mirror of
https://github.com/krahets/hello-algo.git
synced 2026-08-20 07:21:02 +00:00
Add multilingual exercise code (#1959)
Replace the exercise pages' Python-only snippets with source-backed implementations for the 13 visible programming languages, and localize reader-facing comments by site language. Zig remains out of scope. Approval bypass: repository protection requires one approval but does not enforce it for administrators. All 68 completed checks succeeded; four non-required Java jobs remained queued on the existing ubuntu-20.04 workflow, with no failed checks.
This commit is contained in:
@@ -25,23 +25,17 @@
|
||||
|
||||
下面的遞迴函式用分治計算 $x^n$:
|
||||
|
||||
```python
|
||||
def fast_pow(x, n):
|
||||
if n == 0:
|
||||
return 1
|
||||
half = fast_pow(x, n // 2)
|
||||
if n % 2 == 0:
|
||||
return half * half
|
||||
return half * half * x
|
||||
```src
|
||||
[file]{fast_power}-[class]{}-[func]{fast_pow}
|
||||
```
|
||||
|
||||
用它計算 `fast_pow(3, 5)`:
|
||||
令 `x = 3`、`n = 5`,用這個函式計算:
|
||||
|
||||
<!-- numbered-subquestions -->
|
||||
|
||||
1. 遞迴呼叫時,參數 `n` 依次變成哪些值?
|
||||
2. 從最深層開始返回時,各層依次返回什麼值?
|
||||
3. 為什麼要先儲存 `half`,而不是把 `fast_pow(x, n // 2)` 寫兩遍?
|
||||
3. 為什麼要先把遞迴結果儲存為 `half`,而不是在乘法兩邊各呼叫一次相同的子問題?
|
||||
|
||||
??? success "參考答案"
|
||||
|
||||
@@ -50,7 +44,7 @@ def fast_pow(x, n):
|
||||
2. `n = 0` 時返回 1;`n = 1` 時返回 $1×1×3=3$;
|
||||
`n = 2` 時返回 $3×3=9$;`n = 5` 時返回 $9×9×3=243$。
|
||||
|
||||
3. 如果把 `fast_pow(x, n // 2)` 在乘法兩邊各寫一次,兩次遞迴會計算完全相同的子問題。
|
||||
3. 如果在乘法兩邊各呼叫一次相同的子問題,兩次遞迴會進行完全相同的計算。
|
||||
先把結果儲存為 `half`,每層就只遞迴一次,遞迴深度約為 $\log n$;
|
||||
呼叫兩次會造成大量重複計算。
|
||||
|
||||
|
||||
Reference in New Issue
Block a user