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# \[343]\[中等]\[动态规划]\[背包] 整数拆分

## 题目描述

[343. 整数拆分](https://leetcode-cn.com/problems/integer-break/) [剑指 Offer 14- I. 剪绳子](https://leetcode-cn.com/problems/jian-sheng-zi-lcof/)

给定一个正整数 n，将其拆分为至少两个正整数的和，并使这些整数的乘积最大化。 返回你可以获得的最大乘积。

示例 1:

```
输入: 2
输出: 1
解释: 2 = 1 + 1, 1 × 1 = 1。
```

示例 2:

```
输入: 10
输出: 36
解释: 10 = 3 + 3 + 4, 3 × 3 × 4 = 36。
```

说明: 你可以假设 n 不小于 2 且不大于 58。

## 解题思路

[Leetcode: 整数拆分](https://leetcode-cn.com/problems/integer-break/solution/zheng-shu-chai-fen-by-leetcode-solution/)

```python
class Solution:
    def integerBreak(self, n: int) -> int:
        dp = [0] * (n + 1)
        for i in range(1, n + 1):
            for j in range(1, i):  # 物品只遍历到i, 更大的物品i分解不出来, 没有意义
                dp[i] = max(dp[i], j * (i - j), j * dp[i - j])
        return dp[-1]
```