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Sort the coding languages by applications. (#721)

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Yudong Jin
2023-09-04 03:19:08 +08:00
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docs/chapter_dynamic_programming/dp_problem_features.md
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@@ -34,10 +34,10 @@ $$
根据状态转移方程，以及初始状态 $dp[1] = cost[1]$ 和 $dp[2] = cost[2]$ ，我们就可以得到动态规划代码。
=== "Java"
=== "Python"
```java title="min_cost_climbing_stairs_dp.java"
[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDP}
```python title="min_cost_climbing_stairs_dp.py"
[class]{}-[func]{min_cost_climbing_stairs_dp}
```
=== "C++"
@@ -46,10 +46,16 @@ $$
[class]{}-[func]{minCostClimbingStairsDP}
```
=== "Python"
=== "Java"
```python title="min_cost_climbing_stairs_dp.py"
[class]{}-[func]{min_cost_climbing_stairs_dp}
```java title="min_cost_climbing_stairs_dp.java"
[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDP}
```
=== "C#"
```csharp title="min_cost_climbing_stairs_dp.cs"
[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDP}
```
=== "Go"
@@ -58,6 +64,12 @@ $$
[class]{}-[func]{minCostClimbingStairsDP}
```
=== "Swift"
```swift title="min_cost_climbing_stairs_dp.swift"
[class]{}-[func]{minCostClimbingStairsDP}
```
=== "JS"
```javascript title="min_cost_climbing_stairs_dp.js"
@@ -70,30 +82,6 @@ $$
[class]{}-[func]{minCostClimbingStairsDP}
```
=== "C"
```c title="min_cost_climbing_stairs_dp.c"
[class]{}-[func]{minCostClimbingStairsDP}
```
=== "C#"
```csharp title="min_cost_climbing_stairs_dp.cs"
[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDP}
```
=== "Swift"
```swift title="min_cost_climbing_stairs_dp.swift"
[class]{}-[func]{minCostClimbingStairsDP}
```
=== "Zig"
```zig title="min_cost_climbing_stairs_dp.zig"
[class]{}-[func]{minCostClimbingStairsDP}
```
=== "Dart"
```dart title="min_cost_climbing_stairs_dp.dart"
@@ -106,16 +94,28 @@ $$
[class]{}-[func]{min_cost_climbing_stairs_dp}
```
=== "C"
```c title="min_cost_climbing_stairs_dp.c"
[class]{}-[func]{minCostClimbingStairsDP}
```
=== "Zig"
```zig title="min_cost_climbing_stairs_dp.zig"
[class]{}-[func]{minCostClimbingStairsDP}
```
下图展示了以上代码的动态规划过程。
![爬楼梯最小代价的动态规划过程](dp_problem_features.assets/min_cost_cs_dp.png)
本题也可以进行空间优化，将一维压缩至零维，使得空间复杂度从 $O(n)$ 降低至 $O(1)$ 。
=== "Java"
=== "Python"
```java title="min_cost_climbing_stairs_dp.java"
[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDPComp}
```python title="min_cost_climbing_stairs_dp.py"
[class]{}-[func]{min_cost_climbing_stairs_dp_comp}
```
=== "C++"
@@ -124,10 +124,16 @@ $$
[class]{}-[func]{minCostClimbingStairsDPComp}
```
=== "Python"
=== "Java"
```python title="min_cost_climbing_stairs_dp.py"
[class]{}-[func]{min_cost_climbing_stairs_dp_comp}
```java title="min_cost_climbing_stairs_dp.java"
[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDPComp}
```
=== "C#"
```csharp title="min_cost_climbing_stairs_dp.cs"
[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDPComp}
```
=== "Go"
@@ -136,6 +142,12 @@ $$
[class]{}-[func]{minCostClimbingStairsDPComp}
```
=== "Swift"
```swift title="min_cost_climbing_stairs_dp.swift"
[class]{}-[func]{minCostClimbingStairsDPComp}
```
=== "JS"
```javascript title="min_cost_climbing_stairs_dp.js"
@@ -148,30 +160,6 @@ $$
[class]{}-[func]{minCostClimbingStairsDPComp}
```
=== "C"
```c title="min_cost_climbing_stairs_dp.c"
[class]{}-[func]{minCostClimbingStairsDPComp}
```
=== "C#"
```csharp title="min_cost_climbing_stairs_dp.cs"
[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDPComp}
```
=== "Swift"
```swift title="min_cost_climbing_stairs_dp.swift"
[class]{}-[func]{minCostClimbingStairsDPComp}
```
=== "Zig"
```zig title="min_cost_climbing_stairs_dp.zig"
[class]{}-[func]{minCostClimbingStairsDPComp}
```
=== "Dart"
```dart title="min_cost_climbing_stairs_dp.dart"
@@ -184,6 +172,18 @@ $$
[class]{}-[func]{min_cost_climbing_stairs_dp_comp}
```
=== "C"
```c title="min_cost_climbing_stairs_dp.c"
[class]{}-[func]{minCostClimbingStairsDPComp}
```
=== "Zig"
```zig title="min_cost_climbing_stairs_dp.zig"
[class]{}-[func]{minCostClimbingStairsDPComp}
```
## 无后效性
无后效性是动态规划能够有效解决问题的重要特性之一，定义为：**给定一个确定的状态，它的未来发展只与当前状态有关，而与当前状态过去所经历过的所有状态无关**。
@@ -222,10 +222,10 @@ $$
最终，返回 $dp[n, 1] + dp[n, 2]$ 即可，两者之和代表爬到第 $n$ 阶的方案总数。
=== "Java"
=== "Python"
```java title="climbing_stairs_constraint_dp.java"
[class]{climbing_stairs_constraint_dp}-[func]{climbingStairsConstraintDP}
```python title="climbing_stairs_constraint_dp.py"
[class]{}-[func]{climbing_stairs_constraint_dp}
```
=== "C++"
@@ -234,10 +234,16 @@ $$
[class]{}-[func]{climbingStairsConstraintDP}
```
=== "Python"
=== "Java"
```python title="climbing_stairs_constraint_dp.py"
[class]{}-[func]{climbing_stairs_constraint_dp}
```java title="climbing_stairs_constraint_dp.java"
[class]{climbing_stairs_constraint_dp}-[func]{climbingStairsConstraintDP}
```
=== "C#"
```csharp title="climbing_stairs_constraint_dp.cs"
[class]{climbing_stairs_constraint_dp}-[func]{climbingStairsConstraintDP}
```
=== "Go"
@@ -246,6 +252,12 @@ $$
[class]{}-[func]{climbingStairsConstraintDP}
```
=== "Swift"
```swift title="climbing_stairs_constraint_dp.swift"
[class]{}-[func]{climbingStairsConstraintDP}
```
=== "JS"
```javascript title="climbing_stairs_constraint_dp.js"
@@ -258,30 +270,6 @@ $$
[class]{}-[func]{climbingStairsConstraintDP}
```
=== "C"
```c title="climbing_stairs_constraint_dp.c"
[class]{}-[func]{climbingStairsConstraintDP}
```
=== "C#"
```csharp title="climbing_stairs_constraint_dp.cs"
[class]{climbing_stairs_constraint_dp}-[func]{climbingStairsConstraintDP}
```
=== "Swift"
```swift title="climbing_stairs_constraint_dp.swift"
[class]{}-[func]{climbingStairsConstraintDP}
```
=== "Zig"
```zig title="climbing_stairs_constraint_dp.zig"
[class]{}-[func]{climbingStairsConstraintDP}
```
=== "Dart"
```dart title="climbing_stairs_constraint_dp.dart"
@@ -294,6 +282,18 @@ $$
[class]{}-[func]{climbing_stairs_constraint_dp}
```
=== "C"
```c title="climbing_stairs_constraint_dp.c"
[class]{}-[func]{climbingStairsConstraintDP}
```
=== "Zig"
```zig title="climbing_stairs_constraint_dp.zig"
[class]{}-[func]{climbingStairsConstraintDP}
```
在上面的案例中，由于仅需多考虑前面一个状态，我们仍然可以通过扩展状态定义，使得问题重新满足无后效性。然而，某些问题具有非常严重的“有后效性”。
!!! question "爬楼梯与障碍生成"