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krahets 1 year ago
parent e17d618f13
commit 53a75deff4
4 changed files with 199 additions and 15 deletions
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51
chapter_dynamic_programming/dp_problem_features.md
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@ -123,7 +123,22 @@ $$
=== "C#"
```csharp title="min_cost_climbing_stairs_dp.cs"
[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDP}
/* 爬楼梯最小代价：动态规划 */
int minCostClimbingStairsDP(int[] cost) {
int n = cost.Length - 1;
if (n == 1 || n == 2)
return cost[n];
// 初始化 dp 列表，用于存储子问题的解
int[] dp = new int[n + 1];
// 初始状态：预设最小子问题的解
dp[1] = cost[1];
dp[2] = cost[2];
// 状态转移：从较小子问题逐步求解较大子问题
for (int i = 3; i <= n; i++) {
dp[i] = Math.Min(dp[i - 1], dp[i - 2]) + cost[i];
}
return dp[n];
}
```
=== "Swift"
@ -227,7 +242,19 @@ $$
=== "C#"
```csharp title="min_cost_climbing_stairs_dp.cs"
[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDPComp}
/* 爬楼梯最小代价：状态压缩后的动态规划 */
int minCostClimbingStairsDPComp(int[] cost) {
int n = cost.Length - 1;
if (n == 1 || n == 2)
return cost[n];
int a = cost[1], b = cost[2];
for (int i = 3; i <= n; i++) {
int tmp = b;
b = Math.Min(a, tmp) + cost[i];
a = tmp;
}
return b;
}
```
=== "Swift"
@ -384,7 +411,25 @@ $$
=== "C#"
```csharp title="climbing_stairs_constraint_dp.cs"
[class]{climbing_stairs_constraint_dp}-[func]{climbingStairsConstraintDP}
/* 带约束爬楼梯：动态规划 */
int climbingStairsConstraintDP(int n) {
if (n == 1 || n == 2) {
return n;
}
// 初始化 dp 列表，用于存储子问题的解
int[,] dp = new int[n + 1, 3];
// 初始状态：预设最小子问题的解
dp[1, 1] = 1;
dp[1, 2] = 0;
dp[2, 1] = 0;
dp[2, 2] = 1;
// 状态转移：从较小子问题逐步求解较大子问题
for (int i = 3; i <= n; i++) {
dp[i, 1] = dp[i - 1, 2];
dp[i, 2] = dp[i - 2, 1] + dp[i - 2, 2];
}
return dp[n, 1] + dp[n, 2];
}
```
=== "Swift"

92
chapter_dynamic_programming/intro_to_dynamic_programming.md
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@ -140,9 +140,30 @@ comments: true
=== "C#"
```csharp title="climbing_stairs_backtrack.cs"
[class]{climbing_stairs_backtrack}-[func]{backtrack}
/* 回溯 */
void backtrack(List<int> choices, int state, int n, List<int> res) {
// 当爬到第 n 阶时，方案数量加 1
if (state == n)
res[0]++;
// 遍历所有选择
foreach (int choice in choices) {
// 剪枝：不允许越过第 n 阶
if (state + choice > n)
break;
// 尝试：做出选择，更新状态
backtrack(choices, state + choice, n, res);
// 回退
}
}
[class]{climbing_stairs_backtrack}-[func]{climbingStairsBacktrack}
/* 爬楼梯：回溯 */
int climbingStairsBacktrack(int n) {
List<int> choices = new List<int> { 1, 2 }; // 可选择向上爬 1 或 2 阶
int state = 0; // 从第 0 阶开始爬
List<int> res = new List<int> { 0 }; // 使用 res[0] 记录方案数量
backtrack(choices, state, n, res);
return res[0];
}
```
=== "Swift"
@ -285,9 +306,20 @@ $$
=== "C#"
```csharp title="climbing_stairs_dfs.cs"
[class]{climbing_stairs_dfs}-[func]{dfs}
/* 搜索 */
int dfs(int i) {
// 已知 dp[1] 和 dp[2] ，返回之
if (i == 1 || i == 2)
return i;
// dp[i] = dp[i-1] + dp[i-2]
int count = dfs(i - 1) + dfs(i - 2);
return count;
}
[class]{climbing_stairs_dfs}-[func]{climbingStairsDFS}
/* 爬楼梯：搜索 */
int climbingStairsDFS(int n) {
return dfs(n);
}
```
=== "Swift"
@ -441,9 +473,28 @@ $$
=== "C#"
```csharp title="climbing_stairs_dfs_mem.cs"
[class]{climbing_stairs_dfs_mem}-[func]{dfs}
/* 记忆化搜索 */
int dfs(int i, int[] mem) {
// 已知 dp[1] 和 dp[2] ，返回之
if (i == 1 || i == 2)
return i;
// 若存在记录 dp[i] ，则直接返回之
if (mem[i] != -1)
return mem[i];
// dp[i] = dp[i-1] + dp[i-2]
int count = dfs(i - 1, mem) + dfs(i - 2, mem);
// 记录 dp[i]
mem[i] = count;
return count;
}
[class]{climbing_stairs_dfs_mem}-[func]{climbingStairsDFSMem}
/* 爬楼梯：记忆化搜索 */
int climbingStairsDFSMem(int n) {
// mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
int[] mem = new int[n + 1];
Array.Fill(mem, -1);
return dfs(n, mem);
}
```
=== "Swift"
@ -568,7 +619,21 @@ $$
=== "C#"
```csharp title="climbing_stairs_dp.cs"
[class]{climbing_stairs_dp}-[func]{climbingStairsDP}
/* 爬楼梯：动态规划 */
int climbingStairsDP(int n) {
if (n == 1 || n == 2)
return n;
// 初始化 dp 列表，用于存储子问题的解
int[] dp = new int[n + 1];
// 初始状态：预设最小子问题的解
dp[1] = 1;
dp[2] = 2;
// 状态转移：从较小子问题逐步求解较大子问题
for (int i = 3; i <= n; i++) {
dp[i] = dp[i - 1] + dp[i - 2];
}
return dp[n];
}
```
=== "Swift"
@ -675,7 +740,18 @@ $$
=== "C#"
```csharp title="climbing_stairs_dp.cs"
[class]{climbing_stairs_dp}-[func]{climbingStairsDPComp}
/* 爬楼梯：状态压缩后的动态规划 */
int climbingStairsDPComp(int n) {
if (n == 1 || n == 2)
return n;
int a = 1, b = 2;
for (int i = 3; i <= n; i++) {
int tmp = b;
b = a + b;
a = tmp;
}
return b;
}
```
=== "Swift"

70
chapter_hashing/hash_algorithm.md
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@ -309,13 +309,53 @@ index = hash(key) % capacity
=== "Swift"
```swift title="simple_hash.swift"
[class]{}-[func]{addHash}
/* 加法哈希 */
func addHash(key: String) -> Int {
var hash = 0
let MODULUS = 1_000_000_007
for c in key {
for scalar in c.unicodeScalars {
hash = (hash + Int(scalar.value)) % MODULUS
}
}
return hash
}
[class]{}-[func]{mulHash}
/* 乘法哈希 */
func mulHash(key: String) -> Int {
var hash = 0
let MODULUS = 1_000_000_007
for c in key {
for scalar in c.unicodeScalars {
hash = (31 * hash + Int(scalar.value)) % MODULUS
}
}
return hash
}
[class]{}-[func]{xorHash}
/* 异或哈希 */
func xorHash(key: String) -> Int {
var hash = 0
let MODULUS = 1_000_000_007
for c in key {
for scalar in c.unicodeScalars {
hash ^= Int(scalar.value)
}
}
return hash & MODULUS
}
[class]{}-[func]{rotHash}
/* 旋转哈希 */
func rotHash(key: String) -> Int {
var hash = 0
let MODULUS = 1_000_000_007
for c in key {
for scalar in c.unicodeScalars {
hash = ((hash << 4) ^ (hash >> 28) ^ Int(scalar.value)) % MODULUS
}
}
return hash
}
```
=== "Zig"
@ -533,7 +573,29 @@ $$
=== "Swift"
```swift title="built_in_hash.swift"
let num = 3
let hashNum = num.hashValue
// 整数 3 的哈希值为 9047044699613009734
let bol = true
let hashBol = bol.hashValue
// 布尔量 true 的哈希值为 -4431640247352757451
let dec = 3.14159
let hashDec = dec.hashValue
// 小数 3.14159 的哈希值为 -2465384235396674631
let str = "Hello 算法"
let hashStr = str.hashValue
// 字符串 Hello 算法 的哈希值为 -7850626797806988787
let arr = [AnyHashable(12836), AnyHashable("小哈")]
let hashTup = arr.hashValue
// 数组 [AnyHashable(12836), AnyHashable("小哈")] 的哈希值为 -2308633508154532996
let obj = ListNode(x: 0)
let hashObj = obj.hashValue
// 节点对象 utils.ListNode 的哈希值为 -2434780518035996159
```
=== "Zig"

1
index.md
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@ -113,6 +113,7 @@ hide:
<tbody>
<td align="center"><a href="https://github.com/Gonglja"><img src="https://avatars.githubusercontent.com/u/39959756?v=4" width="50px;" alt="Gonglja"/><br /><sub><b>Gonglja</b></sub></a><br /><sub>C / C++</sub></td>
<td align="center"><a href="https://github.com/gvenusleo"><img src="https://avatars.githubusercontent.com/u/79075347?v=4" width="50px;" alt="gvenusleo"/><br /><sub><b>gvenusleo</b></sub></a><br /><sub>Dart</sub></td>
<td align="center"><a href="https://github.com/hpstory"><img src="https://avatars.githubusercontent.com/u/33348162?v=4" width="50px;" alt="hpstory"/><br /><sub><b>hpstory</b></sub></a><br /><sub>C#</sub></td>
<td align="center"><a href="https://github.com/justin-tse"><img src="https://avatars.githubusercontent.com/u/24556310?v=4" width="50px;" alt="justin-tse"/><br /><sub><b>justin-tse</b></sub></a><br /><sub>JS / TS</sub></td>
<td align="center"><a href="https://github.com/krahets"><img src="https://avatars.githubusercontent.com/u/26993056?v=4" width="50px;" alt="krahets"/><br /><sub><b>krahets</b></sub></a><br /><sub>Java / Python</sub></td>
<td align="center"><a href="https://github.com/nuomi1"><img src="https://avatars.githubusercontent.com/u/3739017?v=4" width="50px;" alt="nuomi1"/><br /><sub><b>nuomi1</b></sub></a><br /><sub>Swift</sub></td>

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