedlist/array.c index 11fcb67f9..33dc99903 100644 --- a/codes/c/chapter_array_and_linkedlist/array.c +++ b/codes/c/chapter_array_and_linkedlist/array.c @@ -74,11 +74,11 @@ int main() { int size = 5; int arr[5]; printf("数组 arr = "); - PrintArray(arr, size); + printArray(arr, size); int nums[5] = { 1, 3, 2, 5, 4 }; printf("数组 nums = "); - PrintArray(nums, size); + printArray(nums, size); /* 随机访问 */ int randomNum = randomAccess(nums, size); @@ -89,17 +89,17 @@ int main() { int* res = extend(nums, size, enlarge); size += enlarge; printf("将数组长度扩展至 8 ，得到 nums = "); - PrintArray(res, size); + printArray(res, size); /* 插入元素 */ insert(res, size, 6, 3); printf("在索引 3 处插入数字 6 ，得到 nums = "); - PrintArray(res, size); + printArray(res, size); /* 删除元素 */ removeItem(res, size, 2); printf("删除索引 2 处的元素，得到 nums = "); - PrintArray(res, size); + printArray(res, size); /* 遍历数组 */ traverse(res, size); diff --git a/codes/c/chapter_array_and_linkedlist/linked_list.c b/codes/c/chapter_array_and_linkedlist/linked_list.c new file mode 100644 index 000000000..a8de08735 --- /dev/null +++ b/codes/c/chapter_array_and_linkedlist/linked_list.c @@ -0,0 +1,88 @@ +/** + * File: linked_list.c + * Created Time: 2022-01-12 + * Author: Zero (glj0@outlook.com) + */ + +#include "../include/include.h" + +/* 在链表的结点 n0 之后插入结点 P */ +void insert(ListNode* n0, ListNode* P) { + ListNode *n1 = n0->next; + n0->next = P; + P->next = n1; +} + +/* 删除链表的结点 n0 之后的首个结点 */ +// 由于引入了 stdio.h ，此处无法使用 remove 关键词 +// 详见 https://github.com/krahets/hello-algo/pull/244#discussion_r1067863888 +void removeNode(ListNode* n0) { + if (!n0->next) + return; + // n0 -> P -> n1 + ListNode *P = n0->next; + ListNode *n1 = P->next; + n0->next = n1; + // 释放内存 + free(P); +} + +/* 访问链表中索引为 index 的结点 */ +ListNode* access(ListNode* head, int index) { + while (head && head->next && index) { + head = head->next; + index--; + } + return head; +} + +/* 在链表中查找值为 target 的首个结点 */ +int find(ListNode* head, int target) { + int index = 0; + while (head) { + if (head->val == target) + return index; + head = head->next; + index++; + } + return -1; +} + + +/* Driver Code */ +int main() { + /* 初始化链表 */ + // 初始化各个结点 + ListNode* n0 = newListNode(1); + ListNode* n1 = newListNode(3); + ListNode* n2 = newListNode(2); + ListNode* n3 = newListNode(5); + ListNode* n4 = newListNode(4); + // 构建引用指向 + n0->next = n1; + n1->next = n2; + n2->next = n3; + n3->next = n4; + printf("初始化的链表为\r\n"); + printLinkedList(n0); + + /* 插入结点 */ + insert(n0, newListNode(0)); + printf("插入结点后的链表为\r\n"); + printLinkedList(n0); + + /* 删除结点 */ + removeNode(n0); + printf("删除结点后的链表为\r\n"); + printLinkedList(n0); + + /* 访问结点 */ + ListNode* node = access(n0, 3); + printf("链表中索引 3 处的结点的值 = %d\r\n", node->val); + + /* 查找结点 */ + int index = find(n0, 2); + printf("链表中值为 2 的结点的索引 = %d\r\n", index); + + return 0; +} diff --git a/codes/c/chapter_computational_complexity/worst_best_time_complexity.c b/codes/c/chapter_computational_complexity/worst_best_time_complexity.c index 531a76e51..e5cee821f 100644 --- a/codes/c/chapter_computational_complexity/worst_best_time_complexity.c +++ b/codes/c/chapter_computational_complexity/worst_best_time_complexity.c @@ -41,7 +41,7 @@ int main(int argc, char *argv[]) { int *nums = randomNumbers(n); int index = findOne(nums, n); printf("\n数组 [ 1, 2, ..., n ] 被打乱后 = "); - PrintArray(nums, n); + printArray(nums, n); printf("数字 1 的索引为 %d\n", index); // 释放堆区内存 if (nums != NULL) { diff --git a/codes/c/chapter_sorting/bubble_sort.c b/codes/c/chapter_sorting/bubble_sort.c index 4a2a24b44..51bab6c64 100644 --- a/codes/c/chapter_sorting/bubble_sort.c +++ b/codes/c/chapter_sorting/bubble_sort.c @@ -7,7 +7,7 @@ #include "../include/include.h" /* 冒泡排序 */ -void bubble_sort(int nums[], int size) { +void bubbleSort(int nums[], int size) { // 外循环：待排序元素数量为 n-1, n-2, ..., 1 for (int i = 0; i < size - 1; i++) { @@ -25,7 +25,7 @@ void bubble_sort(int nums[], int size) { } /* 冒泡排序（标志优化）*/ -void bubble_sort_with_flag(int nums[], int size) { +void bubbleSortWithFlag(int nums[], int size) { // 外循环：待排序元素数量为 n-1, n-2, ..., 1 for (int i = 0; i < size - 1; i++) { @@ -51,14 +51,14 @@ void bubble_sort_with_flag(int nums[], int size) { int main() { int nums[6] = {4, 1, 3, 1, 5, 2}; printf("冒泡排序后: "); - bubble_sort(nums, 6); + bubbleSort(nums, 6); for (int i = 0; i < 6; i++) { printf("%d ", nums[i]); } printf("\n优化版冒泡排序后: "); - bubble_sort_with_flag(nums, 6); + bubbleSortWithFlag(nums, 6); for (int i = 0; i < 6; i++) { printf("%d ", nums[i]); diff --git a/codes/c/chapter_tree/binary_tree.c b/codes/c/chapter_tree/binary_tree.c index 0a2f946a7..1eb8e846a 100644 --- a/codes/c/chapter_tree/binary_tree.c +++ b/codes/c/chapter_tree/binary_tree.c @@ -10,34 +10,33 @@ int main() { /* 初始化二叉树 */ // 初始化结点 - TreeNode* n1 = NewTreeNode(1); - TreeNode* n2 = NewTreeNode(2); - TreeNode* n3 = NewTreeNode(3); - TreeNode* n4 = NewTreeNode(4); - TreeNode* n5 = NewTreeNode(5); + TreeNode* n1 = newTreeNode(1); + TreeNode* n2 = newTreeNode(2); + TreeNode* n3 = newTreeNode(3); + TreeNode* n4 = newTreeNode(4); + TreeNode* n5 = newTreeNode(5); // 构建引用指向（即指针） n1->left = n2; n1->right = n3; n2->left = n4; n2->right = n5; printf("初始化二叉树\n"); - PrintTree(n1); + printTree(n1); /* 插入与删除结点 */ - TreeNode* P = NewTreeNode(0); + TreeNode* P = newTreeNode(0); // 在 n1 -> n2 中间插入结点 P n1->left = P; P->left = n2; printf("插入结点 P 后\n"); - PrintTree(n1); + printTree(n1); // 删除结点 P n1->left = n2; // 释放内存 free(P); printf("删除结点 P 后\n"); - PrintTree(n1); + printTree(n1); return 0; } - diff --git a/codes/c/chapter_tree/binary_tree_bfs.c b/codes/c/chapter_tree/binary_tree_bfs.c index abad3735f..c7b83b912 100644 --- a/codes/c/chapter_tree/binary_tree_bfs.c +++ b/codes/c/chapter_tree/binary_tree_bfs.c @@ -52,15 +52,15 @@ int main() { // 这里借助了一个从数组直接生成二叉树的函数 int nums[] = {1, 2, 3, NIL, 5, 6, NIL}; int size = sizeof(nums) / sizeof(int); - TreeNode *root = ArrayToTree(nums, size); + TreeNode *root = arrToTree(nums, size); printf("初始化二叉树\n"); - PrintTree(root); + printTree(root); /* 层序遍历 */ // 需要传入数组的长度 int *arr = levelOrder(root, &size); printf("层序遍历的结点打印序列 = "); - PrintArray(arr, size); + printArray(arr, size); return 0; } \ No newline at end of file diff --git a/codes/c/chapter_tree/binary_tree_dfs.c b/codes/c/chapter_tree/binary_tree_dfs.c index f72e6687b..bafc90fd1 100644 --- a/codes/c/chapter_tree/binary_tree_dfs.c +++ b/codes/c/chapter_tree/binary_tree_dfs.c @@ -43,10 +43,10 @@ int main() { /* 初始化二叉树 */ // 这里借助了一个从数组直接生成二叉树的函数 int nums[] = {1, 2, 3, 4, 5, 6, 7}; - int size = sizeof(nums) / sizt ceof(int); - TreeNode *root = ArrayToTree(nums, size); + int size = sizeof(nums) / sizeof(int); + TreeNode *root = arrToTree(nums, size); printf("初始化二叉树\n"); - PrintTree(root); + printTree(root); /* 前序遍历 */ // 初始化辅助数组 @@ -54,19 +54,19 @@ int main() { size = 0; preOrder(root, &size); printf("前序遍历的结点打印序列 = "); - PrintArray(arr, size); + printArray(arr, size); /* 中序遍历 */ size = 0; inOrder(root, &size); printf("中序遍历的结点打印序列 = "); - PrintArray(arr, size); + printArray(arr, size); /* 后序遍历 */ size = 0; postOrder(root, &size); printf("后序遍历的结点打印序列 = "); - PrintArray(arr, size); + printArray(arr, size); return 0; } diff --git a/codes/c/include/include_test.c b/codes/c/include/include_test.c index baa8e649d..602670d68 100644 --- a/codes/c/include/include_test.c +++ b/codes/c/include/include_test.c @@ -9,24 +9,24 @@ void testListNode() { int nums[] = {2, 3, 5, 6, 7}; int size = sizeof(nums) / sizeof(int); - ListNode *head = ArrayToLinkedList(nums, size); - PrintLinkedList(head); + ListNode *head = arrToLinkedList(nums, size); + printLinkedList(head); - ListNode *node = GetListNode(head, 5); + ListNode *node = getListNode(head, 5); printf("find node: %d\n", node->val); } void testTreeNode() { int nums[] = {1, 2, 3, NIL, 5, 6, NIL}; int size = sizeof(nums) / sizeof(int); - TreeNode *root = ArrayToTree(nums, size); + TreeNode *root = arrToTree(nums, size); // print tree - PrintTree(root); + printTree(root); // tree to arr - int *arr = TreeToArray(root); - PrintArray(arr, size); + int *arr = treeToArr(root); + printArray(arr, size); } int main(int argc, char *argv[]) { diff --git a/codes/c/include/list_node.h b/codes/c/include/list_node.h index 5597d2102..1845ffafd 100644 --- a/codes/c/include/list_node.h +++ b/codes/c/include/list_node.h @@ -22,7 +22,7 @@ struct ListNode { // typedef 为 C 语言的关键字，作用是为一种数据类型定义一个新名字 typedef struct ListNode ListNode; -ListNode *NewListNode(int val) { +ListNode *newListNode(int val) { ListNode *node, *next; node = (ListNode *) malloc(sizeof(ListNode)); node->val = val; @@ -37,15 +37,15 @@ ListNode *NewListNode(int val) { * @return ListNode* */ -ListNode *ArrayToLinkedList(const int *arr, size_t size) { +ListNode *arrToLinkedList(const int *arr, size_t size) { if (size <= 0) { return NULL; } - ListNode *dummy = NewListNode(0); + ListNode *dummy = newListNode(0); ListNode *node = dummy; for (int i = 0; i < size; i++) { - node->next = NewListNode(arr[i]); + node->next = newListNode(arr[i]); node = node->next; } return dummy->next; @@ -58,7 +58,7 @@ ListNode *ArrayToLinkedList(const int *arr, size_t size) { * @param val * @return ListNode* */ -ListNode *GetListNode(ListNode *head, int val) { +ListNode *getListNode(ListNode *head, int val) { while (head != NULL && head->val != val) { head = head->next; } diff --git a/codes/c/include/print_util.h b/codes/c/include/print_util.h index fcb0a4ca6..a0c3a1500 100644 --- a/codes/c/include/print_util.h +++ b/codes/c/include/print_util.h @@ -25,7 +25,7 @@ extern "C" { * @param arr * @param size */ -static void PrintArray(int *arr, int size) { +static void printArray(int *arr, int size) { printf("["); for (int i = 0; i < size - 1; i++) { if (arr[i] != NIL) { @@ -46,7 +46,7 @@ static void PrintArray(int *arr, int size) { * * @param head */ -static void PrintLinkedList(ListNode *node) { +static void printLinkedList(ListNode *node) { if (node == NULL) { return; } @@ -123,7 +123,7 @@ static void printTreeHelper(TreeNode *node, Trunk *prev, bool isLeft) { * * @param head */ -static void PrintTree(TreeNode *root) { +static void printTree(TreeNode *root) { printTreeHelper(root, NULL, false); } diff --git a/codes/c/include/tree_node.h b/codes/c/include/tree_node.h index 4b0e70187..c0438c437 100644 --- a/codes/c/include/tree_node.h +++ b/codes/c/include/tree_node.h @@ -25,7 +25,7 @@ struct TreeNode { typedef struct TreeNode TreeNode; -TreeNode *NewTreeNode(int val) { +TreeNode *newTreeNode(int val) { TreeNode *node; node = (TreeNode *) malloc(sizeof(TreeNode)); @@ -43,7 +43,7 @@ TreeNode *NewTreeNode(int val) { * @param size * @return TreeNode * */ -TreeNode *ArrayToTree(const int *arr, size_t size) { +TreeNode *arrToTree(const int *arr, size_t size) { if (size <= 0) { return NULL; } @@ -53,7 +53,7 @@ TreeNode *ArrayToTree(const int *arr, size_t size) { TreeNode **queue; /* 根结点 */ - root = NewTreeNode(arr[0]); + root = newTreeNode(arr[0]); /* 辅助队列 */ queue = (TreeNode **) malloc(sizeof(TreeNode) * MAX_NODE_SIZE); // 队列指针 @@ -68,14 +68,14 @@ TreeNode *ArrayToTree(const int *arr, size_t size) { index++; if (index < size) { if (arr[index] != NIL) { - node->left = NewTreeNode(arr[index]); + node->left = newTreeNode(arr[index]); queue[rear++] = node->left; } } index++; if (index < size) { if (arr[index] != NIL) { - node->right = NewTreeNode(arr[index]); + node->right = newTreeNode(arr[index]); queue[rear++] = node->right; } } @@ -91,7 +91,7 @@ TreeNode *ArrayToTree(const int *arr, size_t size) { * @param size * @return TreeNode * */ -int *TreeToArray(TreeNode *root) { +int *treeToArr(TreeNode *root) { if (root == NULL) { return NULL; } diff --git a/codes/cpp/include/include.hpp b/codes/cpp/include/include.hpp index 8e4a8070d..03bf9b503 100644 --- a/codes/cpp/include/include.hpp +++ b/codes/cpp/include/include.hpp @@ -17,6 +17,8 @@ #include #include #include +#include +#include #include "ListNode.hpp" #include "TreeNode.hpp" diff --git a/codes/go/chapter_heap/heap.go b/codes/go/chapter_heap/heap.go new file mode 100644 index 000000000..5f846ced4 --- /dev/null +++ b/codes/go/chapter_heap/heap.go @@ -0,0 +1,45 @@ +// File: intHeap.go +// Created Time: 2023-01-12 +// Author: Reanon (793584285@qq.com) + +package chapter_heap + +// Go 语言中可以通过实现 heap.Interface 来构建整数大顶堆 +// 实现 heap.Interface 需要同时实现 sort.Interface +type intHeap []any + +// Push heap.Interface 的方法，实现推入元素到堆 +func (h *intHeap) Push(x any) { + // Push 和 Pop 使用 pointer receiver 作为参数 + // 因为它们不仅会对切片的内容进行调整，还会修改切片的长度。 + *h = append(*h, x.(int)) +} + +// Pop heap.Interface 的方法，实现弹出堆顶元素 +func (h *intHeap) Pop() any { + // 待出堆元素存放在最后 + last := (*h)[len(*h)-1] + *h = (*h)[:len(*h)-1] + return last +} + +// Len sort.Interface 的方法 +func (h *intHeap) Len() int { + return len(*h) +} + +// Less sort.Interface 的方法 +func (h *intHeap) Less(i, j int) bool { + // 如果实现小顶堆，则需要调整为小于号 + return (*h)[i].(int) > (*h)[j].(int) +} + +// Swap sort.Interface 的方法 +func (h *intHeap) Swap(i, j int) { + (*h)[i], (*h)[j] = (*h)[j], (*h)[i] +} + +// Top 获取堆顶元素 +func (h *intHeap) Top() any { + return (*h)[0] +} diff --git a/codes/go/chapter_heap/heap_test.go b/codes/go/chapter_heap/heap_test.go new file mode 100644 index 000000000..db3844efa --- /dev/null +++ b/codes/go/chapter_heap/heap_test.go @@ -0,0 +1,90 @@ +// File: heap_test.go +// Created Time: 2023-01-12 +// Author: Reanon (793584285@qq.com) + +package chapter_heap + +import ( + "container/heap" + "fmt" + "testing" + + . "github.com/krahets/hello-algo/pkg" +) + +func testPush(h *intHeap, val int) { + // 调用 heap.Interface 的方法，来添加元素 + heap.Push(h, val) + fmt.Printf("\n元素 %d 入堆后 \n", val) + PrintHeap(*h) +} + +func testPop(h *intHeap) { + // 调用 heap.Interface 的方法，来移除元素 + val := heap.Pop(h) + fmt.Printf("\n堆顶元素 %d 出堆后 \n", val) + PrintHeap(*h) +} + +func TestHeap(t *testing.T) { + /* 初始化堆 */ + // 初始化大顶堆 + maxHeap := &intHeap{} + heap.Init(maxHeap) + /* 元素入堆 */ + testPush(maxHeap, 1) + testPush(maxHeap, 3) + testPush(maxHeap, 2) + testPush(maxHeap, 5) + testPush(maxHeap, 4) + + /* 获取堆顶元素 */ + top := maxHeap.Top() + fmt.Printf("堆顶元素为 %d\n", top) + + /* 堆顶元素出堆 */ + testPop(maxHeap) + testPop(maxHeap) + testPop(maxHeap) + testPop(maxHeap) + testPop(maxHeap) + + /* 获取堆大小 */ + size := len(*maxHeap) + fmt.Printf("堆元素数量为 %d\n", size) + + /* 判断堆是否为空 */ + isEmpty := len(*maxHeap) == 0 + fmt.Printf("堆是否为空 %t\n", isEmpty) +} + +func TestMyHeap(t *testing.T) { + /* 初始化堆 */ + // 初始化大顶堆 + maxHeap := newMaxHeap([]any{9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2}) + fmt.Printf("输入数组并建堆后\n") + maxHeap.print() + + /* 获取堆顶元素 */ + peek := maxHeap.peek() + fmt.Printf("\n堆顶元素为 %d\n", peek) + + /* 元素入堆 */ + val := 7 + maxHeap.push(val) + fmt.Printf("\n元素 %d 入堆后\n", val) + maxHeap.print() + + /* 堆顶元素出堆 */ + peek = maxHeap.poll() + fmt.Printf("\n堆顶元素 %d 出堆后\n", peek) + maxHeap.print() + + /* 获取堆大小 */ + size := maxHeap.size() + fmt.Printf("\n堆元素数量为 %d\n", size) + + /* 判断堆是否为空 */ + isEmpty := maxHeap.isEmpty() + fmt.Printf("\n堆是否为空 %t\n", isEmpty) +} diff --git a/codes/go/chapter_heap/my_heap.go b/codes/go/chapter_heap/my_heap.go new file mode 100644 index 000000000..0b3d0a3b1 --- /dev/null +++ b/codes/go/chapter_heap/my_heap.go @@ -0,0 +1,139 @@ +// File: my_heap.go +// Created Time: 2023-01-12 +// Author: Reanon (793584285@qq.com) + +package chapter_heap + +import ( + "fmt" + + . "github.com/krahets/hello-algo/pkg" +) + +type maxHeap struct { + // 使用切片而非数组，这样无需考虑扩容问题 + data []any +} + +/* 构造函数，建立空堆 */ +func newHeap() *maxHeap { + return &maxHeap{ + data: make([]any, 0), + } +} + +/* 构造函数，根据切片建堆 */ +func newMaxHeap(nums []any) *maxHeap { + // 所有元素入堆 + h := &maxHeap{data: nums} + for i := len(h.data) - 1; i >= 0; i-- { + // 堆化除叶结点以外的其他所有结点 + h.siftDown(i) + } + return h +} + +/* 获取左子结点索引 */ +func (h *maxHeap) left(i int) int { + return 2*i + 1 +} + +/* 获取右子结点索引 */ +func (h *maxHeap) right(i int) int { + return 2*i + 2 +} + +/* 获取父结点索引 */ +func (h *maxHeap) parent(i int) int { + // 向下整除 + return (i - 1) / 2 +} + +/* 交换元素 */ +func (h *maxHeap) swap(i, j int) { + h.data[i], h.data[j] = h.data[j], h.data[i] +} + +/* 获取堆大小 */ +func (h *maxHeap) size() int { + return len(h.data) +} + +/* 判断堆是否为空 */ +func (h *maxHeap) isEmpty() bool { + return len(h.data) == 0 +} + +/* 访问堆顶元素 */ +func (h *maxHeap) peek() any { + return h.data[0] +} + +/* 元素入堆 */ +func (h *maxHeap) push(val any) { + // 添加结点 + h.data = append(h.data, val) + // 从底至顶堆化 + h.siftUp(len(h.data) - 1) +} + +/* 从结点 i 开始，从底至顶堆化 */ +func (h *maxHeap) siftUp(i int) { + for true { + // 获取结点 i 的父结点 + p := h.parent(i) + // 当“越过根结点”或“结点无需修复”时，结束堆化 + if p < 0 || h.data[i].(int) <= h.data[p].(int) { + break + } + // 交换两结点 + h.swap(i, p) + // 循环向上堆化 + i = p + } +} + +/* 元素出堆 */ +func (h *maxHeap) poll() any { + // 判空处理 + if h.isEmpty() { + fmt.Println("error") + } + // 交换根结点与最右叶结点（即交换首元素与尾元素） + h.swap(0, h.size()-1) + // 删除结点 + val := h.data[len(h.data)-1] + h.data = h.data[:len(h.data)-1] + // 从顶至底堆化 + h.siftDown(0) + + // 返回堆顶元素 + return val +} + +/* 从结点 i 开始，从顶至底堆化 */ +func (h *maxHeap) siftDown(i int) { + for true { + // 判断结点 i, l, r 中值最大的结点，记为 max + l, r, max := h.left(i), h.right(i), i + if l < h.size() && h.data[l].(int) > h.data[max].(int) { + max = l + } + if r < h.size() && h.data[r].(int) > h.data[max].(int) { + max = r + } + // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出 + if max == i { + break + } + // 交换两结点 + h.swap(i, max) + // 循环向下堆化 + i = max + } +} + +/* 打印堆（二叉树） */ +func (h *maxHeap) print() { + PrintHeap(h.data) +} diff --git a/codes/go/pkg/print_utils.go b/codes/go/pkg/print_utils.go index 575ab6b94..d65ebba1d 100644 --- a/codes/go/pkg/print_utils.go +++ b/codes/go/pkg/print_utils.go @@ -29,6 +29,22 @@ func PrintList(list *list.List) { fmt.Print(e.Value, "]\n") } +// PrintMap Print a hash map +func PrintMap[K comparable, V any](m map[K]V) { + for key, value := range m { + fmt.Println(key, "->", value) + } +} + +// PrintHeap Print a heap +func PrintHeap(h []any) { + fmt.Printf("堆的数组表示：") + fmt.Printf("%v", h) + fmt.Printf("\n堆的树状表示：\n") + root := ArrToTree(h) + PrintTree(root) +} + // PrintLinkedList Print a linked list func PrintLinkedList(node *ListNode) { if node == nil { @@ -97,10 +113,3 @@ func showTrunk(t *trunk) { showTrunk(t.prev) fmt.Print(t.str) } - -// PrintMap Print a hash map -func PrintMap[K comparable, V any](m map[K]V) { - for key, value := range m { - fmt.Println(key, "->", value) - } -} diff --git a/codes/java/chapter_hashing/array_hash_map.java b/codes/java/chapter_hashing/array_hash_map.java index 68df1f3b9..980a00ab7 100644 --- a/codes/java/chapter_hashing/array_hash_map.java +++ b/codes/java/chapter_hashing/array_hash_map.java @@ -5,6 +5,7 @@ */ package chapter_hashing; + import java.util.*; /* 键值对 int->String */ diff --git a/codes/java/chapter_hashing/hash_map.java b/codes/java/chapter_hashing/hash_map.java index fe3f822f4..47f4823bf 100644 --- a/codes/java/chapter_hashing/hash_map.java +++ b/codes/java/chapter_hashing/hash_map.java @@ -5,6 +5,7 @@ */ package chapter_hashing; + import java.util.*; import include.*; diff --git a/codes/java/chapter_heap/heap.java b/codes/java/chapter_heap/heap.java new file mode 100644 index 000000000..1a0c53b94 --- /dev/null +++ b/codes/java/chapter_heap/heap.java @@ -0,0 +1,67 @@ +/** + * File: my_heap.java + * Created Time: 2023-01-07 + * Author: Krahets (krahets@163.com) + */ + +package chapter_heap; + +import include.*; +import java.util.*; + + +public class heap { + public static void testPush(Queue heap, int val) { + heap.add(val); // 元素入堆 + System.out.format("\n元素 %d 入堆后\n", val); + PrintUtil.printHeap(heap); + } + + public static void testPoll(Queue heap) { + int val = heap.poll(); // 堆顶元素出堆 + System.out.format("\n堆顶元素 %d 出堆后\n", val); + PrintUtil.printHeap(heap); + } + + public static void main(String[] args) { + /* 初始化堆 */ + // 初始化小顶堆 + Queue minHeap = new PriorityQueue<>(); + // 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可） + Queue maxHeap = new PriorityQueue<>((a, b) -> { return b - a; }); + + System.out.println("\n以下测试样例为大顶堆"); + + /* 元素入堆 */ + testPush(maxHeap, 1); + testPush(maxHeap, 3); + testPush(maxHeap, 2); + testPush(maxHeap, 5); + testPush(maxHeap, 4); + + /* 获取堆顶元素 */ + int peek = maxHeap.peek(); + System.out.format("\n堆顶元素为 %d\n", peek); + + /* 堆顶元素出堆 */ + testPoll(maxHeap); + testPoll(maxHeap); + testPoll(maxHeap); + testPoll(maxHeap); + testPoll(maxHeap); + + /* 获取堆大小 */ + int size = maxHeap.size(); + System.out.format("\n堆元素数量为 %d\n", size); + + /* 判断堆是否为空 */ + boolean isEmpty = maxHeap.isEmpty(); + System.out.format("\n堆是否为空 %b\n", isEmpty); + + /* 输入列表并建堆 */ + // 时间复杂度为 O(n) ，而非 O(nlogn) + minHeap = new PriorityQueue<>(Arrays.asList(1, 3, 2, 5, 4)); + System.out.println("\n输入列表并建立小顶堆后"); + PrintUtil.printHeap(minHeap); + } +} diff --git a/codes/java/chapter_heap/my_heap.java b/codes/java/chapter_heap/my_heap.java new file mode 100644 index 000000000..b80ce6d08 --- /dev/null +++ b/codes/java/chapter_heap/my_heap.java @@ -0,0 +1,177 @@ +/** + * File: my_heap.java + * Created Time: 2023-01-07 + * Author: Krahets (krahets@163.com) + */ + +package chapter_heap; + +import include.*; +import java.util.*; + +class MaxHeap { + // 使用列表而非数组，这样无需考虑扩容问题 + private List maxHeap; + + /* 构造函数，建立空堆 */ + public MaxHeap() { + maxHeap = new ArrayList<>(); + } + + /* 构造函数，根据输入列表建堆 */ + public MaxHeap(List nums) { + // 所有元素入堆 + maxHeap = new ArrayList<>(nums); + // 堆化除叶结点以外的其他所有结点 + for (int i = parent(size() - 1); i >= 0; i--) { + siftDown(i); + } + } + + /* 获取左子结点索引 */ + private int left(int i) { + return 2 * i + 1; + } + + /* 获取右子结点索引 */ + private int right(int i) { + return 2 * i + 2; + } + + /* 获取父结点索引 */ + private int parent(int i) { + return (i - 1) / 2; // 向下整除 + } + + /* 交换元素 */ + private void swap(int i, int j) { + int a = maxHeap.get(i), + b = maxHeap.get(j), + tmp = a; + maxHeap.set(i, b); + maxHeap.set(j, tmp); + } + + /* 获取堆大小 */ + public int size() { + return maxHeap.size(); + } + + /* 判断堆是否为空 */ + public boolean isEmpty() { + return size() == 0; + } + + /* 访问堆顶元素 */ + public int peek() { + return maxHeap.get(0); + } + + /* 元素入堆 */ + public void push(int val) { + // 添加结点 + maxHeap.add(val); + // 从底至顶堆化 + siftUp(size() - 1); + } + + /* 从结点 i 开始，从底至顶堆化 */ + private void siftUp(int i) { + while (true) { + // 获取结点 i 的父结点 + int p = parent(i); + // 当“越过根结点”或“结点无需修复”时，结束堆化 + if (p < 0 || maxHeap.get(i) <= maxHeap.get(p)) + break; + // 交换两结点 + swap(i, p); + // 循环向上堆化 + i = p; + } + } + + /* 元素出堆 */ + public int poll() { + // 判空处理 + if (isEmpty()) + throw new EmptyStackException(); + // 交换根结点与最右叶结点（即交换首元素与尾元素） + swap(0, size() - 1); + // 删除结点 + int val = maxHeap.remove(size() - 1); + // 从顶至底堆化 + siftDown(0); + // 返回堆顶元素 + return val; + } + + /* 从结点 i 开始，从顶至底堆化 */ + private void siftDown(int i) { + while (true) { + // 判断结点 i, l, r 中值最大的结点，记为 ma + int l = left(i), r = right(i), ma = i; + if (l < size() && maxHeap.get(l) > maxHeap.get(ma)) + ma = l; + if (r < size() && maxHeap.get(r) > maxHeap.get(ma)) + ma = r; + // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出 + if (ma == i) break; + // 交换两结点 + swap(i, ma); + // 循环向下堆化 + i = ma; + } + } + + /* 打印堆（二叉树） */ + public void print() { + Queue queue = new PriorityQueue<>((a, b) -> { return b - a; }); + queue.addAll(maxHeap); + PrintUtil.printHeap(queue); + } +} + + +public class my_heap { + public static void testPush(MaxHeap maxHeap, int val) { + maxHeap.push(val); // 元素入堆 + System.out.format("\n添加元素 %d 后\n", val); + maxHeap.print(); + } + + public static void testPoll(MaxHeap maxHeap) { + int val = maxHeap.poll(); // 堆顶元素出堆 + System.out.format("\n出堆元素为 %d\n", val); + maxHeap.print(); + } + + public static void main(String[] args) { + /* 初始化大顶堆 */ + MaxHeap maxHeap = new MaxHeap(Arrays.asList(9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2)); + System.out.println("\n输入列表并建堆后"); + maxHeap.print(); + + /* 获取堆顶元素 */ + int peek = maxHeap.peek(); + System.out.format("\n堆顶元素为 %d\n", peek); + + /* 元素入堆 */ + int val = 7; + maxHeap.push(val); + System.out.format("\n元素 %d 入堆后\n", val); + maxHeap.print(); + + /* 堆顶元素出堆 */ + peek = maxHeap.poll(); + System.out.format("\n堆顶元素 %d 出堆后\n", peek); + maxHeap.print(); + + /* 获取堆大小 */ + int size = maxHeap.size(); + System.out.format("\n堆元素数量为 %d\n", size); + + /* 判断堆是否为空 */ + boolean isEmpty = maxHeap.isEmpty(); + System.out.format("\n堆是否为空 %b\n", isEmpty); + } +} diff --git a/codes/java/chapter_tree/binary_tree_bfs.java b/codes/java/chapter_tree/binary_tree_bfs.java index 450311d08..ffeb352e0 100644 --- a/codes/java/chapter_tree/binary_tree_bfs.java +++ b/codes/java/chapter_tree/binary_tree_bfs.java @@ -30,7 +30,7 @@ public class binary_tree_bfs { public static void main(String[] args) { /* 初始化二叉树 */ // 这里借助了一个从数组直接生成二叉树的函数 - TreeNode root = TreeNode.arrToTree(new Integer[] { 1, 2, 3, 4, 5, 6, 7 }); + TreeNode root = TreeNode.listToTree(Arrays.asList(1, 2, 3, 4, 5, 6, 7)); System.out.println("\n初始化二叉树\n"); PrintUtil.printTree(root); diff --git a/codes/java/chapter_tree/binary_tree_dfs.java b/codes/java/chapter_tree/binary_tree_dfs.java index ad5337f22..9f2d0507d 100644 --- a/codes/java/chapter_tree/binary_tree_dfs.java +++ b/codes/java/chapter_tree/binary_tree_dfs.java @@ -43,7 +43,7 @@ public class binary_tree_dfs { public static void main(String[] args) { /* 初始化二叉树 */ // 这里借助了一个从数组直接生成二叉树的函数 - TreeNode root = TreeNode.arrToTree(new Integer[] { 1, 2, 3, 4, 5, 6, 7 }); + TreeNode root = TreeNode.listToTree(Arrays.asList(1, 2, 3, 4, 5, 6, 7)); System.out.println("\n初始化二叉树\n"); PrintUtil.printTree(root); diff --git a/codes/java/include/PrintUtil.java b/codes/java/include/PrintUtil.java index b2593ac1f..1ebc45ba0 100755 --- a/codes/java/include/PrintUtil.java +++ b/codes/java/include/PrintUtil.java @@ -105,10 +105,16 @@ public class PrintUtil { } } - public static void printHeap(PriorityQueue queue) { - Integer[] nums = (Integer[])queue.toArray(); - TreeNode root = TreeNode.arrToTree(nums); - + /** + * Print a heap (PriorityQueue) + * @param queue + */ + public static void printHeap(Queue queue) { + List list = new ArrayList<>(queue); + System.out.print("堆的数组表示："); + System.out.println(list); + System.out.println("堆的树状表示："); + TreeNode root = TreeNode.listToTree(list); printTree(root); } } diff --git a/codes/java/include/TreeNode.java b/codes/java/include/TreeNode.java index 11d457a10..22a349747 100644 --- a/codes/java/include/TreeNode.java +++ b/codes/java/include/TreeNode.java @@ -23,26 +23,27 @@ public class TreeNode { /** * Generate a binary tree given an array - * @param arr + * @param list * @return */ - public static TreeNode arrToTree(Integer[] arr) { - if (arr.length == 0) + public static TreeNode listToTree(List list) { + int size = list.size(); + if (size == 0) return null; - TreeNode root = new TreeNode(arr[0]); + TreeNode root = new TreeNode(list.get(0)); Queue queue = new LinkedList<>() {{ add(root); }}; int i = 0; while(!queue.isEmpty()) { TreeNode node = queue.poll(); - if (++i >= arr.length) break; - if(arr[i] != null) { - node.left = new TreeNode(arr[i]); + if (++i >= size) break; + if (list.get(i) != null) { + node.left = new TreeNode(list.get(i)); queue.add(node.left); } - if (++i >= arr.length) break; - if(arr[i] != null) { - node.right = new TreeNode(arr[i]); + if (++i >= size) break; + if (list.get(i) != null) { + node.right = new TreeNode(list.get(i)); queue.add(node.right); } } diff --git a/codes/rust/chapter_computational_complexity/time_complexity.rs b/codes/rust/chapter_computational_complexity/time_complexity.rs new file mode 100644 index 000000000..a6aa60b31 --- /dev/null +++ b/codes/rust/chapter_computational_complexity/time_complexity.rs @@ -0,0 +1,163 @@ +#![allow(unused_variables)] + +/* 常数阶 */ +fn constant(n: i32) -> i32 { + let mut count = 0; + let size = 100000; + for _ in 0..size { + count += 1 + } + count +} + +fn linear(n: i32) -> i32 { + let mut count = 0; + for _ in 0..n { + count += 1; + } + count +} + +/* 线性阶（遍历数组） */ +fn array_traversal(nums: &[i32]) -> i32 { + let mut count = 0; + // 循环次数与数组长度成正比 + for _ in nums { + count += 1; + } + count +} + +fn quadratic(n: i32) -> i32 { + let mut count = 0; + // 循环次数与数组长度成平方关系 + for _ in 0..n { + for _ in 0..n { + count += 1; + } + } + count +} + +/* 平方阶（冒泡排序） */ +fn bubble_sort(nums: &mut [i32]) -> i32 { + let mut count = 0; // 计数器 + // 外循环：待排序元素数量为 n-1, n-2, ..., 1 + for i in (1..nums.len()).rev() { + // 内循环：冒泡操作 + for j in 0..i { + if nums[j] > nums[j + 1] { + // 交换 nums[j] 与 nums[j + 1] + let tmp = nums[j]; + nums[j] = nums[j + 1]; + nums[j + 1] = tmp; + count += 3; // 元素交换包含 3 个单元操作 + } + } + } + count +} + +/* 指数阶（循环实现） */ +fn exponential(n: i32) -> i32 { + let mut count = 0; + let mut base = 1; + // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1) + for _ in 0..n { + for _ in 0..base { + count += 1 + } + base *= 2; + } + // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1 + count +} + +/* 指数阶（递归实现） */ +fn exp_recur(n: i32) -> i32 { + if n == 1 { + return 1; + } + exp_recur(n - 1) + exp_recur(n - 1) + 1 +} + +/* 对数阶（循环实现） */ +fn logarithmic(mut n: i32) -> i32 { + let mut count = 0; + + while n > 1 { + n = n / 2; + count += 1; + } + count +} + +fn log_recur(n: i32) -> i32 { + if n <= 1 { + return 0; + } + log_recur(n / 2) + 1 +} + +/* 线性对数阶 */ +fn linear_log_recur(n: f64) -> i32 { + if n <= 1.0 { + return 1; + } + let mut count = linear_log_recur(n / 2.0) + linear_log_recur(n / 2.0); + for _ in 0 ..n as i32 { + count += 1; + } + return count +} + +/* 阶乘阶（递归实现） */ +fn factorial_recur(n: i32) -> i32 { + if n == 0 { + return 1; + } + let mut count = 0; + // 从 1 个分裂出 n 个 + for _ in 0..n { + count += factorial_recur(n - 1); + } + count +} + +/* Driver Code */ +fn main() { + // 可以修改 n 运行，体会一下各种复杂度的操作数量变化趋势 + let n: i32 = 8; + println!("输入数据大小 n = {}", n); + + let mut count = constant(n); + println!("常数阶的计算操作数量 = {}", count); + + count = linear(n); + println!("线性阶的计算操作数量 = {}", count); + count = array_traversal(&vec![0; n as usize]); + println!("线性阶（遍历数组）的计算操作数量 = {}", count); + + count = quadratic(n); + println!("平方阶的计算操作数量 = {}", count); + + let mut nums = (1..=n).rev().collect::>(); // [n,n-1,...,2,1] + count = bubble_sort(&mut nums); + println!("平方阶（冒泡排序）的计算操作数量 = {}", count); + + count = exponential(n); + println!("指数阶（循环实现）的计算操作数量 = {}", count); + count = exp_recur(n); + println!("指数阶（递归实现）的计算操作数量 = {}", count); + + count = logarithmic(n); + println!("对数阶（循环实现）的计算操作数量 = {}", count); + count = log_recur(n); + println!("对数阶（递归实现）的计算操作数量 = {}", count); + + count = linear_log_recur(n.into()); + println!("线性对数阶（递归实现）的计算操作数量 = {}", count); + + count = factorial_recur(n); + println!("阶乘阶（递归实现）的计算操作数量 = {}", count); +} \ No newline at end of file diff --git a/codes/swift/Package.swift b/codes/swift/Package.swift index 6d6eaa8a5..89c03d9f6 100644 --- a/codes/swift/Package.swift +++ b/codes/swift/Package.swift @@ -16,6 +16,9 @@ let package = Package( .executable(name: "stack", targets: ["stack"]), .executable(name: "linkedlist_stack", targets: ["linkedlist_stack"]), .executable(name: "array_stack", targets: ["array_stack"]), + .executable(name: "queue", targets: ["queue"]), + .executable(name: "linkedlist_queue", targets: ["linkedlist_queue"]), + .executable(name: "array_queue", targets: ["array_queue"]), ], targets: [ .target(name: "utils", path: "utils"), @@ -30,5 +33,8 @@ let package = Package( .executableTarget(name: "stack", path: "chapter_stack_and_queue", sources: ["stack.swift"]), .executableTarget(name: "linkedlist_stack", dependencies: ["utils"], path: "chapter_stack_and_queue", sources: ["linkedlist_stack.swift"]), .executableTarget(name: "array_stack", path: "chapter_stack_and_queue", sources: ["array_stack.swift"]), + .executableTarget(name: "queue", path: "chapter_stack_and_queue", sources: ["queue.swift"]), + .executableTarget(name: "linkedlist_queue", dependencies: ["utils"], path: "chapter_stack_and_queue", sources: ["linkedlist_queue.swift"]), + .executableTarget(name: "array_queue", path: "chapter_stack_and_queue", sources: ["array_queue.swift"]), ] ) diff --git a/codes/swift/chapter_stack_and_queue/array_queue.swift b/codes/swift/chapter_stack_and_queue/array_queue.swift new file mode 100644 index 000000000..d76dbc9c5 --- /dev/null +++ b/codes/swift/chapter_stack_and_queue/array_queue.swift @@ -0,0 +1,116 @@ +/** + * File: array_queue.swift + * Created Time: 2023-01-11 + * Author: nuomi1 (nuomi1@qq.com) + */ + +/* 基于环形数组实现的队列 */ +class ArrayQueue { + private var nums: [Int] // 用于存储队列元素的数组 + private var front = 0 // 头指针，指向队首 + private var rear = 0 // 尾指针，指向队尾 + 1 + + init(capacity: Int) { + // 初始化数组 + nums = Array(repeating: 0, count: capacity) + } + + /* 获取队列的容量 */ + func capacity() -> Int { + nums.count + } + + /* 获取队列的长度 */ + func size() -> Int { + let capacity = capacity() + // 由于将数组看作为环形，可能 rear < front ，因此需要取余数 + return (capacity + rear - front) % capacity + } + + /* 判断队列是否为空 */ + func isEmpty() -> Bool { + rear - front == 0 + } + + /* 入队 */ + func offer(num: Int) { + if size() == capacity() { + print("队列已满") + return + } + // 尾结点后添加 num + nums[rear] = num + // 尾指针向后移动一位，越过尾部后返回到数组头部 + rear = (rear + 1) % capacity() + } + + /* 出队 */ + @discardableResult + func poll() -> Int { + let num = peek() + // 队头指针向后移动一位，若越过尾部则返回到数组头部 + front = (front + 1) % capacity() + return num + } + + /* 访问队首元素 */ + func peek() -> Int { + if isEmpty() { + fatalError("队列为空") + } + return nums[front] + } + + /* 返回数组 */ + func toArray() -> [Int] { + let size = size() + let capacity = capacity() + // 仅转换有效长度范围内的列表元素 + var res = Array(repeating: 0, count: size) + for (i, j) in sequence(first: (0, front), next: { $0 < size - 1 ? ($0 + 1, $1 + 1) : nil }) { + res[i] = nums[j % capacity] + } + return res + } +} + +@main +enum _ArrayQueue { + /* Driver Code */ + static func main() { + /* 初始化队列 */ + let capacity = 10 + let queue = ArrayQueue(capacity: capacity) + + /* 元素入队 */ + queue.offer(num: 1) + queue.offer(num: 3) + queue.offer(num: 2) + queue.offer(num: 5) + queue.offer(num: 4) + print("队列 queue = \(queue.toArray())") + + /* 访问队首元素 */ + let peek = queue.peek() + print("队首元素 peek = \(peek)") + + /* 元素出队 */ + let poll = queue.poll() + print("出队元素 poll = \(poll)，出队后 queue = \(queue.toArray())") + + /* 获取队列的长度 */ + let size = queue.size() + print("队列长度 size = \(size)") + + /* 判断队列是否为空 */ + let isEmpty = queue.isEmpty() + print("队列是否为空 = \(isEmpty)") + + /* 测试环形数组 */ + for i in 0 ..< 10 { + queue.offer(num: i) + queue.poll() + print("第 \(i) 轮入队 + 出队后 queue = \(queue.toArray())") + } + } +} diff --git a/codes/swift/chapter_stack_and_queue/array_stack.swift b/codes/swift/chapter_stack_and_queue/array_stack.swift index faeeaa173..144ebec95 100644 --- a/codes/swift/chapter_stack_and_queue/array_stack.swift +++ b/codes/swift/chapter_stack_and_queue/array_stack.swift @@ -29,8 +29,9 @@ class ArrayStack { } /* 出栈 */ + @discardableResult func pop() -> Int { - if stack.isEmpty { + if isEmpty() { fatalError("栈为空") } return stack.removeLast() @@ -38,7 +39,7 @@ class ArrayStack { /* 访问栈顶元素 */ func peek() -> Int { - if stack.isEmpty { + if isEmpty() { fatalError("栈为空") } return stack.last! diff --git a/codes/swift/chapter_stack_and_queue/linkedlist_queue.swift b/codes/swift/chapter_stack_and_queue/linkedlist_queue.swift new file mode 100644 index 000000000..1d671742b --- /dev/null +++ b/codes/swift/chapter_stack_and_queue/linkedlist_queue.swift @@ -0,0 +1,105 @@ +/** + * File: linkedlist_queue.swift + * Created Time: 2023-01-11 + * Author: nuomi1 (nuomi1@qq.com) + */ + +import utils + +/* 基于链表实现的队列 */ +class LinkedListQueue { + private var front: ListNode? // 头结点 + private var rear: ListNode? // 尾结点 + private var _size = 0 + + init() {} + + /* 获取队列的长度 */ + func size() -> Int { + _size + } + + /* 判断队列是否为空 */ + func isEmpty() -> Bool { + size() == 0 + } + + /* 入队 */ + func offer(num: Int) { + // 尾结点后添加 num + let node = ListNode(x: num) + // 如果队列为空，则令头、尾结点都指向该结点 + if front == nil { + front = node + rear = node + } + // 如果队列不为空，则将该结点添加到尾结点后 + else { + rear?.next = node + rear = node + } + _size += 1 + } + + /* 出队 */ + @discardableResult + func poll() -> Int { + let num = peek() + // 删除头结点 + front = front?.next + _size -= 1 + return num + } + + /* 访问队首元素 */ + func peek() -> Int { + if isEmpty() { + fatalError("队列为空") + } + return front!.val + } + + /* 将链表转化为 Array 并返回 */ + func toArray() -> [Int] { + var node = front + var res = Array(repeating: 0, count: size()) + for i in res.indices { + res[i] = node!.val + node = node?.next + } + return res + } +} + +@main +enum _LinkedListQueue { + /* Driver Code */ + static func main() { + /* 初始化队列 */ + let queue = LinkedListQueue() + + /* 元素入队 */ + queue.offer(num: 1) + queue.offer(num: 3) + queue.offer(num: 2) + queue.offer(num: 5) + queue.offer(num: 4) + print("队列 queue = \(queue.toArray())") + + /* 访问队首元素 */ + let peek = queue.peek() + print("队首元素 peek = \(peek)") + + /* 元素出队 */ + let poll = queue.poll() + print("出队元素 poll = \(poll)，出队后 queue = \(queue.toArray())") + + /* 获取队列的长度 */ + let size = queue.size() + print("队列长度 size = \(size)") + + /* 判断队列是否为空 */ + let isEmpty = queue.isEmpty() + print("队列是否为空 = \(isEmpty)") + } +} diff --git a/codes/swift/chapter_stack_and_queue/linkedlist_stack.swift b/codes/swift/chapter_stack_and_queue/linkedlist_stack.swift index 9d3c98b01..97f7dabcc 100644 --- a/codes/swift/chapter_stack_and_queue/linkedlist_stack.swift +++ b/codes/swift/chapter_stack_and_queue/linkedlist_stack.swift @@ -20,7 +20,7 @@ class LinkedListStack { /* 判断栈是否为空 */ func isEmpty() -> Bool { - _size == 0 + size() == 0 } /* 入栈 */ @@ -32,6 +32,7 @@ class LinkedListStack { } /* 出栈 */ + @discardableResult func pop() -> Int { let num = peek() _peek = _peek?.next @@ -41,7 +42,7 @@ class LinkedListStack { /* 访问栈顶元素 */ func peek() -> Int { - if _size == 0 { + if isEmpty() { fatalError("栈为空") } return _peek!.val diff --git a/codes/swift/chapter_stack_and_queue/queue.swift b/codes/swift/chapter_stack_and_queue/queue.swift new file mode 100644 index 000000000..f13af36f5 --- /dev/null +++ b/codes/swift/chapter_stack_and_queue/queue.swift @@ -0,0 +1,39 @@ +/** + * File: queue.swift + * Created Time: 2023-01-11 + * Author: nuomi1 (nuomi1@qq.com) + */ + +@main +enum Queue { + /* Driver Code */ + static func main() { + /* 初始化队列 */ + // Swift 没有内置的队列类，可以把 Array 当作队列来使用 + var queue: [Int] = [] + + /* 元素入队 */ + queue.append(1) + queue.append(3) + queue.append(2) + queue.append(5) + queue.append(4) + print("队列 queue = \(queue)") + + /* 访问队首元素 */ + let peek = queue.first! + print("队首元素 peek = \(peek)") + + /* 元素出队 */ + let pool = queue.removeFirst() + print("出队元素 poll = \(pool)，出队后 queue = \(queue)") + + /* 获取队列的长度 */ + let size = queue.count + print("队列长度 size = \(size)") + + /* 判断队列是否为空 */ + let isEmpty = queue.isEmpty + print("队列是否为空 = \(isEmpty)") + } +} diff --git a/codes/zig/build.zig b/codes/zig/build.zig index 1a9fb0fba..a8738fae9 100644 --- a/codes/zig/build.zig +++ b/codes/zig/build.zig @@ -64,4 +64,127 @@ pub fn build(b: *std.build.Builder) void { if (b.args) |args| run_cmd_leetcode_two_sum.addArgs(args); const run_step_leetcode_two_sum = b.step("run_leetcode_two_sum", "Run leetcode_two_sum"); run_step_leetcode_two_sum.dependOn(&run_cmd_leetcode_two_sum.step); + + // Section: "Array" + // Source File: "chapter_array_and_linkedlist/array.zig" + // Run Command: zig build run_array + const exe_array = b.addExecutable("array", "chapter_array_and_linkedlist/array.zig"); + exe_array.addPackagePath("include", "include/include.zig"); + exe_array.setTarget(target); + exe_array.setBuildMode(mode); + exe_array.install(); + const run_cmd_array = exe_array.run(); + run_cmd_array.step.dependOn(b.getInstallStep()); + if (b.args) |args| run_cmd_array.addArgs(args); + const run_step_array = b.step("run_array", "Run array"); + run_step_array.dependOn(&run_cmd_array.step); + + // Section: "LinkedList" + // Source File: "chapter_array_and_linkedlist/linked_list.zig" + // Run Command: zig build run_linked_list + const exe_linked_list = b.addExecutable("linked_list", "chapter_array_and_linkedlist/linked_list.zig"); + exe_linked_list.addPackagePath("include", "include/include.zig"); + exe_linked_list.setTarget(target); + exe_linked_list.setBuildMode(mode); + exe_linked_list.install(); + const run_cmd_linked_list = exe_linked_list.run(); + run_cmd_linked_list.step.dependOn(b.getInstallStep()); + if (b.args) |args| run_cmd_linked_list.addArgs(args); + const run_step_linked_list = b.step("run_linked_list", "Run linked_list"); + run_step_linked_list.dependOn(&run_cmd_linked_list.step); + + // Section: "List" + // Source File: "chapter_array_and_linkedlist/list.zig" + // Run Command: zig build run_list + const exe_list = b.addExecutable("list", "chapter_array_and_linkedlist/list.zig"); + exe_list.addPackagePath("include", "include/include.zig"); + exe_list.setTarget(target); + exe_list.setBuildMode(mode); + exe_list.install(); + const run_cmd_list = exe_list.run(); + run_cmd_list.step.dependOn(b.getInstallStep()); + if (b.args) |args| run_cmd_list.addArgs(args); + const run_step_list = b.step("run_list", "Run list"); + run_step_list.dependOn(&run_cmd_list.step); + + // Source File: "chapter_array_and_linkedlist/my_list.zig" + // Run Command: zig build run_my_list + const exe_my_list = b.addExecutable("my_list", "chapter_array_and_linkedlist/my_list.zig"); + exe_my_list.addPackagePath("include", "include/include.zig"); + exe_my_list.setTarget(target); + exe_my_list.setBuildMode(mode); + exe_my_list.install(); + const run_cmd_my_list = exe_my_list.run(); + run_cmd_my_list.step.dependOn(b.getInstallStep()); + if (b.args) |args| run_cmd_my_list.addArgs(args); + const run_step_my_list = b.step("run_my_list", "Run my_list"); + run_step_my_list.dependOn(&run_cmd_my_list.step); + + // Section: "Stack" + // Source File: "chapter_stack_and_queue/stack.zig" + // Run Command: zig build run_stack + const exe_stack = b.addExecutable("stack", "chapter_stack_and_queue/stack.zig"); + exe_stack.addPackagePath("include", "include/include.zig"); + exe_stack.setTarget(target); + exe_stack.setBuildMode(mode); + exe_stack.install(); + const run_cmd_stack = exe_stack.run(); + run_cmd_stack.step.dependOn(b.getInstallStep()); + if (b.args) |args| run_cmd_stack.addArgs(args); + const run_step_stack = b.step("run_stack", "Run stack"); + run_step_stack.dependOn(&run_cmd_stack.step); + + // Source File: "chapter_stack_and_queue/linkedlist_stack.zig" + // Run Command: zig build run_linkedlist_stack + const exe_linkedlist_stack = b.addExecutable("linkedlist_stack", "chapter_stack_and_queue/linkedlist_stack.zig"); + exe_linkedlist_stack.addPackagePath("include", "include/include.zig"); + exe_linkedlist_stack.setTarget(target); + exe_linkedlist_stack.setBuildMode(mode); + exe_linkedlist_stack.install(); + const run_cmd_linkedlist_stack = exe_linkedlist_stack.run(); + run_cmd_linkedlist_stack.step.dependOn(b.getInstallStep()); + if (b.args) |args| run_cmd_linkedlist_stack.addArgs(args); + const run_step_linkedlist_stack = b.step("run_linkedlist_stack", "Run linkedlist_stack"); + run_step_linkedlist_stack.dependOn(&run_cmd_linkedlist_stack.step); + + // Source File: "chapter_stack_and_queue/array_stack.zig" + // Run Command: zig build run_array_stack + const exe_array_stack = b.addExecutable("array_stack", "chapter_stack_and_queue/array_stack.zig"); + exe_array_stack.addPackagePath("include", "include/include.zig"); + exe_array_stack.setTarget(target); + exe_array_stack.setBuildMode(mode); + exe_array_stack.install(); + const run_cmd_array_stack = exe_linkedlist_stack.run(); + run_cmd_array_stack.step.dependOn(b.getInstallStep()); + if (b.args) |args| run_cmd_array_stack.addArgs(args); + const run_step_array_stack = b.step("run_array_stack", "Run array_stack"); + run_step_array_stack.dependOn(&run_cmd_array_stack.step); + + // Section: "Bubble Sort" + // Source File: "chapter_sorting/bubble_sort.zig" + // Run Command: zig build run_bubble_sort + const exe_bubble_sort = b.addExecutable("bubble_sort", "chapter_sorting/bubble_sort.zig"); + exe_bubble_sort.addPackagePath("include", "include/include.zig"); + exe_bubble_sort.setTarget(target); + exe_bubble_sort.setBuildMode(mode); + exe_bubble_sort.install(); + const run_cmd_bubble_sort = exe_bubble_sort.run(); + run_cmd_bubble_sort.step.dependOn(b.getInstallStep()); + if (b.args) |args| run_cmd_bubble_sort.addArgs(args); + const run_step_bubble_sort = b.step("run_bubble_sort", "Run bubble_sort"); + run_step_bubble_sort.dependOn(&run_cmd_bubble_sort.step); + + // Section: "Insertion Sort" + // Source File: "chapter_sorting/insertion_sort.zig" + // Run Command: zig build run_insertion_sort + const exe_insertion_sort = b.addExecutable("insertion_sort", "chapter_sorting/insertion_sort.zig"); + exe_insertion_sort.addPackagePath("include", "include/include.zig"); + exe_insertion_sort.setTarget(target); + exe_insertion_sort.setBuildMode(mode); + exe_insertion_sort.install(); + const run_cmd_insertion_sort = exe_insertion_sort.run(); + run_cmd_insertion_sort.step.dependOn(b.getInstallStep()); + if (b.args) |args| run_cmd_insertion_sort.addArgs(args); + const run_step_insertion_sort = b.step("run_insertion_sort", "Run insertion_sort"); + run_step_insertion_sort.dependOn(&run_cmd_insertion_sort.step); } diff --git a/codes/zig/chapter_array_and_linkedlist/array.zig b/codes/zig/chapter_array_and_linkedlist/array.zig new file mode 100644 index 000000000..8c830cf4d --- /dev/null +++ b/codes/zig/chapter_array_and_linkedlist/array.zig @@ -0,0 +1,117 @@ +// File: array.zig +// Created Time: 2023-01-07 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); +const inc = @import("include"); + +// 随机返回一个数组元素 +pub fn randomAccess(nums: []i32) i32 { + // 在区间 [0, nums.len) 中随机抽取一个整数 + var randomIndex = std.crypto.random.intRangeLessThan(usize, 0, nums.len); + // 获取并返回随机元素 + var randomNum = nums[randomIndex]; + return randomNum; +} + +// 扩展数组长度 +pub fn extend(mem_allocator: std.mem.Allocator, nums: []i32, enlarge: usize) ![]i32 { + // 初始化一个扩展长度后的数组 + var res = try mem_allocator.alloc(i32, nums.len + enlarge); + std.mem.set(i32, res, 0); + // 将原数组中的所有元素复制到新数组 + std.mem.copy(i32, res, nums); + // 返回扩展后的新数组 + return res; +} + +// 在数组的索引 index 处插入元素 num +pub fn insert(nums: []i32, num: i32, index: usize) void { + // 把索引 index 以及之后的所有元素向后移动一位 + var i = nums.len - 1; + while (i > index) : (i -= 1) { + nums[i] = nums[i - 1]; + } + // 将 num 赋给 index 处元素 + nums[index] = num; +} + +// 删除索引 index 处元素 +pub fn remove(nums: []i32, index: usize) void { + // 把索引 index 之后的所有元素向前移动一位 + var i = index; + while (i < nums.len - 1) : (i += 1) { + nums[i] = nums[i + 1]; + } +} + +// 遍历数组 +pub fn traverse(nums: []i32) void { + var count: i32 = 0; + // 通过索引遍历数组 + var i: i32 = 0; + while (i < nums.len) : (i += 1) { + count += 1; + } + count = 0; + // 直接遍历数组 + for (nums) |_| { + count += 1; + } +} + +// 在数组中查找指定元素 +pub fn find(nums: []i32, target: i32) i32 { + for (nums) |num, i| { + if (num == target) return @intCast(i32, i); + } + return -1; +} + +// Driver Code +pub fn main() !void { + // 初始化数组 + const size: i32 = 5; + var arr = [_]i32{0} ** size; + std.debug.print("数组 arr = ", .{}); + inc.PrintUtil.printArray(i32, &arr); + + var array = [_]i32{ 1, 3, 2, 5, 4 }; + std.debug.print("\n数组 nums = ", .{}); + inc.PrintUtil.printArray(i32, &array); + + // 随机访问 + var randomNum = randomAccess(&array); + std.debug.print("\n在 nums 中获取随机元素 {}", .{randomNum}); + + // 长度扩展 + var known_at_runtime_zero: usize = 0; + var nums: []i32 = array[known_at_runtime_zero..array.len]; + var mem_arena = std.heap.ArenaAllocator.init(std.heap.page_allocator); + defer mem_arena.deinit(); + const mem_allocator = mem_arena.allocator(); + nums = try extend(mem_allocator, nums, 3); + std.debug.print("\n将数组长度扩展至 8 ，得到 nums = ", .{}); + inc.PrintUtil.printArray(i32, nums); + + // 插入元素 + insert(nums, 6, 3); + std.debug.print("\n在索引 3 处插入数字 6 ，得到 nums = ", .{}); + inc.PrintUtil.printArray(i32, nums); + + // 删除元素 + remove(nums, 2); + std.debug.print("\n删除索引 2 处的元素，得到 nums = ", .{}); + inc.PrintUtil.printArray(i32, nums); + + // 遍历数组 + traverse(nums); + + // 查找元素 + var index = find(nums, 3); + std.debug.print("\n在 nums 中查找元素 3 ，得到索引 = {}\n", .{index}); + + const getchar = try std.io.getStdIn().reader().readByte(); + _ = getchar; +} + diff --git a/codes/zig/chapter_array_and_linkedlist/linked_list.zig b/codes/zig/chapter_array_and_linkedlist/linked_list.zig new file mode 100644 index 000000000..fbaa3f8d7 --- /dev/null +++ b/codes/zig/chapter_array_and_linkedlist/linked_list.zig @@ -0,0 +1,85 @@ +// File: linked_list.zig +// Created Time: 2023-01-07 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); +const inc = @import("include"); + +// 在链表的结点 n0 之后插入结点 P +pub fn insert(n0: ?*inc.ListNode(i32), P: ?*inc.ListNode(i32)) void { + var n1 = n0.?.next; + n0.?.next = P; + P.?.next = n1; +} + +// 删除链表的结点 n0 之后的首个结点 +pub fn remove(n0: ?*inc.ListNode(i32)) void { + if (n0.?.next == null) return; + // n0 -> P -> n1 + var P = n0.?.next; + var n1 = P.?.next; + n0.?.next = n1; +} + +// 访问链表中索引为 index 的结点 +pub fn access(node: ?*inc.ListNode(i32), index: i32) ?*inc.ListNode(i32) { + var head = node; + var i: i32 = 0; + while (i < index) : (i += 1) { + head = head.?.next; + if (head == null) return null; + } + return head; +} + +// 在链表中查找值为 target 的首个结点 +pub fn find(node: ?*inc.ListNode(i32), target: i32) i32 { + var head = node; + var index: i32 = 0; + while (head != null) { + if (head.?.val == target) return index; + head = head.?.next; + index += 1; + } + return -1; +} + +// Driver Code +pub fn main() !void { + // 初始化链表 + // 初始化各个结点 + var n0 = inc.ListNode(i32){.val = 1}; + var n1 = inc.ListNode(i32){.val = 3}; + var n2 = inc.ListNode(i32){.val = 2}; + var n3 = inc.ListNode(i32){.val = 5}; + var n4 = inc.ListNode(i32){.val = 4}; + // 构建引用指向 + n0.next = &n1; + n1.next = &n2; + n2.next = &n3; + n3.next = &n4; + std.debug.print("初始化的链表为", .{}); + try inc.PrintUtil.printLinkedList(i32, &n0); + + // 插入结点 + var tmp = inc.ListNode(i32){.val = 0}; + insert(&n0, &tmp); + std.debug.print("插入结点后的链表为", .{}); + try inc.PrintUtil.printLinkedList(i32, &n0); + + // 删除结点 + remove(&n0); + std.debug.print("删除结点后的链表为", .{}); + try inc.PrintUtil.printLinkedList(i32, &n0); + + // 访问结点 + var node = access(&n0, 3); + std.debug.print("链表中索引 3 处的结点的值 = {}\n", .{node.?.val}); + + // 查找结点 + var index = find(&n0, 2); + std.debug.print("链表中值为 2 的结点的索引 = {}\n", .{index}); + + const getchar = try std.io.getStdIn().reader().readByte(); + _ = getchar; +} \ No newline at end of file diff --git a/codes/zig/chapter_array_and_linkedlist/list.zig b/codes/zig/chapter_array_and_linkedlist/list.zig new file mode 100644 index 000000000..608bce96c --- /dev/null +++ b/codes/zig/chapter_array_and_linkedlist/list.zig @@ -0,0 +1,81 @@ +// File: list.zig +// Created Time: 2023-01-07 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); +const inc = @import("include"); + +// Driver Code +pub fn main() !void { + // 初始化列表 + var list = std.ArrayList(i32).init(std.heap.page_allocator); + // 延迟释放内存 + defer list.deinit(); + try list.appendSlice(&[_]i32{ 1, 3, 2, 5, 4 }); + std.debug.print("列表 list = ", .{}); + inc.PrintUtil.printList(i32, list); + + // 访问元素 + var num = list.items[1]; + std.debug.print("\n访问索引 1 处的元素，得到 num = {}", .{num}); + + // 更新元素 + list.items[1] = 0; + std.debug.print("\n将索引 1 处的元素更新为 0 ，得到 list = ", .{}); + inc.PrintUtil.printList(i32, list); + + // 清空列表 + list.clearRetainingCapacity(); + std.debug.print("\n清空列表后 list = ", .{}); + inc.PrintUtil.printList(i32, list); + + // 尾部添加元素 + try list.append(1); + try list.append(3); + try list.append(2); + try list.append(5); + try list.append(4); + std.debug.print("\n添加元素后 list = ", .{}); + inc.PrintUtil.printList(i32, list); + + // 中间插入元素 + try list.insert(3, 6); + std.debug.print("\n在索引 3 处插入数字 6 ，得到 list = ", .{}); + inc.PrintUtil.printList(i32, list); + + // 删除元素 + var value = list.orderedRemove(3); + _ = value; + std.debug.print("\n删除索引 3 处的元素，得到 list = ", .{}); + inc.PrintUtil.printList(i32, list); + + // 通过索引遍历列表 + var count: i32 = 0; + var i: i32 = 0; + while (i < list.items.len) : (i += 1) { + count += 1; + } + + // 直接遍历列表元素 + count = 0; + for (list.items) |_| { + count += 1; + } + + // 拼接两个列表 + var list1 = std.ArrayList(i32).init(std.heap.page_allocator); + defer list1.deinit(); + try list1.appendSlice(&[_]i32{ 6, 8, 7, 10, 9 }); + try list.insertSlice(list.items.len, list1.items); + std.debug.print("\n将列表 list1 拼接到 list 之后，得到 list = ", .{}); + inc.PrintUtil.printList(i32, list); + + // 排序列表 + std.sort.sort(i32, list.items, {}, comptime std.sort.asc(i32)); + std.debug.print("\n排序列表后 list = ", .{}); + inc.PrintUtil.printList(i32, list); + + const getchar = try std.io.getStdIn().reader().readByte(); + _ = getchar; +} + diff --git a/codes/zig/chapter_array_and_linkedlist/my_list.zig b/codes/zig/chapter_array_and_linkedlist/my_list.zig new file mode 100644 index 000000000..f018e61ca --- /dev/null +++ b/codes/zig/chapter_array_and_linkedlist/my_list.zig @@ -0,0 +1,177 @@ +// File: my_list.zig +// Created Time: 2023-01-08 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); +const inc = @import("include"); + +// 列表类简易实现 +// 编译期泛型 +pub fn MyList(comptime T: type) type { + return struct { + const Self = @This(); + + nums: []T = undefined, // 数组（存储列表元素） + numsCapacity: usize = 10, // 列表容量 + numSize: usize = 0, // 列表长度（即当前元素数量） + extendRatio: usize = 2, // 每次列表扩容的倍数 + mem_arena: ?std.heap.ArenaAllocator = null, + mem_allocator: std.mem.Allocator = undefined, // 内存分配器 + + // 构造函数（分配内存+初始化列表） + pub fn init(self: *Self, allocator: std.mem.Allocator) !void { + if (self.mem_arena == null) { + self.mem_arena = std.heap.ArenaAllocator.init(allocator); + self.mem_allocator = self.mem_arena.?.allocator(); + } + self.nums = try self.mem_allocator.alloc(T, self.numsCapacity); + std.mem.set(T, self.nums, @as(T, 0)); + } + + // 析构函数（释放内存） + pub fn deinit(self: *Self) void { + if (self.mem_arena == null) return; + self.mem_arena.?.deinit(); + } + + // 获取列表长度（即当前元素数量） + pub fn size(self: *Self) usize { + return self.numSize; + } + + // 获取列表容量 + pub fn capacity(self: *Self) usize { + return self.numsCapacity; + } + + // 访问元素 + pub fn get(self: *Self, index: usize) T { + // 索引如果越界则抛出异常，下同 + if (index >= self.size()) @panic("索引越界"); + return self.nums[index]; + } + + // 更新元素 + pub fn set(self: *Self, index: usize, num: T) void { + // 索引如果越界则抛出异常，下同 + if (index >= self.size()) @panic("索引越界"); + self.nums[index] = num; + } + + // 尾部添加元素 + pub fn add(self: *Self, num: T) !void { + // 元素数量超出容量时，触发扩容机制 + if (self.size() == self.capacity()) try self.extendCapacity(); + self.nums[self.size()] = num; + // 更新元素数量 + self.numSize += 1; + } + + // 中间插入元素 + pub fn insert(self: *Self, index: usize, num: T) !void { + if (index >= self.size()) @panic("索引越界"); + // 元素数量超出容量时，触发扩容机制 + if (self.size() == self.capacity()) try self.extendCapacity(); + // 索引 i 以及之后的元素都向后移动一位 + var j = self.size() - 1; + while (j >= index) : (j -= 1) { + self.nums[j + 1] = self.nums[j]; + } + self.nums[index] = num; + // 更新元素数量 + self.numSize += 1; + } + + // 删除元素 + pub fn remove(self: *Self, index: usize) T { + if (index >= self.size()) @panic("索引越界"); + var num = self.nums[index]; + // 索引 i 之后的元素都向前移动一位 + var j = index; + while (j < self.size() - 1) : (j += 1) { + self.nums[j] = self.nums[j + 1]; + } + // 更新元素数量 + self.numSize -= 1; + // 返回被删除元素 + return num; + } + + // 列表扩容 + pub fn extendCapacity(self: *Self) !void { + // 新建一个长度为 size * extendRatio 的数组，并将原数组拷贝到新数组 + var newCapacity = self.capacity() * self.extendRatio; + var extend = try self.mem_allocator.alloc(T, newCapacity); + std.mem.set(T, extend, @as(T, 0)); + // 将原数组中的所有元素复制到新数组 + std.mem.copy(T, extend, self.nums); + self.nums = extend; + // 更新列表容量 + self.numsCapacity = newCapacity; + } + + // 将列表转换为数组 + pub fn toArray(self: *Self) ![]T { + // 仅转换有效长度范围内的列表元素 + var nums = try self.mem_allocator.alloc(T, self.size()); + std.mem.set(T, nums, @as(T, 0)); + for (nums) |*num, i| { + num.* = self.get(i); + } + return nums; + } + }; +} + +// Driver Code +pub fn main() !void { + // 初始化列表 + var list = MyList(i32){}; + try list.init(std.heap.page_allocator); + // 延迟释放内存 + defer list.deinit(); + + // 尾部添加元素 + try list.add(1); + try list.add(3); + try list.add(2); + try list.add(5); + try list.add(4); + std.debug.print("列表 list = ", .{}); + inc.PrintUtil.printArray(i32, try list.toArray()); + std.debug.print(" ，容量 = {} ，长度 = {}", .{list.capacity(), list.size()}); + + // 中间插入元素 + try list.insert(3, 6); + std.debug.print("\n在索引 3 处插入数字 6 ，得到 list = ", .{}); + inc.PrintUtil.printArray(i32, try list.toArray()); + + // 删除元素 + _ = list.remove(3); + std.debug.print("\n删除索引 3 处的元素，得到 list = ", .{}); + inc.PrintUtil.printArray(i32, try list.toArray()); + + // 访问元素 + var num = list.get(1); + std.debug.print("\n访问索引 1 处的元素，得到 num = {}", .{num}); + + // 更新元素 + list.set(1, 0); + std.debug.print("\n将索引 1 处的元素更新为 0 ，得到 list = ", .{}); + inc.PrintUtil.printArray(i32, try list.toArray()); + + // 测试扩容机制 + list.set(1, 0); + var i: i32 = 0; + while (i < 10) : (i += 1) { + // 在 i = 5 时，列表长度将超出列表容量，此时触发扩容机制 + try list.add(i); + } + std.debug.print("\n扩容后的列表 list = ", .{}); + inc.PrintUtil.printArray(i32, try list.toArray()); + std.debug.print(" ，容量 = {} ，长度 = {}\n", .{list.capacity(), list.size()}); + + const getchar = try std.io.getStdIn().reader().readByte(); + _ = getchar; +} + diff --git a/codes/zig/chapter_sorting/bubble_sort.zig b/codes/zig/chapter_sorting/bubble_sort.zig new file mode 100644 index 000000000..863190963 --- /dev/null +++ b/codes/zig/chapter_sorting/bubble_sort.zig @@ -0,0 +1,62 @@ +// File: time_complexity.zig +// Created Time: 2023-01-08 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); +const inc = @import("include"); + +// 冒泡排序 +fn bubbleSort(nums: []i32) void { + // 外循环：待排序元素数量为 n-1, n-2, ..., 1 + var i: usize = nums.len - 1; + while (i > 0) : (i -= 1) { + var j: usize = 0; + // 内循环：冒泡操作 + while (j < i) : (j += 1) { + if (nums[j] > nums[j + 1]) { + // 交换 nums[j] 与 nums[j + 1] + var tmp = nums[j]; + nums[j] = nums[j + 1]; + nums[j + 1] = tmp; + } + } + } +} + +// 冒泡排序（标志优化） +fn bubbleSortWithFlag(nums: []i32) void { + // 外循环：待排序元素数量为 n-1, n-2, ..., 1 + var i: usize = nums.len - 1; + while (i > 0) : (i -= 1) { + var flag = false; // 初始化标志位 + var j: usize = 0; + // 内循环：冒泡操作 + while (j < i) : (j += 1) { + if (nums[j] > nums[j + 1]) { + // 交换 nums[j] 与 nums[j + 1] + var tmp = nums[j]; + nums[j] = nums[j + 1]; + nums[j + 1] = tmp; + flag = true; + } + } + if (!flag) break; // 此轮冒泡未交换任何元素，直接跳出 + } +} + +// Driver Code +pub fn main() !void { + var nums = [_]i32{ 4, 1, 3, 1, 5, 2 }; + bubbleSort(&nums); + std.debug.print("冒泡排序完成后 nums = ", .{}); + inc.PrintUtil.printArray(i32, &nums); + + var nums1 = [_]i32{ 4, 1, 3, 1, 5, 2 }; + bubbleSortWithFlag(&nums1); + std.debug.print("\n冒泡排序完成后 nums1 = ", .{}); + inc.PrintUtil.printArray(i32, &nums1); + + const getchar = try std.io.getStdIn().reader().readByte(); + _ = getchar; +} + diff --git a/codes/zig/chapter_sorting/insertion_sort.zig b/codes/zig/chapter_sorting/insertion_sort.zig new file mode 100644 index 000000000..3c7594c24 --- /dev/null +++ b/codes/zig/chapter_sorting/insertion_sort.zig @@ -0,0 +1,33 @@ +// File: time_complexity.zig +// Created Time: 2023-01-08 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); +const inc = @import("include"); + +// 插入排序 +fn insertionSort(nums: []i32) void { + // 外循环：base = nums[1], nums[2], ..., nums[n-1] + var i: usize = 1; + while (i < nums.len) : (i += 1) { + var base = nums[i]; + var j: usize = i; + // 内循环：将 base 插入到左边的正确位置 + while (j >= 1 and nums[j - 1] > base) : (j -= 1) { + nums[j] = nums[j - 1]; // 1. 将 nums[j] 向右移动一位 + } + nums[j] = base; // 2. 将 base 赋值到正确位置 + } +} + +// Driver Code +pub fn main() !void { + var nums = [_]i32{ 4, 1, 3, 1, 5, 2 }; + insertionSort(&nums); + std.debug.print("插入排序完成后 nums = ", .{}); + inc.PrintUtil.printArray(i32, &nums); + + const getchar = try std.io.getStdIn().reader().readByte(); + _ = getchar; +} + diff --git a/codes/zig/chapter_stack_and_queue/array_stack.zig b/codes/zig/chapter_stack_and_queue/array_stack.zig new file mode 100644 index 000000000..868d9d94d --- /dev/null +++ b/codes/zig/chapter_stack_and_queue/array_stack.zig @@ -0,0 +1,99 @@ +// File: stack.zig +// Created Time: 2023-01-08 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); +const inc = @import("include"); + +// 基于数组实现的栈 +// 编译期泛型 +pub fn ArrayStack(comptime T: type) type { + return struct { + const Self = @This(); + + stack: ?std.ArrayList(T) = null, + + // 构造函数（分配内存+初始化栈） + pub fn init(self: *Self, allocator: std.mem.Allocator) void { + if (self.stack == null) { + self.stack = std.ArrayList(T).init(allocator); + } + } + + // 析构函数（释放内存） + pub fn deinit(self: *Self) void { + if (self.stack == null) return; + self.stack.?.deinit(); + } + + // 获取栈的长度 + pub fn size(self: *Self) usize { + return self.stack.?.items.len; + } + + // 判断栈是否为空 + pub fn empty(self: *Self) bool { + return self.size() == 0; + } + + // 访问栈顶元素 + pub fn top(self: *Self) T { + if (self.size() == 0) @panic("栈为空"); + return self.stack.?.items[self.size() - 1]; + } + + // 入栈 + pub fn push(self: *Self, num: T) !void { + try self.stack.?.append(num); + } + + // 出栈 + pub fn pop(self: *Self) T { + var num = self.stack.?.pop(); + return num; + } + + // 返回 ArrayList + pub fn toList(self: *Self) std.ArrayList(T) { + return self.stack.?; + } + }; +} + +// Driver Code +pub fn main() !void { + // 初始化栈 + var stack = ArrayStack(i32){}; + stack.init(std.heap.page_allocator); + // 延迟释放内存 + defer stack.deinit(); + + // 元素入栈 + try stack.push(1); + try stack.push(3); + try stack.push(2); + try stack.push(5); + try stack.push(4); + std.debug.print("栈 stack = ", .{}); + inc.PrintUtil.printList(i32, stack.toList()); + + // 访问栈顶元素 + var top = stack.top(); + std.debug.print("\n栈顶元素 top = {}", .{top}); + + // 元素出栈 + top = stack.pop(); + std.debug.print("\n出栈元素 pop = {}，出栈后 stack = ", .{top}); + inc.PrintUtil.printList(i32, stack.toList()); + + // 获取栈的长度 + var size = stack.size(); + std.debug.print("\n栈的长度 size = {}", .{size}); + + // 判断栈是否为空 + var empty = stack.empty(); + std.debug.print("\n栈是否为空 = {}", .{empty}); + + const getchar = try std.io.getStdIn().reader().readByte(); + _ = getchar; +} diff --git a/codes/zig/chapter_stack_and_queue/linkedlist_stack.zig b/codes/zig/chapter_stack_and_queue/linkedlist_stack.zig new file mode 100644 index 000000000..633583b45 --- /dev/null +++ b/codes/zig/chapter_stack_and_queue/linkedlist_stack.zig @@ -0,0 +1,120 @@ +// File: linkedlist_stack.zig +// Created Time: 2023-01-08 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); +const inc = @import("include"); + +// 基于链表实现的栈 +// 编译期泛型 +pub fn LinkedListStack(comptime T: type) type { + return struct { + const Self = @This(); + + stackTop: ?*inc.ListNode(T) = null, // 将头结点作为栈顶 + stkSize: usize = 0, // 栈的长度 + mem_arena: ?std.heap.ArenaAllocator = null, + mem_allocator: std.mem.Allocator = undefined, // 内存分配器 + + // 构造函数（分配内存+初始化栈） + pub fn init(self: *Self, allocator: std.mem.Allocator) !void { + if (self.mem_arena == null) { + self.mem_arena = std.heap.ArenaAllocator.init(allocator); + self.mem_allocator = self.mem_arena.?.allocator(); + } + self.stackTop = null; + self.stkSize = 0; + } + + // 析构函数（释放内存） + pub fn deinit(self: *Self) void { + if (self.mem_arena == null) return; + self.mem_arena.?.deinit(); + } + + // 获取栈的长度 + pub fn size(self: *Self) usize { + return self.stkSize; + } + + // 判断栈是否为空 + pub fn empty(self: *Self) bool { + return self.size() == 0; + } + + // 访问栈顶元素 + pub fn top(self: *Self) T { + if (self.size() == 0) @panic("栈为空"); + return self.stackTop.?.val; + } + + // 入栈 + pub fn push(self: *Self, num: T) !void { + var node = try self.mem_allocator.create(inc.ListNode(T)); + node.init(num); + node.next = self.stackTop; + self.stackTop = node; + self.stkSize += 1; + } + + // 出栈 + pub fn pop(self: *Self) T { + var num = self.top(); + self.stackTop = self.stackTop.?.next; + self.stkSize -= 1; + return num; + } + + // 将栈转换为数组 + pub fn toArray(self: *Self) ![]T { + var node = self.stackTop; + var res = try self.mem_allocator.alloc(T, self.size()); + std.mem.set(T, res, @as(T, 0)); + var i: usize = 0; + while (i < res.len) : (i += 1) { + res[res.len - i - 1] = node.?.val; + node = node.?.next; + } + return res; + } + }; +} + +// Driver Code +pub fn main() !void { + // 初始化栈 + var stack = LinkedListStack(i32){}; + try stack.init(std.heap.page_allocator); + // 延迟释放内存 + defer stack.deinit(); + + // 元素入栈 + try stack.push(1); + try stack.push(3); + try stack.push(2); + try stack.push(5); + try stack.push(4); + std.debug.print("栈 stack = ", .{}); + inc.PrintUtil.printArray(i32, try stack.toArray()); + + // 访问栈顶元素 + var top = stack.top(); + std.debug.print("\n栈顶元素 top = {}", .{top}); + + // 元素出栈 + top = stack.pop(); + std.debug.print("\n出栈元素 pop = {}，出栈后 stack = ", .{top}); + inc.PrintUtil.printArray(i32, try stack.toArray()); + + // 获取栈的长度 + var size = stack.size(); + std.debug.print("\n栈的长度 size = {}", .{size}); + + // 判断栈是否为空 + var empty = stack.empty(); + std.debug.print("\n栈是否为空 = {}", .{empty}); + + const getchar = try std.io.getStdIn().reader().readByte(); + _ = getchar; +} + diff --git a/codes/zig/chapter_stack_and_queue/stack.zig b/codes/zig/chapter_stack_and_queue/stack.zig new file mode 100644 index 000000000..95ed427b0 --- /dev/null +++ b/codes/zig/chapter_stack_and_queue/stack.zig @@ -0,0 +1,44 @@ +// File: stack.zig +// Created Time: 2023-01-08 +// Author: sjinzh (sjinzh@gmail.com) + +const std = @import("std"); +const inc = @import("include"); + +// Driver Code +pub fn main() !void { + // 初始化栈 + // 在 zig 中，推荐将 ArrayList 当作栈来使用 + var stack = std.ArrayList(i32).init(std.heap.page_allocator); + // 延迟释放内存 + defer stack.deinit(); + + // 元素入栈 + try stack.append(1); + try stack.append(3); + try stack.append(2); + try stack.append(5); + try stack.append(4); + std.debug.print("栈 stack = ", .{}); + inc.PrintUtil.printList(i32, stack); + + // 访问栈顶元素 + var top = stack.items[stack.items.len - 1]; + std.debug.print("\n栈顶元素 top = {}", .{top}); + + // 元素出栈 + top = stack.pop(); + std.debug.print("\n出栈元素 pop = {}，出栈后 stack = ", .{top}); + inc.PrintUtil.printList(i32, stack); + + // 获取栈的长度 + var size = stack.items.len; + std.debug.print("\n栈的长度 size = {}", .{size}); + + // 判断栈是否为空 + var empty = if (stack.items.len == 0) true else false; + std.debug.print("\n栈是否为空 = {}", .{empty}); + + const getchar = try std.io.getStdIn().reader().readByte(); + _ = getchar; +} diff --git a/codes/zig/include/PrintUtil.zig b/codes/zig/include/PrintUtil.zig index 9e6b18b05..4d2d20893 100644 --- a/codes/zig/include/PrintUtil.zig +++ b/codes/zig/include/PrintUtil.zig @@ -7,16 +7,42 @@ const ListNode = @import("ListNode.zig").ListNode; const TreeNode = @import("TreeNode.zig").TreeNode; // Print an array -// 编译期泛型 pub fn printArray(comptime T: type, nums: []T) void { std.debug.print("[", .{}); if (nums.len > 0) { for (nums) |num, j| { - std.debug.print("{}{s}", .{num, if (j == nums.len-1) "]\n" else ", " }); + std.debug.print("{}{s}", .{num, if (j == nums.len-1) "]" else ", " }); } } else { std.debug.print("]", .{}); - std.debug.print("\n", .{}); + } +} + +// Print a list +pub fn printList(comptime T: type, list: std.ArrayList(T)) void { + std.debug.print("[", .{}); + if (list.items.len > 0) { + for (list.items) |value, i| { + std.debug.print("{}{s}", .{value, if (i == list.items.len-1) "]" else ", " }); + } + } else { + std.debug.print("]", .{}); + } + +} + +// Print a linked list +pub fn printLinkedList(comptime T: type, node: ?*ListNode(T)) !void { + if (node == null) return; + var list = std.ArrayList(i32).init(std.heap.page_allocator); + defer list.deinit(); + var head = node; + while (head != null) { + try list.append(head.?.val); + head = head.?.next; + } + for (list.items) |value, i| { + std.debug.print("{}{s}", .{value, if (i == list.items.len-1) "\n" else "->" }); } } diff --git a/deploy.sh b/deploy.sh index 96a633cba..975d7b2f9 100644 --- a/deploy.sh +++ b/deploy.sh @@ -3,6 +3,6 @@ mkdocs build --clean cd site git init git add -A -git commit -m 'deploy' +git commit -m "deploy" git push -f git@github.com:krahets/hello-algo.git master:gh-pages cd - diff --git a/docker-compose.yml b/docker-compose.yml new file mode 100644 index 000000000..6a472b173 --- /dev/null +++ b/docker-compose.yml @@ -0,0 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000000000..15d22e787 --- /dev/null +++ b/docs/chapter_heap/heap.md @@ -0,0 +1,798 @@ +--- +comments: true +--- + +# 堆 + +「堆 Heap」是一颗限定条件下的「完全二叉树」。根据成立条件，堆主要分为两种类型： + +- 「大顶堆 Max Heap」，任意结点的值 $\geq$ 其子结点的值； +- 「小顶堆 Min Heap」，任意结点的值 $\leq$ 其子结点的值； + +![min_heap_and_max_heap](heap.assets/min_heap_and_max_heap.png) + +## 堆术语与性质 + +- 由于堆是完全二叉树，因此最底层结点靠左填充，其它层结点皆被填满。 +- 二叉树中的根结点对应「堆顶」，底层最靠右结点对应「堆底」。 +- 对于大顶堆 / 小顶堆，其堆顶元素（即根结点）的值最大 / 最小。 + +## 堆常用操作 + +值得说明的是，多数编程语言提供的是「优先队列 Priority Queue」，其是一种抽象数据结构，**定义为具有出队优先级的队列**。 + +而恰好，**堆的定义与优先队列的操作逻辑完全吻合**，大顶堆就是一个元素从大到小出队的优先队列。从使用角度看，我们可以将「优先队列」和「堆」理解为等价的数据结构。因此，本文与代码对两者不做特别区分，统一使用「堆」来命名。 + +堆的常用操作见下表（方法命名以 Java 为例）。 + +

Table. 堆的常用操作

+ +
+ +| 方法 | 描述 | 时间复杂度 | +| --------- | -------------------------------------------- | ----------- | +| add() | 元素入堆 | $O(\log n)$ | +| poll() | 堆顶元素出堆 | $O(\log n)$ | +| peek() | 访问堆顶元素（大 / 小顶堆分别为最大 / 小值） | $O(1)$ | +| size() | 获取堆的元素数量 | $O(1)$ | +| isEmpty() | 判断堆是否为空 | $O(1)$ | + +
+ +我们可以直接使用编程语言提供的堆类（或优先队列类）。 + +!!! tip + + 类似于排序中“从小到大排列”和“从大到小排列”，“大顶堆”和“小顶堆”可仅通过修改 Comparator 来互相转换。 + +=== "Java" + + ```java title="heap.java" + /* 初始化堆 */ + // 初始化小顶堆 + Queue minHeap = new PriorityQueue<>(); + // 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可） + Queue maxHeap = new PriorityQueue<>((a, b) -> { return b - a; }); + + /* 元素入堆 */ + maxHeap.add(1); + maxHeap.add(3); + maxHeap.add(2); + maxHeap.add(5); + maxHeap.add(4); + + /* 获取堆顶元素 */ + int peek = maxHeap.peek(); // 5 + + /* 堆顶元素出堆 */ + // 出堆元素会形成一个从大到小的序列 + peek = heap.poll(); // 5 + peek = heap.poll(); // 4 + peek = heap.poll(); // 3 + peek = heap.poll(); // 2 + peek = heap.poll(); // 1 + + /* 获取堆大小 */ + int size = maxHeap.size(); + + /* 判断堆是否为空 */ + boolean isEmpty = maxHeap.isEmpty(); + + /* 输入列表并建堆 */ + minHeap = new PriorityQueue<>(Arrays.asList(1, 3, 2, 5, 4)); + ``` + +=== "C++" + + ```cpp title="heap.cpp" + + ``` + +=== "Python" + + ```python title="heap.py" + + ``` + +=== "Go" + + ```go title="heap.go" + // Go 语言中可以通过实现 heap.Interface 来构建整数大顶堆 + // 实现 heap.Interface 需要同时实现 sort.Interface + type intHeap []any + + // Push heap.Interface 的方法，实现推入元素到堆 + func (h *intHeap) Push(x any) { + // Push 和 Pop 使用 pointer receiver 作为参数 + // 因为它们不仅会对切片的内容进行调整，还会修改切片的长度。 + *h = append(*h, x.(int)) + } + + // Pop heap.Interface 的方法，实现弹出堆顶元素 + func (h *intHeap) Pop() any { + // 待出堆元素存放在最后 + last := (*h)[len(*h)-1] + *h = (*h)[:len(*h)-1] + return last + } + + // Len sort.Interface 的方法 + func (h *intHeap) Len() int { + return len(*h) + } + + // Less sort.Interface 的方法 + func (h *intHeap) Less(i, j int) bool { + // 如果实现小顶堆，则需要调整为小于号 + return (*h)[i].(int) > (*h)[j].(int) + } + + // Swap sort.Interface 的方法 + func (h *intHeap) Swap(i, j int) { + (*h)[i], (*h)[j] = (*h)[j], (*h)[i] + } + + // Top 获取堆顶元素 + func (h *intHeap) Top() any { + return (*h)[0] + } + + /* Driver Code */ + func TestHeap(t *testing.T) { + /* 初始化堆 */ + // 初始化大顶堆 + maxHeap := &intHeap{} + heap.Init(maxHeap) + /* 元素入堆 */ + // 调用 heap.Interface 的方法，来添加元素 + heap.Push(maxHeap, 1) + heap.Push(maxHeap, 3) + heap.Push(maxHeap, 2) + heap.Push(maxHeap, 4) + heap.Push(maxHeap, 5) + + /* 获取堆顶元素 */ + top := maxHeap.Top() + fmt.Printf("堆顶元素为 %d\n", top) + + /* 堆顶元素出堆 */ + // 调用 heap.Interface 的方法，来移除元素 + heap.Pop(maxHeap) + heap.Pop(maxHeap) + heap.Pop(maxHeap) + heap.Pop(maxHeap) + heap.Pop(maxHeap) + + /* 获取堆大小 */ + size := len(*maxHeap) + fmt.Printf("堆元素数量为 %d\n", size) + + /* 判断堆是否为空 */ + isEmpty := len(*maxHeap) == 0 + fmt.Printf("堆是否为空 %t\n", isEmpty) + } + ``` + +=== "JavaScript" + + ```js title="heap.js" + + ``` + +=== "TypeScript" + + ```typescript title="heap.ts" + + ``` + +=== "C" + + ```c title="heap.c" + + ``` + +=== "C#" + + ```csharp title="heap.cs" + + ``` + +=== "Swift" + + ```swift title="heap.swift" + + ``` + +## 堆的实现 + +下文实现的是「大顶堆」，若想转换为「小顶堆」，将所有大小逻辑判断取逆（例如将 $\geq$ 替换为 $\leq$ ）即可，有兴趣的同学可自行实现。 + +### 堆的存储与表示 + +在二叉树章节我们学过，「完全二叉树」非常适合使用「数组」来表示，而堆恰好是一颗完全二叉树，**因而我们采用「数组」来存储「堆」**。 + +**二叉树指针**。使用数组表示二叉树时，元素代表结点值，索引代表结点在二叉树中的位置，**而结点指针通过索引映射公式来实现**。 + +具体地，给定索引 $i$ ，那么其左子结点索引为 $2i + 1$ 、右子结点索引为 $2i + 2$ 、父结点索引为 $(i - 1) / 2$ （向下整除）。当索引越界时，代表空结点或结点不存在。 + +![representation_of_heap](heap.assets/representation_of_heap.png) + +我们将索引映射公式封装成函数，以便后续使用。 + +=== "Java" + + ```java title="my_heap.java" + // 使用列表而非数组，这样无需考虑扩容问题 + List maxHeap; + + /* 构造函数，建立空堆 */ + public MaxHeap() { + maxHeap = new ArrayList<>(); + } + + /* 获取左子结点索引 */ + int left(int i) { + return 2 * i + 1; + } + + /* 获取右子结点索引 */ + int right(int i) { + return 2 * i + 2; + } + + /* 获取父结点索引 */ + int parent(int i) { + return (i - 1) / 2; // 向下整除 + } + ``` + +=== "C++" + + ```cpp title="my_heap.cpp" + + ``` + +=== "Python" + + ```python title="my_heap.py" + + ``` + +=== "Go" + + ```go title="my_heap.go" + type maxHeap struct { + // 使用切片而非数组，这样无需考虑扩容问题 + data []any + } + + /* 构造函数，建立空堆 */ + func newHeap() *maxHeap { + return &maxHeap{ + data: make([]any, 0), + } + } + + /* 获取左子结点索引 */ + func (h *maxHeap) left(i int) int { + return 2*i + 1 + } + + /* 获取右子结点索引 */ + func (h *maxHeap) right(i int) int { + return 2*i + 2 + } + + /* 获取父结点索引 */ + func (h *maxHeap) parent(i int) int { + // 向下整除 + return (i - 1) / 2 + } + ``` + +=== "JavaScript" + + ```js title="my_heap.js" + + ``` + +=== "TypeScript" + + ```typescript title="my_heap.ts" + + ``` + +=== "C" + + ```c title="my_heap.c" + + ``` + +=== "C#" + + ```csharp title="my_heap.cs" + + ``` + +=== "Swift" + + ```swift title="my_heap.swift" + + ``` + +### 访问堆顶元素 + +堆顶元素是二叉树的根结点，即列表首元素。 + +=== "Java" + + ```java title="my_heap.java" + /* 访问堆顶元素 */ + public int peek() { + return maxHeap.get(0); + } + ``` + +=== "C++" + + ```cpp title="my_heap.cpp" + + ``` + +=== "Python" + + ```python title="my_heap.py" + + ``` + +=== "Go" + + ```go title="my_heap.go" + /* 访问堆顶元素 */ + func (h *maxHeap) peek() any { + return h.data[0] + } + ``` + +=== "JavaScript" + + ```js title="my_heap.js" + + ``` + +=== "TypeScript" + + ```typescript title="my_heap.ts" + + ``` + +=== "C" + + ```c title="my_heap.c" + + ``` + +=== "C#" + + ```csharp title="my_heap.cs" + + ``` + +=== "Swift" + + ```swift title="my_heap.swift" + + ``` + +### 元素入堆 + +给定元素 `val` ，我们先将其添加到堆底。添加后，由于 `val` 可能大于堆中其它元素，此时堆的成立条件可能已经被破坏，**因此需要修复从插入结点到根结点这条路径上的各个结点**，该操作被称为「堆化 Heapify」。 + +考虑从入堆结点开始，**从底至顶执行堆化**。具体地，比较插入结点与其父结点的值，若插入结点更大则将它们交换；并循环以上操作，从底至顶地修复堆中的各个结点；直至越过根结点时结束，或当遇到无需交换的结点时提前结束。 + +=== "Step 1" + ![heap_push_step1](heap.assets/heap_push_step1.png) + +=== "Step 2" + ![heap_push_step2](heap.assets/heap_push_step2.png) + +=== "Step 3" + ![heap_push_step3](heap.assets/heap_push_step3.png) + +=== "Step 4" + ![heap_push_step4](heap.assets/heap_push_step4.png) + +=== "Step 5" + ![heap_push_step5](heap.assets/heap_push_step5.png) + +=== "Step 6" + ![heap_push_step6](heap.assets/heap_push_step6.png) + +设结点总数为 $n$ ，则树的高度为 $O(\log n)$ ，易得堆化操作的循环轮数最多为 $O(\log n)$ ，**因而元素入堆操作的时间复杂度为 $O(\log n)$** 。 + +=== "Java" + + ```java title="my_heap.java" + /* 元素入堆 */ + void push(int val) { + // 添加结点 + maxHeap.add(val); + // 从底至顶堆化 + siftUp(size() - 1); + } + + /* 从结点 i 开始，从底至顶堆化 */ + void siftUp(int i) { + while (true) { + // 获取结点 i 的父结点 + int p = parent(i); + // 若“越过根结点”或“结点无需修复”，则结束堆化 + if (p < 0 || maxHeap.get(i) <= maxHeap.get(p)) + break; + // 交换两结点 + swap(i, p); + // 循环向上堆化 + i = p; + } + } + ``` + +=== "C++" + + ```cpp title="my_heap.cpp" + + ``` + +=== "Python" + + ```python title="my_heap.py" + + ``` + +=== "Go" + + ```go title="my_heap.go" + /* 元素入堆 */ + func (h *maxHeap) push(val any) { + // 添加结点 + h.data = append(h.data, val) + // 从底至顶堆化 + h.siftUp(len(h.data) - 1) + } + + /* 从结点 i 开始，从底至顶堆化 */ + func (h *maxHeap) siftUp(i int) { + for true { + // 获取结点 i 的父结点 + p := h.parent(i) + // 当“越过根结点”或“结点无需修复”时，结束堆化 + if p < 0 || h.data[i].(int) <= h.data[p].(int) { + break + } + // 交换两结点 + h.swap(i, p) + // 循环向上堆化 + i = p + } + } + ``` + +=== "JavaScript" + + ```js title="my_heap.js" + + ``` + +=== "TypeScript" + + ```typescript title="my_heap.ts" + + ``` + +=== "C" + + ```c title="my_heap.c" + + ``` + +=== "C#" + + ```csharp title="my_heap.cs" + + ``` + +=== "Swift" + + ```swift title="my_heap.swift" + + ``` + +### 堆顶元素出堆 + +堆顶元素是二叉树根结点，即列表首元素，如果我们直接将首元素从列表中删除，则二叉树中所有结点都会随之发生移位（索引发生变化），这样后续使用堆化修复就很麻烦了。为了尽量减少元素索引变动，采取以下操作步骤： + +1. 交换堆顶元素与堆底元素（即交换根结点与最右叶结点）； +2. 交换完成后，将堆底从列表中删除（注意，因为已经交换，实际上删除的是原来的堆顶元素）； +3. 从根结点开始，**从顶至底执行堆化**； + +顾名思义，**从顶至底堆化的操作方向与从底至顶堆化相反**，我们比较根结点的值与其两个子结点的值，将最大的子结点与根结点执行交换，并循环以上操作，直到越过叶结点时结束，或当遇到无需交换的结点时提前结束。 + +=== "Step 1" + ![heap_poll_step1](heap.assets/heap_poll_step1.png) + +=== "Step 2" + ![heap_poll_step2](heap.assets/heap_poll_step2.png) + +=== "Step 3" + ![heap_poll_step3](heap.assets/heap_poll_step3.png) + +=== "Step 4" + ![heap_poll_step4](heap.assets/heap_poll_step4.png) + +=== "Step 5" + ![heap_poll_step5](heap.assets/heap_poll_step5.png) + +=== "Step 6" + ![heap_poll_step6](heap.assets/heap_poll_step6.png) + +=== "Step 7" + ![heap_poll_step7](heap.assets/heap_poll_step7.png) + +=== "Step 8" + ![heap_poll_step8](heap.assets/heap_poll_step8.png) + +=== "Step 9" + ![heap_poll_step9](heap.assets/heap_poll_step9.png) + +=== "Step 10" + ![heap_poll_step10](heap.assets/heap_poll_step10.png) + +与元素入堆操作类似，**堆顶元素出堆操作的时间复杂度为 $O(\log n)$** 。 + +=== "Java" + + ```java title="my_heap.java" + /* 元素出堆 */ + int poll() { + // 判空处理 + if (isEmpty()) + throw new EmptyStackException(); + // 交换根结点与最右叶结点（即交换首元素与尾元素） + swap(0, size() - 1); + // 删除结点 + int val = maxHeap.remove(size() - 1); + // 从顶至底堆化 + siftDown(0); + // 返回堆顶元素 + return val; + } + + /* 从结点 i 开始，从顶至底堆化 */ + void siftDown(int i) { + while (true) { + // 判断结点 i, l, r 中值最大的结点，记为 ma + int l = left(i), r = right(i), ma = i; + if (l < size() && maxHeap.get(l) > maxHeap.get(ma)) + ma = l; + if (r < size() && maxHeap.get(r) > maxHeap.get(ma)) + ma = r; + // 若“结点 i 最大”或“越过叶结点”，则结束堆化 + if (ma == i) break; + // 交换两结点 + swap(i, ma); + // 循环向下堆化 + i = ma; + } + } + ``` + +=== "C++" + + ```cpp title="my_heap.cpp" + + ``` + +=== "Python" + + ```python title="my_heap.py" + + ``` + +=== "Go" + + ```go title="my_heap.go" + /* 元素出堆 */ + func (h *maxHeap) poll() any { + // 判空处理 + if h.isEmpty() { + fmt.Println("error") + } + // 交换根结点与最右叶结点（即交换首元素与尾元素） + h.swap(0, h.size()-1) + // 删除结点 + val := h.data[len(h.data)-1] + h.data = h.data[:len(h.data)-1] + // 从顶至底堆化 + h.siftDown(0) + + // 返回堆顶元素 + return val + } + + /* 从结点 i 开始，从顶至底堆化 */ + func (h *maxHeap) siftDown(i int) { + for true { + // 判断结点 i, l, r 中值最大的结点，记为 max + l, r, max := h.left(i), h.right(i), i + if l < h.size() && h.data[l].(int) > h.data[max].(int) { + max = l + } + if r < h.size() && h.data[r].(int) > h.data[max].(int) { + max = r + } + // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出 + if max == i { + break + } + // 交换两结点 + h.swap(i, max) + // 循环向下堆化 + i = max + } + } + ``` + +=== "JavaScript" + + ```js title="my_heap.js" + + ``` + +=== "TypeScript" + + ```typescript title="my_heap.ts" + + ``` + +=== "C" + + ```c title="my_heap.c" + + ``` + +=== "C#" + + ```csharp title="my_heap.cs" + + ``` + +=== "Swift" + + ```swift title="my_heap.swift" + + ``` + +### 输入数据并建堆 * + +如果我们想要直接输入一个列表并将其建堆，那么该怎么做呢？最直接地，考虑使用「元素入堆」方法，将列表元素依次入堆。元素入堆的时间复杂度为 $O(n)$ ，而平均长度为 $\frac{n}{2}$ ，因此该方法的总体时间复杂度为 $O(n \log n)$ 。 + +然而，存在一种更加优雅的建堆方法。设结点数量为 $n$ ，我们先将列表所有元素原封不动添加进堆，**然后迭代地对各个结点执行「从顶至底堆化」**。当然，**无需对叶结点执行堆化**，因为其没有子结点。 + +=== "Java" + + ```java title="my_heap.java" + /* 构造函数，根据输入列表建堆 */ + public MaxHeap(List nums) { + // 将列表元素原封不动添加进堆 + maxHeap = new ArrayList<>(nums); + // 堆化除叶结点以外的其他所有结点 + for (int i = parent(size() - 1); i >= 0; i--) { + siftDown(i); + } + } + ``` + +=== "C++" + + ```cpp title="my_heap.cpp" + + ``` + +=== "Python" + + ```python title="my_heap.py" + + ``` + +=== "Go" + + ```go title="my_heap.go" + /* 构造函数，根据切片建堆 */ + func newMaxHeap(nums []any) *maxHeap { + // 所有元素入堆 + h := &maxHeap{data: nums} + for i := len(h.data) - 1; i >= 0; i-- { + // 堆化除叶结点以外的其他所有结点 + h.siftDown(i) + } + return h + } + ``` + +=== "JavaScript" + + ```js title="my_heap.js" + + ``` + +=== "TypeScript" + + ```typescript title="my_heap.ts" + + ``` + +=== "C" + + ```c title="my_heap.c" + + ``` + +=== "C#" + + ```csharp title="my_heap.cs" + + ``` + +=== "Swift" + + ```swift title="my_heap.swift" + + ``` + +那么，第二种建堆方法的时间复杂度时多少呢？我们来做一下简单推算。 + +- 完全二叉树中，设结点总数为 $n$ ，则叶结点数量为 $(n + 1) / 2$ ，其中 $/$ 为向下整除。因此在排除叶结点后，需要堆化结点数量为 $(n - 1)/2$ ，即为 $O(n)$ ； +- 从顶至底堆化中，每个结点最多堆化至叶结点，因此最大迭代次数为二叉树高度 $O(\log n)$ ； + +将上述两者相乘，可得时间复杂度为 $O(n \log n)$ 。然而，该估算结果仍不够准确，因为我们没有考虑到 **二叉树底层结点远多于顶层结点** 的性质。 + +下面我们来尝试展开计算。为了减小计算难度，我们假设树是一个「完美二叉树」，该假设不会影响计算结果的正确性。设二叉树（即堆）结点数量为 $n$ ，树高度为 $h$ 。上文提到，**结点堆化最大迭代次数等于该结点到叶结点的距离，而这正是“结点高度”**。因此，我们将各层的“结点数量 $\times$ 结点高度”求和，即可得到所有结点的堆化的迭代次数总和。 + +$$ +T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \cdots + 2^{(h-1)}\times1 +$$ + +![heapify_count](heap.assets/heapify_count.png) + +化简上式需要借助中学的数列知识，先对 $T(h)$ 乘以 $2$ ，易得 + +$$ +\begin{aligned} +T(h) & = 2^0h + 2^1(h-1) + 2^2(h-2) + \cdots + 2^{h-1}\times1 \newline +2 T(h) & = 2^1h + 2^2(h-1) + 2^3(h-2) + \cdots + 2^{h}\times1 \newline +\end{aligned} +$$ + +**使用错位相减法**，令下式 $2 T(h)$ 减去上式 $T(h)$ ，可得 + +$$ +2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \cdots + 2^{h-1} + 2^h +$$ + +观察上式，$T(h)$ 是一个等比数列，可直接使用求和公式，得到时间复杂度为 + +$$ +\begin{aligned} +T(h) & = 2 \frac{1 - 2^h}{1 - 2} - h \newline +& = 2^{h+1} - h \newline +& = O(2^h) +\end{aligned} +$$ + +进一步地，高度为 $h$ 的完美二叉树的结点数量为 $n = 2^{h+1} - 1$ ，易得复杂度为 $O(2^h) = O(n)$。以上推算表明，**输入列表并建堆的时间复杂度为 $O(n)$ ，非常高效**。 + +## 堆常见应用 + +- **优先队列**。堆常作为实现优先队列的首选数据结构，入队和出队操作时间复杂度为 $O(\log n)$ ，建队操作为 $O(n)$ ，皆非常高效。 +- **堆排序**。给定一组数据，我们使用其建堆，并依次全部弹出，则可以得到有序的序列。当然，堆排序一般无需弹出元素，仅需每轮将堆顶元素交换至数组尾部并减小堆的长度即可。 +- **获取最大的 $k$ 个元素**。这既是一道经典算法题目，也是一种常见应用，例如选取热度前 10 的新闻作为微博热搜，选取前 10 销量的商品等。 diff --git a/docs/chapter_introduction/what_is_dsa.md b/docs/chapter_introduction/what_is_dsa.md index 67b3c37e1..10ea25133 100644 --- a/docs/chapter_introduction/what_is_dsa.md +++ b/docs/chapter_introduction/what_is_dsa.md @@ -6,7 +6,7 @@ comments: true ## 算法定义 -「算法 Algorithm」是在有限时间内解决问题的一组指令或操作步骤。算法具有以下特性： +「算法 Algorithm」是在有限时间内解决特定问题的一组指令或操作步骤。算法具有以下特性： - 问题是明确的，需要拥有明确的输入和输出定义。 - 解具有确定性，即给定相同输入时，输出一定相同。 diff --git a/docs/chapter_preface/contribution.md b/docs/chapter_preface/contribution.md index c710e6de5..498002c72 100644 --- a/docs/chapter_preface/contribution.md +++ b/docs/chapter_preface/contribution.md @@ -41,4 +41,25 @@ comments: true 非常欢迎您和我一同来创作本书！ +## 本地部署 hello-algo + +### Docker + +请确保 Docker 已经安装并启动，并根据如下命令离线部署。 + +稍等片刻，即可使用浏览器打开 `http://localhost:8000` 访问本项目。 + +```bash +git clone https://github.com/krahets/hello-algo.git +cd hello-algo + +docker-compose up -d +``` + +使用如下命令即可删除部署。 + +```bash +docker-compose down +``` + （TODO：教学视频） diff --git a/docs/chapter_preface/installation.md b/docs/chapter_preface/installation.md index c6c1b2ee9..e23608a68 100644 --- a/docs/chapter_preface/installation.md +++ b/docs/chapter_preface/installation.md @@ -15,10 +15,9 @@ comments: true 1. 下载并安装 [OpenJDK](https://jdk.java.net/18/)（版本需满足 > JDK 9）。 2. 在 VSCode 的插件市场中搜索 `java` ，安装 Java Extension Pack 。 +## C/C++ 环境 -## C++ 环境 - -1. Windows 系统需要安装 [MinGW](https://www.mingw-w64.org/downloads/) ，MacOS 自带 Clang 无需安装。 +1. Windows 系统需要安装 [MinGW](https://sourceforge.net/projects/mingw-w64/files/) （[完整配置教程](https://zhuanlan.zhihu.com/p/77074009)），MacOS 自带 Clang 无需安装。 2. 在 VSCode 的插件市场中搜索 `c++` ，安装 C/C++ Extension Pack 。 ## Python 环境 @@ -46,3 +45,8 @@ comments: true 1. 下载并安装 [Swift](https://www.swift.org/download/)； 2. 在 VSCode 的插件市场中搜索 `swift`，安装 [Swift for Visual Studio Code](https://marketplace.visualstudio.com/items?itemName=sswg.swift-lang)。 + +## Rust 环境 + +1. 下载并安装 [Rust](https://www.rust-lang.org/tools/install)； +2. 在 VSCode 的插件市场中搜索 `rust`，安装 [rust-analyzer](https://marketplace.visualstudio.com/items?itemName=rust-lang.rust-analyzer)。 diff --git a/docs/chapter_sorting/bubble_sort.md b/docs/chapter_sorting/bubble_sort.md index e3e394b20..3bb0bc994 100644 --- a/docs/chapter_sorting/bubble_sort.md +++ b/docs/chapter_sorting/bubble_sort.md @@ -170,7 +170,7 @@ comments: true ```c title="bubble_sort.c" /* 冒泡排序 */ - void bubble_sort(int nums[], int size) { + void bubbleSort(int nums[], int size) { // 外循环：待排序元素数量为 n-1, n-2, ..., 1 for (int i = 0; i < size - 1; i++) { @@ -373,7 +373,7 @@ comments: true ```c title="bubble_sort.c" /* 冒泡排序 */ - void bubble_sort(int nums[], int size) { + void bubbleSortWithFlag(int nums[], int size) { // 外循环：待排序元素数量为 n-1, n-2, ..., 1 for (int i = 0; i < size - 1; i++) { diff --git a/docs/chapter_stack_and_queue/deque.md b/docs/chapter_stack_and_queue/deque.md index 52b0540d5..4671d5c9e 100644 --- a/docs/chapter_stack_and_queue/deque.md +++ b/docs/chapter_stack_and_queue/deque.md @@ -18,16 +18,16 @@ comments: true
-| 方法 | 描述 | -| ------------ | ---------------- | -| offerFirst() | 将元素添加至队首 | -| offerLast() | 将元素添加至队尾 | -| pollFirst() | 删除队首元素 | -| pollLast() | 删除队尾元素 | -| peekFirst() | 访问队首元素 | -| peekLast() | 访问队尾元素 | -| size() | 获取队列的长度 | -| isEmpty() | 判断队列是否为空 | +| 方法 | 描述 | 时间复杂度 | +| ------------ | ---------------- | ---------- | +| offerFirst() | 将元素添加至队首 | $O(1)$ | +| offerLast() | 将元素添加至队尾 | $O(1)$ | +| pollFirst() | 删除队首元素 | $O(1)$ | +| pollLast() | 删除队尾元素 | $O(1)$ | +| peekFirst() | 访问队首元素 | $O(1)$ | +| peekLast() | 访问队尾元素 | $O(1)$ | +| size() | 获取队列的长度 | $O(1)$ | +| isEmpty() | 判断队列是否为空 | $O(1)$ |
@@ -196,5 +196,5 @@ comments: true === "Swift" ```swift title="deque.swift" - + ``` diff --git a/docs/chapter_stack_and_queue/queue.md b/docs/chapter_stack_and_queue/queue.md index 0c589fa69..d70b3e528 100644 --- a/docs/chapter_stack_and_queue/queue.md +++ b/docs/chapter_stack_and_queue/queue.md @@ -20,13 +20,13 @@ comments: true
-| 方法 | 描述 | -| --------- | ---------------------------- | -| offer() | 元素入队，即将元素添加至队尾 | -| poll() | 队首元素出队 | -| front() | 访问队首元素 | -| size() | 获取队列的长度 | -| isEmpty() | 判断队列是否为空 | +| 方法 | 描述 | 时间复杂度 | +| --------- | ---------------------------- | ---------- | +| offer() | 元素入队，即将元素添加至队尾 | $O(1)$ | +| poll() | 队首元素出队 | $O(1)$ | +| front() | 访问队首元素 | $O(1)$ | +| size() | 获取队列的长度 | $O(1)$ | +| isEmpty() | 判断队列是否为空 | $O(1)$ |
@@ -231,7 +231,28 @@ comments: true === "Swift" ```swift title="queue.swift" + /* 初始化队列 */ + // Swift 没有内置的队列类，可以把 Array 当作队列来使用 + var queue: [Int] = [] + /* 元素入队 */ + queue.append(1) + queue.append(3) + queue.append(2) + queue.append(5) + queue.append(4) + + /* 访问队首元素 */ + let peek = queue.first! + + /* 元素出队 */ + let pool = queue.removeFirst() + + /* 获取队列的长度 */ + let size = queue.count + + /* 判断队列是否为空 */ + let isEmpty = queue.isEmpty ``` ## 队列实现 @@ -627,7 +648,59 @@ comments: true === "Swift" ```swift title="linkedlist_queue.swift" + /* 基于链表实现的队列 */ + class LinkedListQueue { + private var front: ListNode? // 头结点 + private var rear: ListNode? // 尾结点 + private var _size = 0 + init() {} + + /* 获取队列的长度 */ + func size() -> Int { + _size + } + + /* 判断队列是否为空 */ + func isEmpty() -> Bool { + size() == 0 + } + + /* 入队 */ + func offer(num: Int) { + // 尾结点后添加 num + let node = ListNode(x: num) + // 如果队列为空，则令头、尾结点都指向该结点 + if front == nil { + front = node + rear = node + } + // 如果队列不为空，则将该结点添加到尾结点后 + else { + rear?.next = node + rear = node + } + _size += 1 + } + + /* 出队 */ + @discardableResult + func poll() -> Int { + let num = peek() + // 删除头结点 + front = front?.next + _size -= 1 + return num + } + + /* 访问队首元素 */ + func peek() -> Int { + if isEmpty() { + fatalError("队列为空") + } + return front!.val + } + } ``` ### 基于数组的实现 @@ -1042,7 +1115,63 @@ comments: true === "Swift" ```swift title="array_queue.swift" + /* 基于环形数组实现的队列 */ + class ArrayQueue { + private var nums: [Int] // 用于存储队列元素的数组 + private var front = 0 // 头指针，指向队首 + private var rear = 0 // 尾指针，指向队尾 + 1 + init(capacity: Int) { + // 初始化数组 + nums = Array(repeating: 0, count: capacity) + } + + /* 获取队列的容量 */ + func capacity() -> Int { + nums.count + } + + /* 获取队列的长度 */ + func size() -> Int { + let capacity = capacity() + // 由于将数组看作为环形，可能 rear < front ，因此需要取余数 + return (capacity + rear - front) % capacity + } + + /* 判断队列是否为空 */ + func isEmpty() -> Bool { + rear - front == 0 + } + + /* 入队 */ + func offer(num: Int) { + if size() == capacity() { + print("队列已满") + return + } + // 尾结点后添加 num + nums[rear] = num + // 尾指针向后移动一位，越过尾部后返回到数组头部 + rear = (rear + 1) % capacity() + } + + /* 出队 */ + @discardableResult + func poll() -> Int { + let num = peek() + // 队头指针向后移动一位，若越过尾部则返回到数组头部 + front = (front + 1) % capacity() + return num + } + + /* 访问队首元素 */ + func peek() -> Int { + if isEmpty() { + fatalError("队列为空") + } + return nums[front] + } + } ``` ## 队列典型应用 diff --git a/docs/chapter_stack_and_queue/stack.md b/docs/chapter_stack_and_queue/stack.md index 04825695c..c47f7cc82 100644 --- a/docs/chapter_stack_and_queue/stack.md +++ b/docs/chapter_stack_and_queue/stack.md @@ -22,13 +22,13 @@ comments: true
-| 方法 | 描述 | -| --------- | ---------------------- | -| push() | 元素入栈（添加至栈顶） | -| pop() | 栈顶元素出栈 | -| peek() | 访问栈顶元素 | -| size() | 获取栈的长度 | -| isEmpty() | 判断栈是否为空 | +| 方法 | 描述 | 时间复杂度 | +| --------- | ---------------------- | ---------- | +| push() | 元素入栈（添加至栈顶） | $O(1)$ | +| pop() | 栈顶元素出栈 | $O(1)$ | +| peek() | 访问栈顶元素 | $O(1)$ | +| size() | 获取栈的长度 | $O(1)$ | +| isEmpty() | 判断栈是否为空 | $O(1)$ |
@@ -641,7 +641,7 @@ comments: true /* 判断栈是否为空 */ func isEmpty() -> Bool { - _size == 0 + size() == 0 } /* 入栈 */ @@ -653,6 +653,7 @@ comments: true } /* 出栈 */ + @discardableResult func pop() -> Int { let num = peek() _peek = _peek?.next @@ -662,22 +663,11 @@ comments: true /* 访问栈顶元素 */ func peek() -> Int { - if _size == 0 { + if isEmpty() { fatalError("栈为空") } return _peek!.val } - - /* 将 List 转化为 Array 并返回 */ - func toArray() -> [Int] { - var node = _peek - var res = Array(repeating: 0, count: _size) - for i in sequence(first: res.count - 1, next: { $0 >= 0 + 1 ? $0 - 1 : nil }) { - res[i] = node!.val - node = node?.next - } - return res - } } ``` @@ -994,8 +984,9 @@ comments: true } /* 出栈 */ + @discardableResult func pop() -> Int { - if stack.isEmpty { + if isEmpty() { fatalError("栈为空") } return stack.removeLast() @@ -1003,16 +994,11 @@ comments: true /* 访问栈顶元素 */ func peek() -> Int { - if stack.isEmpty { + if isEmpty() { fatalError("栈为空") } return stack.last! } - - /* 将 List 转化为 Array 并返回 */ - func toArray() -> [Int] { - stack - } } ``` diff --git a/docs/chapter_tree/binary_tree.md b/docs/chapter_tree/binary_tree.md index 1061e019d..0201f6a2a 100644 --- a/docs/chapter_tree/binary_tree.md +++ b/docs/chapter_tree/binary_tree.md @@ -114,7 +114,7 @@ comments: true 结点的两个指针分别指向「左子结点 Left Child Node」和「右子结点 Right Child Node」，并且称该结点为两个子结点的「父结点 Parent Node」。给定二叉树某结点，将左子结点以下的树称为该结点的「左子树 Left Subtree」，右子树同理。 -除了叶结点外，每个结点都有子结点和子树。例如，若将上图的「结点 2」看作父结点，那么其左子结点和右子结点分别为「结点 4」和「结点 5」，左子树和右子树分别为「结点 4 及其以下结点形成的树」和「结点 5 及其以下结点形成的树」。 +除了叶结点外，每个结点都有子结点和子树。例如，若将下图的「结点 2」看作父结点，那么其左子结点和右子结点分别为「结点 4」和「结点 5」，左子树和右子树分别为「结点 4 及其以下结点形成的树」和「结点 5 及其以下结点形成的树」。 ![binary_tree_definition](binary_tree.assets/binary_tree_definition.png) diff --git a/docs/chapter_tree/summary.md b/docs/chapter_tree/summary.md index a46a253f9..15dc2f6d3 100644 --- a/docs/chapter_tree/summary.md +++ b/docs/chapter_tree/summary.md @@ -15,4 +15,4 @@ comments: true - 前序、中序、后序遍历是深度优先搜索，体现着“走到头、再回头继续”的回溯遍历方式，通常使用递归实现。 - 二叉搜索树是一种高效的元素查找数据结构，查找、插入、删除操作的时间复杂度皆为 $O(\log n)$ 。二叉搜索树退化为链表后，各项时间复杂度劣化至 $O(n)$ ，因此如何避免退化是非常重要的课题。 - AVL 树又称平衡二叉搜索树，其通过旋转操作，使得在不断插入与删除结点后，仍然可以保持二叉树的平衡（不退化）。 -- AVL 树的旋转操作分为右旋、左旋、先右旋后左旋、先左旋后右旋。在插入或删除结点后，AVL 树会从底置顶地执行旋转操作，使树恢复平衡。 +- AVL 树的旋转操作分为右旋、左旋、先右旋后左旋、先左旋后右旋。在插入或删除结点后，AVL 树会从底至顶地执行旋转操作，使树恢复平衡。 diff --git a/mkdocs.yml b/mkdocs.yml index 9ddae9f39..ad836ae9f 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -161,6 +161,8 @@ nav: - 二叉搜索树: chapter_tree/binary_search_tree.md - AVL 树 *: chapter_tree/avl_tree.md - 小结: chapter_tree/summary.md + - 堆: + - 堆（Heap）: chapter_heap/heap.md - 查找算法: - 线性查找: chapter_searching/linear_search.md - 二分查找: chapter_searching/binary_search.md