# 66.构建乘积数组

### 一、 题目

给定一个数组 A\[0,1,…,n-1]，请构建一个数组 B\[0,1,…,n-1]，其中 B\[i] 的值是数组 A 中除了下标 i 以外的元素的积, 即 B\[i]=A\[0]×A\[1]×…×A\[i-1]×A\[i+1]×…×A\[n-1]。

不能使用除法。

示例:

输入: \[1,2,3,4,5]

输出: \[120,60,40,30,24]

提示：

所有元素乘积之和不会溢出 32 位整数

a.length <= 100000

来源：力扣（LeetCode）

链接：<https://leetcode-cn.com/problems/gou-jian-cheng-ji-shu-zu-lcof>

著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

### 二、 解法

动态规划

```
func constructArr(_ a: [Int]) -> [Int] {
    guard a.isEmpty == false else {
        return []
    }
    var res: [Int] = []
    /// 某位之前的乘积
    var dpL: [Int : Int] = [0 : 1]
    /// 某位之后的乘积
    var dpR: [Int : Int] = [(a.count - 1) : 1]
    
    for idx in 1..<a.count {
        let lastIdx = idx - 1
        if let last = dpL[lastIdx] {
            dpL[idx] = last * a[lastIdx]
        }
        
        let backwordIdx = a.count - idx - 1
        if let last = dpR[backwordIdx + 1] {
            dpR[backwordIdx] = last * a[backwordIdx + 1]
        }
        
    }

    for idx in 0..<a.count {
        if let l = dpL[idx], let r = dpR[idx] {
            res.append(l * r)
        }
    }
    
    return res
}
```


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