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Squash the language code blocks and fix list.md (#865)
This commit is contained in:
Yudong Jin
@ -34,77 +34,9 @@ $$
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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。
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=== "Python"
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```python title="min_cost_climbing_stairs_dp.py"
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[class]{}-[func]{min_cost_climbing_stairs_dp}
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```
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=== "C++"
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```cpp title="min_cost_climbing_stairs_dp.cpp"
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[class]{}-[func]{minCostClimbingStairsDP}
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```
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=== "Java"
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```java title="min_cost_climbing_stairs_dp.java"
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[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDP}
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```
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=== "C#"
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```csharp title="min_cost_climbing_stairs_dp.cs"
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[class]{min_cost_climbing_stairs_dp}-[func]{MinCostClimbingStairsDP}
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```
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=== "Go"
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```go title="min_cost_climbing_stairs_dp.go"
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[class]{}-[func]{minCostClimbingStairsDP}
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```
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=== "Swift"
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```swift title="min_cost_climbing_stairs_dp.swift"
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[class]{}-[func]{minCostClimbingStairsDP}
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```
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=== "JS"
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```javascript title="min_cost_climbing_stairs_dp.js"
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[class]{}-[func]{minCostClimbingStairsDP}
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```
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=== "TS"
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```typescript title="min_cost_climbing_stairs_dp.ts"
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[class]{}-[func]{minCostClimbingStairsDP}
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```
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=== "Dart"
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```dart title="min_cost_climbing_stairs_dp.dart"
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[class]{}-[func]{minCostClimbingStairsDP}
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```
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=== "Rust"
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```rust title="min_cost_climbing_stairs_dp.rs"
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[class]{}-[func]{min_cost_climbing_stairs_dp}
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```
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=== "C"
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```c title="min_cost_climbing_stairs_dp.c"
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[class]{}-[func]{minCostClimbingStairsDP}
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```
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=== "Zig"
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```zig title="min_cost_climbing_stairs_dp.zig"
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[class]{}-[func]{minCostClimbingStairsDP}
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```
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```src
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[file]{min_cost_climbing_stairs_dp}-[class]{}-[func]{min_cost_climbing_stairs_dp}
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```
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下图展示了以上代码的动态规划过程。
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@ -112,77 +44,9 @@ $$
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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 $O(1)$ 。
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=== "Python"
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```python title="min_cost_climbing_stairs_dp.py"
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[class]{}-[func]{min_cost_climbing_stairs_dp_comp}
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```
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=== "C++"
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```cpp title="min_cost_climbing_stairs_dp.cpp"
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[class]{}-[func]{minCostClimbingStairsDPComp}
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```
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=== "Java"
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```java title="min_cost_climbing_stairs_dp.java"
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[class]{min_cost_climbing_stairs_dp}-[func]{minCostClimbingStairsDPComp}
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```
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=== "C#"
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```csharp title="min_cost_climbing_stairs_dp.cs"
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[class]{min_cost_climbing_stairs_dp}-[func]{MinCostClimbingStairsDPComp}
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```
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=== "Go"
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```go title="min_cost_climbing_stairs_dp.go"
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[class]{}-[func]{minCostClimbingStairsDPComp}
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```
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=== "Swift"
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```swift title="min_cost_climbing_stairs_dp.swift"
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[class]{}-[func]{minCostClimbingStairsDPComp}
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```
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=== "JS"
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```javascript title="min_cost_climbing_stairs_dp.js"
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[class]{}-[func]{minCostClimbingStairsDPComp}
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```
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=== "TS"
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```typescript title="min_cost_climbing_stairs_dp.ts"
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[class]{}-[func]{minCostClimbingStairsDPComp}
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```
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=== "Dart"
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```dart title="min_cost_climbing_stairs_dp.dart"
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[class]{}-[func]{minCostClimbingStairsDPComp}
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```
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=== "Rust"
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```rust title="min_cost_climbing_stairs_dp.rs"
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[class]{}-[func]{min_cost_climbing_stairs_dp_comp}
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```
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=== "C"
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```c title="min_cost_climbing_stairs_dp.c"
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[class]{}-[func]{minCostClimbingStairsDPComp}
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```
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=== "Zig"
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```zig title="min_cost_climbing_stairs_dp.zig"
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[class]{}-[func]{minCostClimbingStairsDPComp}
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```
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```src
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[file]{min_cost_climbing_stairs_dp}-[class]{}-[func]{min_cost_climbing_stairs_dp_comp}
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```
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## 无后效性
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@ -222,77 +86,9 @@ $$
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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。
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=== "Python"
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```python title="climbing_stairs_constraint_dp.py"
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[class]{}-[func]{climbing_stairs_constraint_dp}
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```
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=== "C++"
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```cpp title="climbing_stairs_constraint_dp.cpp"
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[class]{}-[func]{climbingStairsConstraintDP}
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```
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=== "Java"
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```java title="climbing_stairs_constraint_dp.java"
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[class]{climbing_stairs_constraint_dp}-[func]{climbingStairsConstraintDP}
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```
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=== "C#"
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```csharp title="climbing_stairs_constraint_dp.cs"
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[class]{climbing_stairs_constraint_dp}-[func]{ClimbingStairsConstraintDP}
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```
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=== "Go"
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```go title="climbing_stairs_constraint_dp.go"
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[class]{}-[func]{climbingStairsConstraintDP}
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```
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=== "Swift"
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```swift title="climbing_stairs_constraint_dp.swift"
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[class]{}-[func]{climbingStairsConstraintDP}
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```
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=== "JS"
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```javascript title="climbing_stairs_constraint_dp.js"
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[class]{}-[func]{climbingStairsConstraintDP}
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```
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=== "TS"
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```typescript title="climbing_stairs_constraint_dp.ts"
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[class]{}-[func]{climbingStairsConstraintDP}
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```
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=== "Dart"
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```dart title="climbing_stairs_constraint_dp.dart"
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[class]{}-[func]{climbingStairsConstraintDP}
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```
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=== "Rust"
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```rust title="climbing_stairs_constraint_dp.rs"
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[class]{}-[func]{climbing_stairs_constraint_dp}
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```
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=== "C"
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```c title="climbing_stairs_constraint_dp.c"
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[class]{}-[func]{climbingStairsConstraintDP}
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```
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=== "Zig"
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```zig title="climbing_stairs_constraint_dp.zig"
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[class]{}-[func]{climbingStairsConstraintDP}
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```
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```src
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[file]{climbing_stairs_constraint_dp}-[class]{}-[func]{climbing_stairs_constraint_dp}
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```
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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”。
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@ -98,77 +98,9 @@ $$
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- **终止条件**：当 $i = 0$ 且 $j = 0$ 时，返回代价 $grid[0, 0]$ 。
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- **剪枝**：当 $i < 0$ 时或 $j < 0$ 时索引越界，此时返回代价 $+\infty$ ，代表不可行。
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=== "Python"
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```python title="min_path_sum.py"
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[class]{}-[func]{min_path_sum_dfs}
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```
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=== "C++"
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```cpp title="min_path_sum.cpp"
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[class]{}-[func]{minPathSumDFS}
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```
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=== "Java"
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```java title="min_path_sum.java"
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[class]{min_path_sum}-[func]{minPathSumDFS}
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```
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=== "C#"
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```csharp title="min_path_sum.cs"
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[class]{min_path_sum}-[func]{MinPathSumDFS}
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```
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=== "Go"
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```go title="min_path_sum.go"
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[class]{}-[func]{minPathSumDFS}
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```
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=== "Swift"
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```swift title="min_path_sum.swift"
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[class]{}-[func]{minPathSumDFS}
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```
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=== "JS"
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```javascript title="min_path_sum.js"
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[class]{}-[func]{minPathSumDFS}
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```
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=== "TS"
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```typescript title="min_path_sum.ts"
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[class]{}-[func]{minPathSumDFS}
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```
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|
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=== "Dart"
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||||
|
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```dart title="min_path_sum.dart"
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[class]{}-[func]{minPathSumDFS}
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```
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|
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=== "Rust"
|
||||
|
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```rust title="min_path_sum.rs"
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[class]{}-[func]{min_path_sum_dfs}
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```
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|
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=== "C"
|
||||
|
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```c title="min_path_sum.c"
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[class]{}-[func]{minPathSumDFS}
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```
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|
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=== "Zig"
|
||||
|
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```zig title="min_path_sum.zig"
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[class]{}-[func]{minPathSumDFS}
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```
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```src
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[file]{min_path_sum}-[class]{}-[func]{min_path_sum_dfs}
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```
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下图给出了以 $dp[2, 1]$ 为根节点的递归树，其中包含一些重叠子问题，其数量会随着网格 `grid` 的尺寸变大而急剧增多。
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@ -182,77 +114,9 @@ $$
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我们引入一个和网格 `grid` 相同尺寸的记忆列表 `mem` ，用于记录各个子问题的解，并将重叠子问题进行剪枝。
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=== "Python"
|
||||
|
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```python title="min_path_sum.py"
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||||
[class]{}-[func]{min_path_sum_dfs_mem}
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```
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=== "C++"
|
||||
|
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```cpp title="min_path_sum.cpp"
|
||||
[class]{}-[func]{minPathSumDFSMem}
|
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```
|
||||
|
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=== "Java"
|
||||
|
||||
```java title="min_path_sum.java"
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[class]{min_path_sum}-[func]{minPathSumDFSMem}
|
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```
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|
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=== "C#"
|
||||
|
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```csharp title="min_path_sum.cs"
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[class]{min_path_sum}-[func]{MinPathSumDFSMem}
|
||||
```
|
||||
|
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=== "Go"
|
||||
|
||||
```go title="min_path_sum.go"
|
||||
[class]{}-[func]{minPathSumDFSMem}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="min_path_sum.swift"
|
||||
[class]{}-[func]{minPathSumDFSMem}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="min_path_sum.js"
|
||||
[class]{}-[func]{minPathSumDFSMem}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="min_path_sum.ts"
|
||||
[class]{}-[func]{minPathSumDFSMem}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="min_path_sum.dart"
|
||||
[class]{}-[func]{minPathSumDFSMem}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="min_path_sum.rs"
|
||||
[class]{}-[func]{min_path_sum_dfs_mem}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="min_path_sum.c"
|
||||
[class]{}-[func]{minPathSumDFSMem}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="min_path_sum.zig"
|
||||
[class]{}-[func]{minPathSumDFSMem}
|
||||
```
|
||||
```src
|
||||
[file]{min_path_sum}-[class]{}-[func]{min_path_sum_dfs_mem}
|
||||
```
|
||||
|
||||
如下图所示，在引入记忆化后，所有子问题的解只需计算一次，因此时间复杂度取决于状态总数，即网格尺寸 $O(nm)$ 。
|
||||
|
||||
@ -262,77 +126,9 @@ $$
|
||||
|
||||
基于迭代实现动态规划解法。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="min_path_sum.py"
|
||||
[class]{}-[func]{min_path_sum_dp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="min_path_sum.cpp"
|
||||
[class]{}-[func]{minPathSumDP}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="min_path_sum.java"
|
||||
[class]{min_path_sum}-[func]{minPathSumDP}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="min_path_sum.cs"
|
||||
[class]{min_path_sum}-[func]{MinPathSumDP}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="min_path_sum.go"
|
||||
[class]{}-[func]{minPathSumDP}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="min_path_sum.swift"
|
||||
[class]{}-[func]{minPathSumDP}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="min_path_sum.js"
|
||||
[class]{}-[func]{minPathSumDP}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="min_path_sum.ts"
|
||||
[class]{}-[func]{minPathSumDP}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="min_path_sum.dart"
|
||||
[class]{}-[func]{minPathSumDP}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="min_path_sum.rs"
|
||||
[class]{}-[func]{min_path_sum_dp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="min_path_sum.c"
|
||||
[class]{}-[func]{minPathSumDP}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="min_path_sum.zig"
|
||||
[class]{}-[func]{minPathSumDP}
|
||||
```
|
||||
```src
|
||||
[file]{min_path_sum}-[class]{}-[func]{min_path_sum_dp}
|
||||
```
|
||||
|
||||
下图展示了最小路径和的状态转移过程，其遍历了整个网格，**因此时间复杂度为 $O(nm)$** 。
|
||||
|
||||
@ -380,74 +176,6 @@ $$
|
||||
|
||||
请注意，因为数组 `dp` 只能表示一行的状态，所以我们无法提前初始化首列状态，而是在遍历每行中更新它。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="min_path_sum.py"
|
||||
[class]{}-[func]{min_path_sum_dp_comp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="min_path_sum.cpp"
|
||||
[class]{}-[func]{minPathSumDPComp}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="min_path_sum.java"
|
||||
[class]{min_path_sum}-[func]{minPathSumDPComp}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="min_path_sum.cs"
|
||||
[class]{min_path_sum}-[func]{MinPathSumDPComp}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="min_path_sum.go"
|
||||
[class]{}-[func]{minPathSumDPComp}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="min_path_sum.swift"
|
||||
[class]{}-[func]{minPathSumDPComp}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="min_path_sum.js"
|
||||
[class]{}-[func]{minPathSumDPComp}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="min_path_sum.ts"
|
||||
[class]{}-[func]{minPathSumDPComp}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="min_path_sum.dart"
|
||||
[class]{}-[func]{minPathSumDPComp}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="min_path_sum.rs"
|
||||
[class]{}-[func]{min_path_sum_dp_comp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="min_path_sum.c"
|
||||
[class]{}-[func]{minPathSumDPComp}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="min_path_sum.zig"
|
||||
[class]{}-[func]{minPathSumDPComp}
|
||||
```
|
||||
```src
|
||||
[file]{min_path_sum}-[class]{}-[func]{min_path_sum_dp_comp}
|
||||
```
|
||||
|
||||
@ -67,77 +67,9 @@ $$
|
||||
|
||||
### 代码实现
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="edit_distance.py"
|
||||
[class]{}-[func]{edit_distance_dp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="edit_distance.cpp"
|
||||
[class]{}-[func]{editDistanceDP}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="edit_distance.java"
|
||||
[class]{edit_distance}-[func]{editDistanceDP}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="edit_distance.cs"
|
||||
[class]{edit_distance}-[func]{EditDistanceDP}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="edit_distance.go"
|
||||
[class]{}-[func]{editDistanceDP}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="edit_distance.swift"
|
||||
[class]{}-[func]{editDistanceDP}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="edit_distance.js"
|
||||
[class]{}-[func]{editDistanceDP}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="edit_distance.ts"
|
||||
[class]{}-[func]{editDistanceDP}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="edit_distance.dart"
|
||||
[class]{}-[func]{editDistanceDP}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="edit_distance.rs"
|
||||
[class]{}-[func]{edit_distance_dp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="edit_distance.c"
|
||||
[class]{}-[func]{editDistanceDP}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="edit_distance.zig"
|
||||
[class]{}-[func]{editDistanceDP}
|
||||
```
|
||||
```src
|
||||
[file]{edit_distance}-[class]{}-[func]{edit_distance_dp}
|
||||
```
|
||||
|
||||
如下图所示，编辑距离问题的状态转移过程与背包问题非常类似，都可以看作是填写一个二维网格的过程。
|
||||
|
||||
@ -192,74 +124,6 @@ $$
|
||||
|
||||
为此，我们可以使用一个变量 `leftup` 来暂存左上方的解 $dp[i-1, j-1]$ ，从而只需考虑左方和上方的解。此时的情况与完全背包问题相同，可使用正序遍历。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="edit_distance.py"
|
||||
[class]{}-[func]{edit_distance_dp_comp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="edit_distance.cpp"
|
||||
[class]{}-[func]{editDistanceDPComp}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="edit_distance.java"
|
||||
[class]{edit_distance}-[func]{editDistanceDPComp}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="edit_distance.cs"
|
||||
[class]{edit_distance}-[func]{EditDistanceDPComp}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="edit_distance.go"
|
||||
[class]{}-[func]{editDistanceDPComp}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="edit_distance.swift"
|
||||
[class]{}-[func]{editDistanceDPComp}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="edit_distance.js"
|
||||
[class]{}-[func]{editDistanceDPComp}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="edit_distance.ts"
|
||||
[class]{}-[func]{editDistanceDPComp}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="edit_distance.dart"
|
||||
[class]{}-[func]{editDistanceDPComp}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="edit_distance.rs"
|
||||
[class]{}-[func]{edit_distance_dp_comp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="edit_distance.c"
|
||||
[class]{}-[func]{editDistanceDPComp}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="edit_distance.zig"
|
||||
[class]{}-[func]{editDistanceDPComp}
|
||||
```
|
||||
```src
|
||||
[file]{edit_distance}-[class]{}-[func]{edit_distance_dp_comp}
|
||||
```
|
||||
|
||||
@ -14,101 +14,9 @@
|
||||
|
||||
本题的目标是求解方案数量，**我们可以考虑通过回溯来穷举所有可能性**。具体来说，将爬楼梯想象为一个多轮选择的过程：从地面出发，每轮选择上 $1$ 阶或 $2$ 阶，每当到达楼梯顶部时就将方案数量加 $1$ ，当越过楼梯顶部时就将其剪枝。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="climbing_stairs_backtrack.py"
|
||||
[class]{}-[func]{backtrack}
|
||||
|
||||
[class]{}-[func]{climbing_stairs_backtrack}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="climbing_stairs_backtrack.cpp"
|
||||
[class]{}-[func]{backtrack}
|
||||
|
||||
[class]{}-[func]{climbingStairsBacktrack}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="climbing_stairs_backtrack.java"
|
||||
[class]{climbing_stairs_backtrack}-[func]{backtrack}
|
||||
|
||||
[class]{climbing_stairs_backtrack}-[func]{climbingStairsBacktrack}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="climbing_stairs_backtrack.cs"
|
||||
[class]{climbing_stairs_backtrack}-[func]{Backtrack}
|
||||
|
||||
[class]{climbing_stairs_backtrack}-[func]{ClimbingStairsBacktrack}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="climbing_stairs_backtrack.go"
|
||||
[class]{}-[func]{backtrack}
|
||||
|
||||
[class]{}-[func]{climbingStairsBacktrack}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="climbing_stairs_backtrack.swift"
|
||||
[class]{}-[func]{backtrack}
|
||||
|
||||
[class]{}-[func]{climbingStairsBacktrack}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="climbing_stairs_backtrack.js"
|
||||
[class]{}-[func]{backtrack}
|
||||
|
||||
[class]{}-[func]{climbingStairsBacktrack}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="climbing_stairs_backtrack.ts"
|
||||
[class]{}-[func]{backtrack}
|
||||
|
||||
[class]{}-[func]{climbingStairsBacktrack}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="climbing_stairs_backtrack.dart"
|
||||
[class]{}-[func]{backtrack}
|
||||
|
||||
[class]{}-[func]{climbingStairsBacktrack}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="climbing_stairs_backtrack.rs"
|
||||
[class]{}-[func]{backtrack}
|
||||
|
||||
[class]{}-[func]{climbing_stairs_backtrack}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="climbing_stairs_backtrack.c"
|
||||
[class]{}-[func]{backtrack}
|
||||
|
||||
[class]{}-[func]{climbingStairsBacktrack}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="climbing_stairs_backtrack.zig"
|
||||
[class]{}-[func]{backtrack}
|
||||
|
||||
[class]{}-[func]{climbingStairsBacktrack}
|
||||
```
|
||||
```src
|
||||
[file]{climbing_stairs_backtrack}-[class]{}-[func]{climbing_stairs_backtrack}
|
||||
```
|
||||
|
||||
## 方法一：暴力搜索
|
||||
|
||||
@ -136,101 +44,9 @@ $$
|
||||
|
||||
观察以下代码，它和标准回溯代码都属于深度优先搜索，但更加简洁。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="climbing_stairs_dfs.py"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbing_stairs_dfs}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="climbing_stairs_dfs.cpp"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFS}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="climbing_stairs_dfs.java"
|
||||
[class]{climbing_stairs_dfs}-[func]{dfs}
|
||||
|
||||
[class]{climbing_stairs_dfs}-[func]{climbingStairsDFS}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="climbing_stairs_dfs.cs"
|
||||
[class]{climbing_stairs_dfs}-[func]{DFS}
|
||||
|
||||
[class]{climbing_stairs_dfs}-[func]{ClimbingStairsDFS}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="climbing_stairs_dfs.go"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFS}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="climbing_stairs_dfs.swift"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFS}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="climbing_stairs_dfs.js"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFS}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="climbing_stairs_dfs.ts"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFS}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="climbing_stairs_dfs.dart"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFS}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="climbing_stairs_dfs.rs"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbing_stairs_dfs}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="climbing_stairs_dfs.c"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFS}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="climbing_stairs_dfs.zig"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFS}
|
||||
```
|
||||
```src
|
||||
[file]{climbing_stairs_dfs}-[class]{}-[func]{climbing_stairs_dfs}
|
||||
```
|
||||
|
||||
下图展示了暴力搜索形成的递归树。对于问题 $dp[n]$ ，其递归树的深度为 $n$ ，时间复杂度为 $O(2^n)$ 。指数阶属于爆炸式增长，如果我们输入一个比较大的 $n$ ，则会陷入漫长的等待之中。
|
||||
|
||||
@ -247,101 +63,9 @@ $$
|
||||
1. 当首次计算 $dp[i]$ 时，我们将其记录至 `mem[i]` ，以便之后使用。
|
||||
2. 当再次需要计算 $dp[i]$ 时，我们便可直接从 `mem[i]` 中获取结果，从而避免重复计算该子问题。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="climbing_stairs_dfs_mem.py"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbing_stairs_dfs_mem}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="climbing_stairs_dfs_mem.cpp"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFSMem}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="climbing_stairs_dfs_mem.java"
|
||||
[class]{climbing_stairs_dfs_mem}-[func]{dfs}
|
||||
|
||||
[class]{climbing_stairs_dfs_mem}-[func]{climbingStairsDFSMem}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="climbing_stairs_dfs_mem.cs"
|
||||
[class]{climbing_stairs_dfs_mem}-[func]{DFS}
|
||||
|
||||
[class]{climbing_stairs_dfs_mem}-[func]{ClimbingStairsDFSMem}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="climbing_stairs_dfs_mem.go"
|
||||
[class]{}-[func]{dfsMem}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFSMem}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="climbing_stairs_dfs_mem.swift"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFSMem}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="climbing_stairs_dfs_mem.js"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFSMem}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="climbing_stairs_dfs_mem.ts"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFSMem}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="climbing_stairs_dfs_mem.dart"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFSMem}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="climbing_stairs_dfs_mem.rs"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbing_stairs_dfs_mem}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="climbing_stairs_dfs_mem.c"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFSMem}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="climbing_stairs_dfs_mem.zig"
|
||||
[class]{}-[func]{dfs}
|
||||
|
||||
[class]{}-[func]{climbingStairsDFSMem}
|
||||
```
|
||||
```src
|
||||
[file]{climbing_stairs_dfs_mem}-[class]{}-[func]{climbing_stairs_dfs_mem}
|
||||
```
|
||||
|
||||
观察下图，**经过记忆化处理后，所有重叠子问题都只需被计算一次，时间复杂度被优化至 $O(n)$** ，这是一个巨大的飞跃。
|
||||
|
||||
@ -355,77 +79,9 @@ $$
|
||||
|
||||
由于动态规划不包含回溯过程，因此只需使用循环迭代实现，无须使用递归。在以下代码中，我们初始化一个数组 `dp` 来存储子问题的解，它起到了记忆化搜索中数组 `mem` 相同的记录作用。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="climbing_stairs_dp.py"
|
||||
[class]{}-[func]{climbing_stairs_dp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="climbing_stairs_dp.cpp"
|
||||
[class]{}-[func]{climbingStairsDP}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="climbing_stairs_dp.java"
|
||||
[class]{climbing_stairs_dp}-[func]{climbingStairsDP}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="climbing_stairs_dp.cs"
|
||||
[class]{climbing_stairs_dp}-[func]{ClimbingStairsDP}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="climbing_stairs_dp.go"
|
||||
[class]{}-[func]{climbingStairsDP}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="climbing_stairs_dp.swift"
|
||||
[class]{}-[func]{climbingStairsDP}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="climbing_stairs_dp.js"
|
||||
[class]{}-[func]{climbingStairsDP}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="climbing_stairs_dp.ts"
|
||||
[class]{}-[func]{climbingStairsDP}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="climbing_stairs_dp.dart"
|
||||
[class]{}-[func]{climbingStairsDP}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="climbing_stairs_dp.rs"
|
||||
[class]{}-[func]{climbing_stairs_dp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="climbing_stairs_dp.c"
|
||||
[class]{}-[func]{climbingStairsDP}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="climbing_stairs_dp.zig"
|
||||
[class]{}-[func]{climbingStairsDP}
|
||||
```
|
||||
```src
|
||||
[file]{climbing_stairs_dp}-[class]{}-[func]{climbing_stairs_dp}
|
||||
```
|
||||
|
||||
下图模拟了以上代码的执行过程。
|
||||
|
||||
@ -443,77 +99,9 @@ $$
|
||||
|
||||
细心的你可能发现，**由于 $dp[i]$ 只与 $dp[i-1]$ 和 $dp[i-2]$ 有关，因此我们无须使用一个数组 `dp` 来存储所有子问题的解**，而只需两个变量滚动前进即可。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="climbing_stairs_dp.py"
|
||||
[class]{}-[func]{climbing_stairs_dp_comp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="climbing_stairs_dp.cpp"
|
||||
[class]{}-[func]{climbingStairsDPComp}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="climbing_stairs_dp.java"
|
||||
[class]{climbing_stairs_dp}-[func]{climbingStairsDPComp}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="climbing_stairs_dp.cs"
|
||||
[class]{climbing_stairs_dp}-[func]{ClimbingStairsDPComp}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="climbing_stairs_dp.go"
|
||||
[class]{}-[func]{climbingStairsDPComp}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="climbing_stairs_dp.swift"
|
||||
[class]{}-[func]{climbingStairsDPComp}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="climbing_stairs_dp.js"
|
||||
[class]{}-[func]{climbingStairsDPComp}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="climbing_stairs_dp.ts"
|
||||
[class]{}-[func]{climbingStairsDPComp}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="climbing_stairs_dp.dart"
|
||||
[class]{}-[func]{climbingStairsDPComp}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="climbing_stairs_dp.rs"
|
||||
[class]{}-[func]{climbing_stairs_dp_comp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="climbing_stairs_dp.c"
|
||||
[class]{}-[func]{climbingStairsDPComp}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="climbing_stairs_dp.zig"
|
||||
[class]{}-[func]{climbingStairsDPComp}
|
||||
```
|
||||
```src
|
||||
[file]{climbing_stairs_dp}-[class]{}-[func]{climbing_stairs_dp_comp}
|
||||
```
|
||||
|
||||
观察以上代码，由于省去了数组 `dp` 占用的空间，因此空间复杂度从 $O(n)$ 降低至 $O(1)$ 。
|
||||
|
||||
|
||||
@ -56,77 +56,9 @@ $$
|
||||
- **终止条件**：当物品编号越界 $i = 0$ 或背包剩余容量为 $0$ 时，终止递归并返回价值 $0$ 。
|
||||
- **剪枝**：若当前物品重量超出背包剩余容量，则只能不放入背包。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="knapsack.py"
|
||||
[class]{}-[func]{knapsack_dfs}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="knapsack.cpp"
|
||||
[class]{}-[func]{knapsackDFS}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="knapsack.java"
|
||||
[class]{knapsack}-[func]{knapsackDFS}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="knapsack.cs"
|
||||
[class]{knapsack}-[func]{KnapsackDFS}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="knapsack.go"
|
||||
[class]{}-[func]{knapsackDFS}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="knapsack.swift"
|
||||
[class]{}-[func]{knapsackDFS}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="knapsack.js"
|
||||
[class]{}-[func]{knapsackDFS}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="knapsack.ts"
|
||||
[class]{}-[func]{knapsackDFS}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="knapsack.dart"
|
||||
[class]{}-[func]{knapsackDFS}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="knapsack.rs"
|
||||
[class]{}-[func]{knapsack_dfs}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="knapsack.c"
|
||||
[class]{}-[func]{knapsackDFS}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="knapsack.zig"
|
||||
[class]{}-[func]{knapsackDFS}
|
||||
```
|
||||
```src
|
||||
[file]{knapsack}-[class]{}-[func]{knapsack_dfs}
|
||||
```
|
||||
|
||||
如下图所示，由于每个物品都会产生不选和选两条搜索分支，因此时间复杂度为 $O(2^n)$ 。
|
||||
|
||||
@ -140,77 +72,9 @@ $$
|
||||
|
||||
引入记忆化之后，**时间复杂度取决于子问题数量**，也就是 $O(n \times cap)$ 。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="knapsack.py"
|
||||
[class]{}-[func]{knapsack_dfs_mem}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="knapsack.cpp"
|
||||
[class]{}-[func]{knapsackDFSMem}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="knapsack.java"
|
||||
[class]{knapsack}-[func]{knapsackDFSMem}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="knapsack.cs"
|
||||
[class]{knapsack}-[func]{KnapsackDFSMem}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="knapsack.go"
|
||||
[class]{}-[func]{knapsackDFSMem}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="knapsack.swift"
|
||||
[class]{}-[func]{knapsackDFSMem}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="knapsack.js"
|
||||
[class]{}-[func]{knapsackDFSMem}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="knapsack.ts"
|
||||
[class]{}-[func]{knapsackDFSMem}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="knapsack.dart"
|
||||
[class]{}-[func]{knapsackDFSMem}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="knapsack.rs"
|
||||
[class]{}-[func]{knapsack_dfs_mem}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="knapsack.c"
|
||||
[class]{}-[func]{knapsackDFSMem}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="knapsack.zig"
|
||||
[class]{}-[func]{knapsackDFSMem}
|
||||
```
|
||||
```src
|
||||
[file]{knapsack}-[class]{}-[func]{knapsack_dfs_mem}
|
||||
```
|
||||
|
||||
下图展示了在记忆化递归中被剪掉的搜索分支。
|
||||
|
||||
@ -220,77 +84,9 @@ $$
|
||||
|
||||
动态规划实质上就是在状态转移中填充 $dp$ 表的过程，代码如下所示。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="knapsack.py"
|
||||
[class]{}-[func]{knapsack_dp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="knapsack.cpp"
|
||||
[class]{}-[func]{knapsackDP}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="knapsack.java"
|
||||
[class]{knapsack}-[func]{knapsackDP}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="knapsack.cs"
|
||||
[class]{knapsack}-[func]{KnapsackDP}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="knapsack.go"
|
||||
[class]{}-[func]{knapsackDP}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="knapsack.swift"
|
||||
[class]{}-[func]{knapsackDP}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="knapsack.js"
|
||||
[class]{}-[func]{knapsackDP}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="knapsack.ts"
|
||||
[class]{}-[func]{knapsackDP}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="knapsack.dart"
|
||||
[class]{}-[func]{knapsackDP}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="knapsack.rs"
|
||||
[class]{}-[func]{knapsack_dp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="knapsack.c"
|
||||
[class]{}-[func]{knapsackDP}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="knapsack.zig"
|
||||
[class]{}-[func]{knapsackDP}
|
||||
```
|
||||
```src
|
||||
[file]{knapsack}-[class]{}-[func]{knapsack_dp}
|
||||
```
|
||||
|
||||
如下图所示，时间复杂度和空间复杂度都由数组 `dp` 大小决定，即 $O(n \times cap)$ 。
|
||||
|
||||
@ -367,74 +163,6 @@ $$
|
||||
|
||||
在代码实现中，我们仅需将数组 `dp` 的第一维 $i$ 直接删除，并且把内循环更改为倒序遍历即可。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="knapsack.py"
|
||||
[class]{}-[func]{knapsack_dp_comp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="knapsack.cpp"
|
||||
[class]{}-[func]{knapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="knapsack.java"
|
||||
[class]{knapsack}-[func]{knapsackDPComp}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="knapsack.cs"
|
||||
[class]{knapsack}-[func]{KnapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="knapsack.go"
|
||||
[class]{}-[func]{knapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="knapsack.swift"
|
||||
[class]{}-[func]{knapsackDPComp}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="knapsack.js"
|
||||
[class]{}-[func]{knapsackDPComp}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="knapsack.ts"
|
||||
[class]{}-[func]{knapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="knapsack.dart"
|
||||
[class]{}-[func]{knapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="knapsack.rs"
|
||||
[class]{}-[func]{knapsack_dp_comp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="knapsack.c"
|
||||
[class]{}-[func]{knapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="knapsack.zig"
|
||||
[class]{}-[func]{knapsackDPComp}
|
||||
```
|
||||
```src
|
||||
[file]{knapsack}-[class]{}-[func]{knapsack_dp_comp}
|
||||
```
|
||||
|
||||
@ -32,77 +32,9 @@ $$
|
||||
|
||||
对比两道题目的代码，状态转移中有一处从 $i-1$ 变为 $i$ ，其余完全一致。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="unbounded_knapsack.py"
|
||||
[class]{}-[func]{unbounded_knapsack_dp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="unbounded_knapsack.cpp"
|
||||
[class]{}-[func]{unboundedKnapsackDP}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="unbounded_knapsack.java"
|
||||
[class]{unbounded_knapsack}-[func]{unboundedKnapsackDP}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="unbounded_knapsack.cs"
|
||||
[class]{unbounded_knapsack}-[func]{UnboundedKnapsackDP}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="unbounded_knapsack.go"
|
||||
[class]{}-[func]{unboundedKnapsackDP}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="unbounded_knapsack.swift"
|
||||
[class]{}-[func]{unboundedKnapsackDP}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="unbounded_knapsack.js"
|
||||
[class]{}-[func]{unboundedKnapsackDP}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="unbounded_knapsack.ts"
|
||||
[class]{}-[func]{unboundedKnapsackDP}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="unbounded_knapsack.dart"
|
||||
[class]{}-[func]{unboundedKnapsackDP}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="unbounded_knapsack.rs"
|
||||
[class]{}-[func]{unbounded_knapsack_dp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="unbounded_knapsack.c"
|
||||
[class]{}-[func]{unboundedKnapsackDP}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="unbounded_knapsack.zig"
|
||||
[class]{}-[func]{unboundedKnapsackDP}
|
||||
```
|
||||
```src
|
||||
[file]{unbounded_knapsack}-[class]{}-[func]{unbounded_knapsack_dp}
|
||||
```
|
||||
|
||||
### 空间优化
|
||||
|
||||
@ -130,77 +62,9 @@ $$
|
||||
|
||||
代码实现比较简单，仅需将数组 `dp` 的第一维删除。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="unbounded_knapsack.py"
|
||||
[class]{}-[func]{unbounded_knapsack_dp_comp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="unbounded_knapsack.cpp"
|
||||
[class]{}-[func]{unboundedKnapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="unbounded_knapsack.java"
|
||||
[class]{unbounded_knapsack}-[func]{unboundedKnapsackDPComp}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="unbounded_knapsack.cs"
|
||||
[class]{unbounded_knapsack}-[func]{UnboundedKnapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="unbounded_knapsack.go"
|
||||
[class]{}-[func]{unboundedKnapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="unbounded_knapsack.swift"
|
||||
[class]{}-[func]{unboundedKnapsackDPComp}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="unbounded_knapsack.js"
|
||||
[class]{}-[func]{unboundedKnapsackDPComp}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="unbounded_knapsack.ts"
|
||||
[class]{}-[func]{unboundedKnapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="unbounded_knapsack.dart"
|
||||
[class]{}-[func]{unboundedKnapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="unbounded_knapsack.rs"
|
||||
[class]{}-[func]{unbounded_knapsack_dp_comp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="unbounded_knapsack.c"
|
||||
[class]{}-[func]{unboundedKnapsackDPComp}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="unbounded_knapsack.zig"
|
||||
[class]{}-[func]{unboundedKnapsackDPComp}
|
||||
```
|
||||
```src
|
||||
[file]{unbounded_knapsack}-[class]{}-[func]{unbounded_knapsack_dp_comp}
|
||||
```
|
||||
|
||||
## 零钱兑换问题
|
||||
|
||||
@ -251,77 +115,9 @@ $$
|
||||
|
||||
最后返回前，判断 $dp[n, amt]$ 是否等于 $amt + 1$ ，若是则返回 $-1$ ，代表无法凑出目标金额。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="coin_change.py"
|
||||
[class]{}-[func]{coin_change_dp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="coin_change.cpp"
|
||||
[class]{}-[func]{coinChangeDP}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="coin_change.java"
|
||||
[class]{coin_change}-[func]{coinChangeDP}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="coin_change.cs"
|
||||
[class]{coin_change}-[func]{CoinChangeDP}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="coin_change.go"
|
||||
[class]{}-[func]{coinChangeDP}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="coin_change.swift"
|
||||
[class]{}-[func]{coinChangeDP}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="coin_change.js"
|
||||
[class]{}-[func]{coinChangeDP}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="coin_change.ts"
|
||||
[class]{}-[func]{coinChangeDP}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="coin_change.dart"
|
||||
[class]{}-[func]{coinChangeDP}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="coin_change.rs"
|
||||
[class]{}-[func]{coin_change_dp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="coin_change.c"
|
||||
[class]{}-[func]{coinChangeDP}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="coin_change.zig"
|
||||
[class]{}-[func]{coinChangeDP}
|
||||
```
|
||||
```src
|
||||
[file]{coin_change}-[class]{}-[func]{coin_change_dp}
|
||||
```
|
||||
|
||||
下图展示了零钱兑换的动态规划过程，和完全背包非常相似。
|
||||
|
||||
@ -374,77 +170,9 @@ $$
|
||||
|
||||
零钱兑换的空间优化的处理方式和完全背包一致。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="coin_change.py"
|
||||
[class]{}-[func]{coin_change_dp_comp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="coin_change.cpp"
|
||||
[class]{}-[func]{coinChangeDPComp}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="coin_change.java"
|
||||
[class]{coin_change}-[func]{coinChangeDPComp}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="coin_change.cs"
|
||||
[class]{coin_change}-[func]{CoinChangeDPComp}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="coin_change.go"
|
||||
[class]{}-[func]{coinChangeDPComp}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="coin_change.swift"
|
||||
[class]{}-[func]{coinChangeDPComp}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="coin_change.js"
|
||||
[class]{}-[func]{coinChangeDPComp}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="coin_change.ts"
|
||||
[class]{}-[func]{coinChangeDPComp}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="coin_change.dart"
|
||||
[class]{}-[func]{coinChangeDPComp}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="coin_change.rs"
|
||||
[class]{}-[func]{coin_change_dp_comp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="coin_change.c"
|
||||
[class]{}-[func]{coinChangeDPComp}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="coin_change.zig"
|
||||
[class]{}-[func]{coinChangeDPComp}
|
||||
```
|
||||
```src
|
||||
[file]{coin_change}-[class]{}-[func]{coin_change_dp_comp}
|
||||
```
|
||||
|
||||
## 零钱兑换问题 II
|
||||
|
||||
@ -468,150 +196,14 @@ $$
|
||||
|
||||
### 代码实现
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="coin_change_ii.py"
|
||||
[class]{}-[func]{coin_change_ii_dp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="coin_change_ii.cpp"
|
||||
[class]{}-[func]{coinChangeIIDP}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="coin_change_ii.java"
|
||||
[class]{coin_change_ii}-[func]{coinChangeIIDP}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="coin_change_ii.cs"
|
||||
[class]{coin_change_ii}-[func]{CoinChangeIIDP}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="coin_change_ii.go"
|
||||
[class]{}-[func]{coinChangeIIDP}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="coin_change_ii.swift"
|
||||
[class]{}-[func]{coinChangeIIDP}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="coin_change_ii.js"
|
||||
[class]{}-[func]{coinChangeIIDP}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="coin_change_ii.ts"
|
||||
[class]{}-[func]{coinChangeIIDP}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="coin_change_ii.dart"
|
||||
[class]{}-[func]{coinChangeIIDP}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="coin_change_ii.rs"
|
||||
[class]{}-[func]{coin_change_ii_dp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="coin_change_ii.c"
|
||||
[class]{}-[func]{coinChangeIIDP}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="coin_change_ii.zig"
|
||||
[class]{}-[func]{coinChangeIIDP}
|
||||
```
|
||||
```src
|
||||
[file]{coin_change_ii}-[class]{}-[func]{coin_change_ii_dp}
|
||||
```
|
||||
|
||||
### 空间优化
|
||||
|
||||
空间优化处理方式相同，删除硬币维度即可。
|
||||
|
||||
=== "Python"
|
||||
|
||||
```python title="coin_change_ii.py"
|
||||
[class]{}-[func]{coin_change_ii_dp_comp}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
|
||||
```cpp title="coin_change_ii.cpp"
|
||||
[class]{}-[func]{coinChangeIIDPComp}
|
||||
```
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="coin_change_ii.java"
|
||||
[class]{coin_change_ii}-[func]{coinChangeIIDPComp}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="coin_change_ii.cs"
|
||||
[class]{coin_change_ii}-[func]{CoinChangeIIDPComp}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
||||
```go title="coin_change_ii.go"
|
||||
[class]{}-[func]{coinChangeIIDPComp}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="coin_change_ii.swift"
|
||||
[class]{}-[func]{coinChangeIIDPComp}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="coin_change_ii.js"
|
||||
[class]{}-[func]{coinChangeIIDPComp}
|
||||
```
|
||||
|
||||
=== "TS"
|
||||
|
||||
```typescript title="coin_change_ii.ts"
|
||||
[class]{}-[func]{coinChangeIIDPComp}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="coin_change_ii.dart"
|
||||
[class]{}-[func]{coinChangeIIDPComp}
|
||||
```
|
||||
|
||||
=== "Rust"
|
||||
|
||||
```rust title="coin_change_ii.rs"
|
||||
[class]{}-[func]{coin_change_ii_dp_comp}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="coin_change_ii.c"
|
||||
[class]{}-[func]{coinChangeIIDPComp}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="coin_change_ii.zig"
|
||||
[class]{}-[func]{coinChangeIIDPComp}
|
||||
```
|
||||
```src
|
||||
[file]{coin_change_ii}-[class]{}-[func]{coin_change_ii_dp_comp}
|
||||
```
|
||||
|
||||
Reference in New Issue
Block a user