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Update max_product_cutting_problem.md #1758

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4 changes: 2 additions & 2 deletions docs/chapter_greedy/max_product_cutting_problem.md
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Expand Up @@ -78,8 +78,8 @@ $$

### 正确性证明

使用反证法，只分析 $n \geq 3$ 的情况。
使用反证法，只分析 $n \geq 4$ 的情况。

1. **所有因子 $\leq 3$** ：假设最优切分方案中存在 $\geq 4$ 的因子 $x$ ，那么一定可以将其继续划分为 $2(x-2)$ ，从而获得更大的乘积。这与假设矛盾。
1. **所有因子 $\leq 3$** ：假设最优切分方案中存在 $\geq 4$ 的因子 $x$ ，那么一定可以将其继续划分为 $2(x-2)$ ，从而获得更大或可替代的乘积。这与假设矛盾。
2. **切分方案不包含 $1$** ：假设最优切分方案中存在一个因子 $1$ ，那么它一定可以合并入另外一个因子中，以获得更大的乘积。这与假设矛盾。
3. **切分方案最多包含两个 $2$** ：假设最优切分方案中包含三个 $2$ ，那么一定可以替换为两个 $3$ ，乘积更大。这与假设矛盾。