788. Rotated Digits

Description

An integer x is a good if after rotating each digit individually by 180 degrees, we get a valid number that is different from x. Each digit must be rotated - we cannot choose to leave it alone.

A number is valid if each digit remains a digit after rotation. For example:

0, 1, and 8 rotate to themselves,
2 and 5 rotate to each other (in this case they are rotated in a different direction, in other words, 2 or 5 gets mirrored),
6 and 9 rotate to each other, and
the rest of the numbers do not rotate to any other number and become invalid.

Given an integer n, return the number of good integers in the range [1, n].

Example 1:

Input: n = 10
Output: 4
Explanation: There are four good numbers in the range [1, 10] : 2, 5, 6, 9.
Note that 1 and 10 are not good numbers, since they remain unchanged after rotating.

Example 2:

Input: n = 1
Output: 0

Example 3:

Input: n = 2
Output: 1

Constraints:

1 <= n <= 10⁴

Solutions

Solution 1: Direct Enumeration

An intuitive and effective approach is to directly enumerate each number in $[1,2,..n]$ and determine whether it is a good number. If it is a good number, increment the answer by one.

The key to the problem is how to determine whether a number $x$ is a good number. The logic is as follows:

We first use an array $d$ of length 10 to record the rotated digits corresponding to each valid digit. In this problem, the valid digits are $[0, 1, 8, 2, 5, 6, 9]$, which correspond to the rotated digits $[0, 1, 8, 5, 2, 9, 6]$ respectively. If a digit is not valid, we set the corresponding rotated digit to $-1$.

Then, we traverse each digit $v$ of the number $x$. If $v$ is not a valid digit, it means $x$ is not a good number, and we directly return $\textit{false}$. Otherwise, we add the rotated digit $d[v]$ corresponding to the digit $v$ to $y$. Finally, we check whether $x$ and $y$ are equal. If they are not equal, it means $x$ is a good number, and we return $\textit{true}$.

The time complexity is $O(n \times \log n)$, where $n$ is the given number. The space complexity is $O(1)$.

Similar problems:

1056. Confusing Number

Python3JavaC++GoTypeScript

class Solution:
    def rotatedDigits(self, n: int) -> int:
        def check(x):
            y, t = 0, x
            k = 1
            while t:
                v = t % 10
                if d[v] == -1:
                    return False
                y = d[v] * k + y
                k *= 10
                t //= 10
            return x != y

        d = [0, 1, 5, -1, -1, 2, 9, -1, 8, 6]
        return sum(check(i) for i in range(1, n + 1))

class Solution {
    private int[] d = new int[] {0, 1, 5, -1, -1, 2, 9, -1, 8, 6};

    public int rotatedDigits(int n) {
        int ans = 0;
        for (int i = 1; i <= n; ++i) {
            if (check(i)) {
                ++ans;
            }
        }
        return ans;
    }

    private boolean check(int x) {
        int y = 0, t = x;
        int k = 1;
        while (t > 0) {
            int v = t % 10;
            if (d[v] == -1) {
                return false;
            }
            y = d[v] * k + y;
            k *= 10;
            t /= 10;
        }
        return x != y;
    }
}

class Solution {
public:
    int rotatedDigits(int n) {
        int d[10] = {0, 1, 5, -1, -1, 2, 9, -1, 8, 6};
        auto check = [&](int x) -> bool {
            int y = 0, t = x;
            int k = 1;
            while (t) {
                int v = t % 10;
                if (d[v] == -1) {
                    return false;
                }
                y = d[v] * k + y;
                k *= 10;
                t /= 10;
            }
            return x != y;
        };
        int ans = 0;
        for (int i = 1; i <= n; ++i) {
            ans += check(i);
        }
        return ans;
    }
};

func rotatedDigits