This commit is contained in:
krahets 2023-09-24 22:52:34 +08:00
parent 7f7d03924d
commit 9faf85b7a3
3 changed files with 94 additions and 71 deletions

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@ -987,7 +987,7 @@ status: new
以上述的求和函数为例,设问题 $f(n) = 1 + 2 + \dots + n$ 。
- **迭代**:在循环中模拟求和过程,从 $1$ 遍历到 $n$ ,每轮执行求和操作,即可求得 $f(n)$ 。
- **递归**:将问题分解为子问题 $f(n) = n + f(n-1)$ ,不断(递归地)分解下去,直至基本情况 $f(0) = 0$ 时终止。
- **递归**:将问题分解为子问题 $f(n) = n + f(n-1)$ ,不断(递归地)分解下去,直至基本情况 $f(1) = 1$ 时终止。
### 1.   调用栈
@ -1499,7 +1499,24 @@ status: new
=== "Swift"
```swift title="recursion.swift"
[class]{}-[func]{forLoopRecur}
/* 使用迭代模拟递归 */
func forLoopRecur(n: Int) -> Int {
// 使用一个显式的栈来模拟系统调用栈
var stack: [Int] = []
var res = 0
// 递:递归调用
for i in stride(from: n, to: 0, by: -1) {
// 通过“入栈操作”模拟“递”
stack.append(i)
}
// 归:返回结果
while !stack.isEmpty {
// 通过“出栈操作”模拟“归”
res += stack.removeLast()
}
// res = 1+2+3+...+n
return res
}
```
=== "JS"

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@ -155,8 +155,8 @@ $$
// 初始化 dp 表,用于存储子问题的解
var dp = Array(repeating: 0, count: n + 1)
// 初始状态:预设最小子问题的解
dp[1] = 1
dp[2] = 2
dp[1] = cost[1]
dp[2] = cost[2]
// 状态转移:从较小子问题逐步求解较大子问题
for i in stride(from: 3, through: n, by: 1) {
dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]

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@ -35,7 +35,7 @@ comments: true
以下代码给出了链式地址哈希表的简单实现,需要注意两点。
- 使用列表(动态数组)代替链表,从而简化代码。在这种设定下,哈希表(数组)包含多个桶,每个桶都是一个列表。
- 以下实现包含哈希表扩容方法。当负载因子超过 $0.75$ 时,我们将哈希表扩容至 $2$ 倍。
- 以下实现包含哈希表扩容方法。当负载因子超过 $\frac{2}{3}$ 时,我们将哈希表扩容至 $2$ 倍。
=== "Python"
@ -47,7 +47,7 @@ comments: true
"""构造方法"""
self.size = 0 # 键值对数量
self.capacity = 4 # 哈希表容量
self.load_thres = 2 / 3 # 触发扩容的负载因子阈值
self.load_thres = 2.0 / 3.0 # 触发扩容的负载因子阈值
self.extend_ratio = 2 # 扩容倍数
self.buckets = [[] for _ in range(self.capacity)] # 桶数组
@ -134,7 +134,7 @@ comments: true
public:
/* 构造方法 */
HashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3), extendRatio(2) {
HashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3.0), extendRatio(2) {
buckets.resize(capacity);
}
@ -253,7 +253,7 @@ comments: true
public HashMapChaining() {
size = 0;
capacity = 4;
loadThres = 2 / 3.0;
loadThres = 2.0 / 3.0;
extendRatio = 2;
buckets = new ArrayList<>(capacity);
for (int i = 0; i < capacity; i++) {
@ -367,7 +367,7 @@ comments: true
public HashMapChaining() {
size = 0;
capacity = 4;
loadThres = 2 / 3.0;
loadThres = 2.0 / 3.0;
extendRatio = 2;
buckets = new List<List<Pair>>(capacity);
for (int i = 0; i < capacity; i++) {
@ -485,7 +485,7 @@ comments: true
return &hashMapChaining{
size: 0,
capacity: 4,
loadThres: 2 / 3.0,
loadThres: 2.0 / 3.0,
extendRatio: 2,
buckets: buckets,
}
@ -606,7 +606,7 @@ comments: true
init() {
size = 0
capacity = 4
loadThres = 2 / 3
loadThres = 2.0 / 3.0
extendRatio = 2
buckets = Array(repeating: [], count: capacity)
}
@ -710,7 +710,7 @@ comments: true
constructor() {
this.#size = 0;
this.#capacity = 4;
this.#loadThres = 2 / 3.0;
this.#loadThres = 2.0 / 3.0;
this.#extendRatio = 2;
this.#buckets = new Array(this.#capacity).fill(null).map((x) => []);
}
@ -818,7 +818,7 @@ comments: true
constructor() {
this.#size = 0;
this.#capacity = 4;
this.#loadThres = 2 / 3.0;
this.#loadThres = 2.0 / 3.0;
this.#extendRatio = 2;
this.#buckets = new Array(this.#capacity).fill(null).map((x) => []);
}
@ -926,7 +926,7 @@ comments: true
HashMapChaining() {
size = 0;
capacity = 4;
loadThres = 2 / 3.0;
loadThres = 2.0 / 3.0;
extendRatio = 2;
buckets = List.generate(capacity, (_) => []);
}
@ -1173,7 +1173,7 @@ comments: true
hashmap->capacity = tableSize;
hashmap->size = 0;
hashmap->extendRatio = 2;
hashmap->loadThres = 2.0 / 3;
hashmap->loadThres = 2.0 / 3.0;
return hashmap;
}
@ -1377,7 +1377,7 @@ comments: true
"""构造方法"""
self.size = 0 # 键值对数量
self.capacity = 4 # 哈希表容量
self.load_thres = 2 / 3 # 触发扩容的负载因子阈值
self.load_thres = 2.0 / 3.0 # 触发扩容的负载因子阈值
self.extend_ratio = 2 # 扩容倍数
self.buckets: list[Pair | None] = [None] * self.capacity # 桶数组
self.TOMBSTONE = Pair(-1, "-1") # 删除标记
@ -1478,7 +1478,7 @@ comments: true
private:
int size; // 键值对数量
int capacity = 4; // 哈希表容量
const double loadThres = 2.0 / 3; // 触发扩容的负载因子阈值
const double loadThres = 2.0 / 3.0; // 触发扩容的负载因子阈值
const int extendRatio = 2; // 扩容倍数
vector<Pair *> buckets; // 桶数组
Pair *TOMBSTONE = new Pair(-1, "-1"); // 删除标记
@ -1616,7 +1616,7 @@ comments: true
class HashMapOpenAddressing {
private int size; // 键值对数量
private int capacity = 4; // 哈希表容量
private final double loadThres = 2.0 / 3; // 触发扩容的负载因子阈值
private final double loadThres = 2.0 / 3.0; // 触发扩容的负载因子阈值
private final int extendRatio = 2; // 扩容倍数
private Pair[] buckets; // 桶数组
private final Pair TOMBSTONE = new Pair(-1, "-1"); // 删除标记
@ -1743,7 +1743,7 @@ comments: true
class HashMapOpenAddressing {
private int size; // 键值对数量
private int capacity = 4; // 哈希表容量
private double loadThres = 2.0 / 3; // 触发扩容的负载因子阈值
private double loadThres = 2.0 / 3.0; // 触发扩容的负载因子阈值
private int extendRatio = 2; // 扩容倍数
private Pair[] buckets; // 桶数组
private Pair TOMBSTONE = new Pair(-1, "-1"); // 删除标记
@ -1882,7 +1882,7 @@ comments: true
return &hashMapOpenAddressing{
size: 0,
capacity: 4,
loadThres: 2 / 3.0,
loadThres: 2.0 / 3.0,
extendRatio: 2,
buckets: buckets,
removed: pair{
@ -2009,16 +2009,16 @@ comments: true
var loadThres: Double // 触发扩容的负载因子阈值
var extendRatio: Int // 扩容倍数
var buckets: [Pair?] // 桶数组
var removed: Pair // 删除标记
var TOMBSTONE: Pair // 删除标记
/* 构造方法 */
init() {
size = 0
capacity = 4
loadThres = 2 / 3
loadThres = 2.0 / 3.0
extendRatio = 2
buckets = Array(repeating: nil, count: capacity)
removed = Pair(key: -1, val: "-1")
TOMBSTONE = Pair(key: -1, val: "-1")
}
/* 哈希函数 */
@ -2031,22 +2031,42 @@ comments: true
Double(size / capacity)
}
/* 搜索 key 对应的桶索引 */
func findBucket(key: Int) -> Int {
var index = hashFunc(key: key)
var firstTombstone = -1
// 线性探测,当遇到空桶时跳出
while buckets[index] != nil {
// 若遇到 key ,返回对应桶索引
if buckets[index]!.key == key {
// 若之前遇到了删除标记,则将键值对移动至该索引
if firstTombstone != -1 {
buckets[firstTombstone] = buckets[index]
buckets[index] = TOMBSTONE
return firstTombstone // 返回移动后的桶索引
}
return index // 返回桶索引
}
// 记录遇到的首个删除标记
if firstTombstone == -1 && buckets[index] == TOMBSTONE {
firstTombstone = index
}
// 计算桶索引,越过尾部返回头部
index = (index + 1) % capacity
}
// 若 key 不存在,则返回添加点的索引
return firstTombstone == -1 ? index : firstTombstone
}
/* 查询操作 */
func get(key: Int) -> String? {
let index = hashFunc(key: key)
// 线性探测,从 index 开始向后遍历
for i in stride(from: 0, to: capacity, by: 1) {
// 计算桶索引,越过尾部返回头部
let j = (index + i) % capacity
// 若遇到空桶,说明无此 key ,则返回 nil
if buckets[j] == nil {
return nil
}
// 若遇到指定 key ,则返回对应 val
if buckets[j]?.key == key, buckets[j] != removed {
return buckets[j]?.val
}
// 搜索 key 对应的桶索引
let index = findBucket(key: key)
// 若找到键值对,则返回对应 val
if buckets[index] != nil, buckets[index] != TOMBSTONE {
return buckets[index]!.val
}
// 若键值对不存在,则返回 null
return nil
}
@ -2056,42 +2076,26 @@ comments: true
if loadFactor() > loadThres {
extend()
}
let index = hashFunc(key: key)
// 线性探测,从 index 开始向后遍历
for i in stride(from: 0, through: capacity, by: 1) {
// 计算桶索引,越过尾部返回头部
let j = (index + i) % capacity
// 若遇到空桶、或带有删除标记的桶,则将键值对放入该桶
if buckets[j] == nil || buckets[j] == removed {
buckets[j] = Pair(key: key, val: val)
size += 1
return
}
// 若遇到指定 key ,则更新对应 val
if buckets[j]?.key == key {
buckets[j]?.val = val
return
}
// 搜索 key 对应的桶索引
let index = findBucket(key: key)
// 若找到键值对,则覆盖 val 并返回
if buckets[index] != nil, buckets[index] != TOMBSTONE {
buckets[index]!.val = val
return
}
// 若键值对不存在,则添加该键值对
buckets[index] = Pair(key: key, val: val)
size += 1
}
/* 删除操作 */
func remove(key: Int) {
let index = hashFunc(key: key)
// 线性探测,从 index 开始向后遍历
for i in stride(from: 0, to: capacity, by: 1) {
// 计算桶索引,越过尾部返回头部
let j = (index + i) % capacity
// 若遇到空桶,说明无此 key ,则直接返回
if buckets[j] == nil {
return
}
// 若遇到指定 key ,则标记删除并返回
if buckets[j]?.key == key {
buckets[j] = removed
size -= 1
return
}
// 搜索 key 对应的桶索引
let index = findBucket(key: key)
// 若找到键值对,则用删除标记覆盖它
if buckets[index] != nil, buckets[index] != TOMBSTONE {
buckets[index] = TOMBSTONE
size -= 1
}
}
@ -2105,7 +2109,7 @@ comments: true
size = 0
// 将键值对从原哈希表搬运至新哈希表
for pair in bucketsTmp {
if let pair, pair != removed {
if let pair, pair != TOMBSTONE {
put(key: pair.key, val: pair.val)
}
}
@ -2114,10 +2118,12 @@ comments: true
/* 打印哈希表 */
func print() {
for pair in buckets {
if let pair {
Swift.print("\(pair.key) -> \(pair.val)")
} else {
if pair == nil {
Swift.print("null")
} else if pair == TOMBSTONE {
Swift.print("TOMBSTONE")
} else {
Swift.print("\(pair!.key) -> \(pair!.val)")
}
}
}