> For the complete documentation index, see [llms.txt](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/math/1056.-confusing-number.md).

# 1056. Confusing Number

Given a number `N`, return `true` if and only if it is a *confusing number*, which satisfies the following condition:

We can rotate digits by 180 degrees to form new digits. When 0, 1, 6, 8, 9 are rotated 180 degrees, they become 0, 1, 9, 8, 6 respectively. When 2, 3, 4, 5 and 7 are rotated 180 degrees, they become invalid. A *confusing number* is a number that when rotated 180 degrees becomes a **different** number with each digit valid.

**Example 1:**

![](https://assets.leetcode.com/uploads/2019/03/23/1268_1.png)

```
Input: 6
Output: true
Explanation: 
We get 9 after rotating 6, 9 is a valid number and 9!=6.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2019/03/23/1268_2.png)

```
Input: 89
Output: true
Explanation: 
We get 68 after rotating 89, 86 is a valid number and 86!=89.
```

**Example 3:**

![](https://assets.leetcode.com/uploads/2019/03/26/1268_3.png)

```
Input: 11
Output: false
Explanation: 
We get 11 after rotating 11, 11 is a valid number but the value remains the same, thus 11 is not a confusing number.
```

**Example 4:**

![](https://assets.leetcode.com/uploads/2019/03/23/1268_4.png)

```
Input: 25
Output: false
Explanation: 
We get an invalid number after rotating 25.
```

**Note:**

1. `0 <= N <= 10^9`
2. After the rotation we can ignore leading zeros, for example if after rotation we have `0008` then this number is considered as just `8`.

```cpp
bool confusingNumber(int N) { // time: O(logN); space: O(1)
    vector<int> rotate(10, -1);
    rotate[0] = 0;
    rotate[1] = 1;
    rotate[6] = 9;
    rotate[8] = 8;
    rotate[9] = 6;
    int num = 0, orig = N;
    while (N) {
        if (rotate[N % 10] == -1) return false;
        num = num * 10 + rotate[N % 10];
        N /= 10;
    }
    return num != orig;
}
```