# 面试题66

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 中的元素 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

## Solutions

* The same as `problem 238`

1. **prefix/suffix producy O(n) S(1)**

```cpp
class Solution {
public:
    vector<int> constructArr(vector<int>& a) {
        if (a.size() <= 1) return a;
        vector<int> res(a.size(), 1);
        for (int i = 1; i < a.size(); i++)
            res[i] = res[i - 1] * a[i - 1];

        int suffix = 1;
        for (int i = a.size() - 1; i >= 0; i--) {
            res[i] *= suffix;
            suffix *= a[i];
        }

        return res;
    }
};
```

Or update prefix/suffix product in one loop.

```cpp
class Solution {
public:
    vector<int> constructArr(vector<int>& a) {
        if (a.size() <= 1) return a;
        vector<int> res(a.size(), 1);

        int prefixp = 1, suffixp = 1;
        for (int i = 0, j = a.size() - 1; j >= 0; i++, j--) {
            res[i] *= prefixp;
            res[j] *= suffixp;
            prefixp *= a[i];
            suffixp *= a[j];
        }

        return res;
    }
};
```
