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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.
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@@ -25,23 +25,17 @@
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下面的递归函数用分治计算 $x^n$:
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```python
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def fast_pow(x, n):
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if n == 0:
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return 1
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half = fast_pow(x, n // 2)
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if n % 2 == 0:
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return half * half
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return half * half * x
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```src
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[file]{fast_power}-[class]{}-[func]{fast_pow}
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```
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用它计算 `fast_pow(3, 5)`:
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令 `x = 3`、`n = 5`,用这个函数计算:
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<!-- numbered-subquestions -->
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1. 递归调用时,参数 `n` 依次变成哪些值?
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2. 从最深层开始返回时,各层依次返回什么值?
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3. 为什么要先保存 `half`,而不是把 `fast_pow(x, n // 2)` 写两遍?
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3. 为什么要先把递归结果保存为 `half`,而不是在乘法两边各调用一次相同的子问题?
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??? success "参考答案"
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@@ -50,7 +44,7 @@ def fast_pow(x, n):
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2. `n = 0` 时返回 1;`n = 1` 时返回 $1×1×3=3$;
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`n = 2` 时返回 $3×3=9$;`n = 5` 时返回 $9×9×3=243$。
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3. 如果把 `fast_pow(x, n // 2)` 在乘法两边各写一次,两次递归会计算完全相同的子问题。
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3. 如果在乘法两边各调用一次相同的子问题,两次递归会进行完全相同的计算。
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先把结果保存为 `half`,每层就只递归一次,递归深度约为 $\log n$;
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调用两次会造成大量重复计算。
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