This commit is contained in:
steak-zhuo 2023-01-14 23:27:31 +08:00
commit 3129b65b3f
77 changed files with 3122 additions and 139 deletions

View file

@ -1,4 +0,0 @@
{
"tabWidth": 4,
"useTabs": false
}

16
Dockerfile Normal file
View file

@ -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"]

View file

@ -1 +1,2 @@
add_executable(array array.c)
add_executable(linked_list linked_list.c)

View file

@ -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);

View file

@ -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;
}

View file

@ -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) {

View file

@ -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]);

View file

@ -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;
}

View file

@ -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;
}

View file

@ -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;
}

View file

@ -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[]) {

View file

@ -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;
}

View file

@ -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);
}

View file

@ -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;
}

View file

@ -17,6 +17,8 @@
#include <unordered_set>
#include <set>
#include <random>
#include <chrono>
#include <algorithm>
#include "ListNode.hpp"
#include "TreeNode.hpp"

View file

@ -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]
}

View file

@ -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)
}

View file

@ -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)
}

View file

@ -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)
}
}

View file

@ -5,6 +5,7 @@
*/
package chapter_hashing;
import java.util.*;
/* 键值对 int->String */

View file

@ -5,6 +5,7 @@
*/
package chapter_hashing;
import java.util.*;
import include.*;

View file

@ -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<Integer> 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<Integer> 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<Integer> minHeap = new PriorityQueue<>();
// 初始化大顶堆使用 lambda 表达式修改 Comparator 即可
Queue<Integer> 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);
}
}

View file

@ -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<Integer> 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<Integer> 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);
// 越过根结点结点无需修复结束堆化
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<Integer> 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);
}
}

View file

@ -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);

View file

@ -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);

View file

@ -105,10 +105,16 @@ public class PrintUtil {
}
}
public static void printHeap(PriorityQueue<Integer> queue) {
Integer[] nums = (Integer[])queue.toArray();
TreeNode root = TreeNode.arrToTree(nums);
/**
* Print a heap (PriorityQueue)
* @param queue
*/
public static void printHeap(Queue<Integer> queue) {
List<Integer> 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);
}
}

View file

@ -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<Integer> list) {
int size = list.size();
if (size == 0)
return null;
TreeNode root = new TreeNode(arr[0]);
TreeNode root = new TreeNode(list.get(0));
Queue<TreeNode> 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);
}
}

View file

@ -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::<Vec<_>>(); // [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);
}

View file

@ -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"]),
]
)

View file

@ -0,0 +1,116 @@
/**
* File: array_queue.swift
* Created Time: 2023-01-11
* Author: nuomi1 (nuomi1@qq.com)
*/
/* */
class ArrayQueue {
private var nums: [Int] //
private var front = 0 //
private var rear = 0 // + 1
init(capacity: Int) {
//
nums = Array(repeating: 0, count: capacity)
}
/* */
func capacity() -> Int {
nums.count
}
/* */
func size() -> Int {
let capacity = capacity()
// rear < front
return (capacity + rear - front) % capacity
}
/* */
func isEmpty() -> Bool {
rear - front == 0
}
/* */
func offer(num: Int) {
if size() == capacity() {
print("队列已满")
return
}
// num
nums[rear] = num
//
rear = (rear + 1) % capacity()
}
/* */
@discardableResult
func poll() -> Int {
let num = peek()
//
front = (front + 1) % capacity()
return num
}
/* 访 */
func peek() -> Int {
if isEmpty() {
fatalError("队列为空")
}
return nums[front]
}
/* */
func toArray() -> [Int] {
let size = size()
let capacity = capacity()
//
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() {
/* */
let capacity = 10
let queue = ArrayQueue(capacity: capacity)
/* */
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 */
let peek = queue.peek()
print("队首元素 peek = \(peek)")
/* */
let poll = queue.poll()
print("出队元素 poll = \(poll),出队后 queue = \(queue.toArray())")
/* */
let size = queue.size()
print("队列长度 size = \(size)")
/* */
let isEmpty = queue.isEmpty()
print("队列是否为空 = \(isEmpty)")
/* */
for i in 0 ..< 10 {
queue.offer(num: i)
queue.poll()
print("\(i) 轮入队 + 出队后 queue = \(queue.toArray())")
}
}
}

View file

@ -29,8 +29,9 @@ class ArrayStack {
}
/* */
@discardableResult
func pop() -> Int {
if stack.isEmpty {
if isEmpty() {
fatalError("栈为空")
}
return stack.removeLast()
@ -38,7 +39,7 @@ class ArrayStack {
/* 访 */
func peek() -> Int {
if stack.isEmpty {
if isEmpty() {
fatalError("栈为空")
}
return stack.last!

View file

@ -0,0 +1,105 @@
/**
* File: linkedlist_queue.swift
* Created Time: 2023-01-11
* Author: nuomi1 (nuomi1@qq.com)
*/
import utils
/* */
class LinkedListQueue {
private var front: ListNode? //
private var rear: ListNode? //
private var _size = 0
init() {}
/* */
func size() -> Int {
_size
}
/* */
func isEmpty() -> Bool {
size() == 0
}
/* */
func offer(num: Int) {
// num
let node = ListNode(x: num)
//
if front == nil {
front = node
rear = node
}
//
else {
rear?.next = node
rear = node
}
_size += 1
}
/* */
@discardableResult
func poll() -> Int {
let num = peek()
//
front = front?.next
_size -= 1
return num
}
/* 访 */
func peek() -> Int {
if isEmpty() {
fatalError("队列为空")
}
return front!.val
}
/* Array */
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() {
/* */
let queue = LinkedListQueue()
/* */
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 */
let peek = queue.peek()
print("队首元素 peek = \(peek)")
/* */
let poll = queue.poll()
print("出队元素 poll = \(poll),出队后 queue = \(queue.toArray())")
/* */
let size = queue.size()
print("队列长度 size = \(size)")
/* */
let isEmpty = queue.isEmpty()
print("队列是否为空 = \(isEmpty)")
}
}

View file

@ -20,7 +20,7 @@ class LinkedListStack {
/* */
func isEmpty() -> Bool {
_size == 0
size() == 0
}
/* */
@ -32,6 +32,7 @@ class LinkedListStack {
}
/* */
@discardableResult
func pop() -> Int {
let num = peek()
_peek = _peek?.next
@ -41,7 +42,7 @@ class LinkedListStack {
/* 访 */
func peek() -> Int {
if _size == 0 {
if isEmpty() {
fatalError("栈为空")
}
return _peek!.val

View file

@ -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() {
/* */
// Swift Array 使
var queue: [Int] = []
/* */
queue.append(1)
queue.append(3)
queue.append(2)
queue.append(5)
queue.append(4)
print("队列 queue = \(queue)")
/* 访 */
let peek = queue.first!
print("队首元素 peek = \(peek)")
/* */
let pool = queue.removeFirst()
print("出队元素 poll = \(pool),出队后 queue = \(queue)")
/* */
let size = queue.count
print("队列长度 size = \(size)")
/* */
let isEmpty = queue.isEmpty
print("队列是否为空 = \(isEmpty)")
}
}

View file

@ -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);
}

View file

@ -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");
//
pub fn randomAccess(nums: []i32) i32 {
// [0, nums.len)
var randomIndex = std.crypto.random.intRangeLessThan(usize, 0, nums.len);
//
var randomNum = nums[randomIndex];
return randomNum;
}
//
pub fn extend(mem_allocator: std.mem.Allocator, nums: []i32, enlarge: usize) ![]i32 {
//
var res = try mem_allocator.alloc(i32, nums.len + enlarge);
std.mem.set(i32, res, 0);
//
std.mem.copy(i32, res, nums);
//
return res;
}
// index num
pub fn insert(nums: []i32, num: i32, index: usize) void {
// index
var i = nums.len - 1;
while (i > index) : (i -= 1) {
nums[i] = nums[i - 1];
}
// num index
nums[index] = num;
}
// index
pub fn remove(nums: []i32, index: usize) void {
// index
var i = index;
while (i < nums.len - 1) : (i += 1) {
nums[i] = nums[i + 1];
}
}
//
pub fn traverse(nums: []i32) void {
var count: i32 = 0;
//
var i: i32 = 0;
while (i < nums.len) : (i += 1) {
count += 1;
}
count = 0;
//
for (nums) |_| {
count += 1;
}
}
//
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 {
//
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);
// 访
var randomNum = randomAccess(&array);
std.debug.print("\n在 nums 中获取随机元素 {}", .{randomNum});
//
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);
//
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);
//
remove(nums, 2);
std.debug.print("\n删除索引 2 处的元素,得到 nums = ", .{});
inc.PrintUtil.printArray(i32, nums);
//
traverse(nums);
//
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;
}

View file

@ -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");
// n0 P
pub fn insert(n0: ?*inc.ListNode(i32), P: ?*inc.ListNode(i32)) void {
var n1 = n0.?.next;
n0.?.next = P;
P.?.next = n1;
}
// n0
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 index
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;
}
// target
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 {
//
//
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};
//
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);
//
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);
//
remove(&n0);
std.debug.print("删除结点后的链表为", .{});
try inc.PrintUtil.printLinkedList(i32, &n0);
// 访
var node = access(&n0, 3);
std.debug.print("链表中索引 3 处的结点的值 = {}\n", .{node.?.val});
//
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;
}

View file

@ -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 {
//
var list = std.ArrayList(i32).init(std.heap.page_allocator);
//
defer list.deinit();
try list.appendSlice(&[_]i32{ 1, 3, 2, 5, 4 });
std.debug.print("列表 list = ", .{});
inc.PrintUtil.printList(i32, list);
// 访
var num = list.items[1];
std.debug.print("\n访问索引 1 处的元素,得到 num = {}", .{num});
//
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);
//
list.clearRetainingCapacity();
std.debug.print("\n清空列表后 list = ", .{});
inc.PrintUtil.printList(i32, list);
//
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);
//
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);
//
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);
//
var count: i32 = 0;
var i: i32 = 0;
while (i < list.items.len) : (i += 1) {
count += 1;
}
//
count = 0;
for (list.items) |_| {
count += 1;
}
//
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);
//
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;
}

View file

@ -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");
//
//
pub fn MyList(comptime T: type) type {
return struct {
const Self = @This();
nums: []T = undefined, //
numsCapacity: usize = 10, //
numSize: usize = 0, //
extendRatio: usize = 2, //
mem_arena: ?std.heap.ArenaAllocator = null,
mem_allocator: std.mem.Allocator = undefined, //
// +
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));
}
//
pub fn deinit(self: *Self) void {
if (self.mem_arena == null) return;
self.mem_arena.?.deinit();
}
//
pub fn size(self: *Self) usize {
return self.numSize;
}
//
pub fn capacity(self: *Self) usize {
return self.numsCapacity;
}
// 访
pub fn get(self: *Self, index: usize) T {
//
if (index >= self.size()) @panic("索引越界");
return self.nums[index];
}
//
pub fn set(self: *Self, index: usize, num: T) void {
//
if (index >= self.size()) @panic("索引越界");
self.nums[index] = num;
}
//
pub fn add(self: *Self, num: T) !void {
//
if (self.size() == self.capacity()) try self.extendCapacity();
self.nums[self.size()] = num;
//
self.numSize += 1;
}
//
pub fn insert(self: *Self, index: usize, num: T) !void {
if (index >= self.size()) @panic("索引越界");
//
if (self.size() == self.capacity()) try self.extendCapacity();
// i
var j = self.size() - 1;
while (j >= index) : (j -= 1) {
self.nums[j + 1] = self.nums[j];
}
self.nums[index] = num;
//
self.numSize += 1;
}
//
pub fn remove(self: *Self, index: usize) T {
if (index >= self.size()) @panic("索引越界");
var num = self.nums[index];
// i
var j = index;
while (j < self.size() - 1) : (j += 1) {
self.nums[j] = self.nums[j + 1];
}
//
self.numSize -= 1;
//
return num;
}
//
pub fn extendCapacity(self: *Self) !void {
// size * extendRatio
var newCapacity = self.capacity() * self.extendRatio;
var extend = try self.mem_allocator.alloc(T, newCapacity);
std.mem.set(T, extend, @as(T, 0));
//
std.mem.copy(T, extend, self.nums);
self.nums = extend;
//
self.numsCapacity = newCapacity;
}
//
pub fn toArray(self: *Self) ![]T {
//
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 {
//
var list = MyList(i32){};
try list.init(std.heap.page_allocator);
//
defer list.deinit();
//
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()});
//
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());
//
_ = 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
var num = list.get(1);
std.debug.print("\n访问索引 1 处的元素,得到 num = {}", .{num});
//
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());
//
list.set(1, 0);
var i: i32 = 0;
while (i < 10) : (i += 1) {
// i = 5
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;
}

View file

@ -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");
//
fn bubbleSort(nums: []i32) void {
// n-1, n-2, ..., 1
var i: usize = nums.len - 1;
while (i > 0) : (i -= 1) {
var j: usize = 0;
//
while (j < i) : (j += 1) {
if (nums[j] > nums[j + 1]) {
// nums[j] nums[j + 1]
var tmp = nums[j];
nums[j] = nums[j + 1];
nums[j + 1] = tmp;
}
}
}
}
//
fn bubbleSortWithFlag(nums: []i32) void {
// n-1, n-2, ..., 1
var i: usize = nums.len - 1;
while (i > 0) : (i -= 1) {
var flag = false; //
var j: usize = 0;
//
while (j < i) : (j += 1) {
if (nums[j] > nums[j + 1]) {
// nums[j] nums[j + 1]
var tmp = nums[j];
nums[j] = nums[j + 1];
nums[j + 1] = tmp;
flag = true;
}
}
if (!flag) break; //
}
}
// 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;
}

View file

@ -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");
//
fn insertionSort(nums: []i32) void {
// 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;
// base
while (j >= 1 and nums[j - 1] > base) : (j -= 1) {
nums[j] = nums[j - 1]; // 1. nums[j]
}
nums[j] = base; // 2. base
}
}
// 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;
}

View file

@ -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");
//
//
pub fn ArrayStack(comptime T: type) type {
return struct {
const Self = @This();
stack: ?std.ArrayList(T) = null,
// +
pub fn init(self: *Self, allocator: std.mem.Allocator) void {
if (self.stack == null) {
self.stack = std.ArrayList(T).init(allocator);
}
}
//
pub fn deinit(self: *Self) void {
if (self.stack == null) return;
self.stack.?.deinit();
}
//
pub fn size(self: *Self) usize {
return self.stack.?.items.len;
}
//
pub fn empty(self: *Self) bool {
return self.size() == 0;
}
// 访
pub fn top(self: *Self) T {
if (self.size() == 0) @panic("栈为空");
return self.stack.?.items[self.size() - 1];
}
//
pub fn push(self: *Self, num: T) !void {
try self.stack.?.append(num);
}
//
pub fn pop(self: *Self) T {
var num = self.stack.?.pop();
return num;
}
// ArrayList
pub fn toList(self: *Self) std.ArrayList(T) {
return self.stack.?;
}
};
}
// Driver Code
pub fn main() !void {
//
var stack = ArrayStack(i32){};
stack.init(std.heap.page_allocator);
//
defer stack.deinit();
//
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
var top = stack.top();
std.debug.print("\n栈顶元素 top = {}", .{top});
//
top = stack.pop();
std.debug.print("\n出栈元素 pop = {},出栈后 stack = ", .{top});
inc.PrintUtil.printList(i32, stack.toList());
//
var size = stack.size();
std.debug.print("\n栈的长度 size = {}", .{size});
//
var empty = stack.empty();
std.debug.print("\n栈是否为空 = {}", .{empty});
const getchar = try std.io.getStdIn().reader().readByte();
_ = getchar;
}

View file

@ -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");
//
//
pub fn LinkedListStack(comptime T: type) type {
return struct {
const Self = @This();
stackTop: ?*inc.ListNode(T) = null, //
stkSize: usize = 0, //
mem_arena: ?std.heap.ArenaAllocator = null,
mem_allocator: std.mem.Allocator = undefined, //
// +
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;
}
//
pub fn deinit(self: *Self) void {
if (self.mem_arena == null) return;
self.mem_arena.?.deinit();
}
//
pub fn size(self: *Self) usize {
return self.stkSize;
}
//
pub fn empty(self: *Self) bool {
return self.size() == 0;
}
// 访
pub fn top(self: *Self) T {
if (self.size() == 0) @panic("栈为空");
return self.stackTop.?.val;
}
//
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;
}
//
pub fn pop(self: *Self) T {
var num = self.top();
self.stackTop = self.stackTop.?.next;
self.stkSize -= 1;
return num;
}
//
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 {
//
var stack = LinkedListStack(i32){};
try stack.init(std.heap.page_allocator);
//
defer stack.deinit();
//
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
var top = stack.top();
std.debug.print("\n栈顶元素 top = {}", .{top});
//
top = stack.pop();
std.debug.print("\n出栈元素 pop = {},出栈后 stack = ", .{top});
inc.PrintUtil.printArray(i32, try stack.toArray());
//
var size = stack.size();
std.debug.print("\n栈的长度 size = {}", .{size});
//
var empty = stack.empty();
std.debug.print("\n栈是否为空 = {}", .{empty});
const getchar = try std.io.getStdIn().reader().readByte();
_ = getchar;
}

View file

@ -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 {
//
// zig ArrayList 使
var stack = std.ArrayList(i32).init(std.heap.page_allocator);
//
defer stack.deinit();
//
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
var top = stack.items[stack.items.len - 1];
std.debug.print("\n栈顶元素 top = {}", .{top});
//
top = stack.pop();
std.debug.print("\n出栈元素 pop = {},出栈后 stack = ", .{top});
inc.PrintUtil.printList(i32, stack);
//
var size = stack.items.len;
std.debug.print("\n栈的长度 size = {}", .{size});
//
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;
}

View file

@ -7,16 +7,42 @@ const ListNode = @import("ListNode.zig").ListNode;
const TreeNode = @import("TreeNode.zig").TreeNode;
// Print an array
//
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 "->" });
}
}

View file

@ -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 -

7
docker-compose.yml Normal file
View file

@ -0,0 +1,7 @@
version: '3'
services:
hello-algo:
build: .
ports:
- "8000:8000"

Binary file not shown.

After

Width:  |  Height:  |  Size: 69 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 89 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 66 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 69 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 81 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 89 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 85 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 94 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 87 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 96 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 69 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 66 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 81 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 84 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 85 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 85 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 64 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 80 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 113 KiB

798
docs/chapter_heap/heap.md Normal file
View file

@ -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)。
<p align="center"> Table. 堆的常用操作 </p>
<div class="center-table" markdown>
| 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 | $O(1)$ |
</div>
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<Integer> minHeap = new PriorityQueue<>();
// 初始化大顶堆(使用 lambda 表达式修改 Comparator 即可)
Queue<Integer> 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<Integer> 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<Integer> 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。

View file

@ -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。

View file

@ -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

View file

@ -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)。

View file

@ -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++)
{

View file

@ -18,16 +18,16 @@ comments: true
<div class="center-table" markdown>
| 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 | $O(1)$ |
</div>

View file

@ -20,13 +20,13 @@ comments: true
<div class="center-table" markdown>
| 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 | $O(1)$ |
</div>
@ -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

View file

@ -22,13 +22,13 @@ comments: true
<div class="center-table" markdown>
| 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 | $O(1)$ |
</div>
@ -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
}
}
```

View file

@ -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)

View file

@ -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 树会从底顶地执行旋转操作,使树恢复平衡。

View file

@ -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:
- 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