Skip to content

788. Rotated Digits

Difficulty Topics

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

Solution

rotated-digits.py
class Solution:
    def rotatedDigits(self, n: int) -> int:
        digits = []

        while n > 0:
            digits.append(n % 10)
            n //= 10

        digits.reverse()

        N = len(digits)

        rotations = {0:0, 1:1, 8:8, 2:5, 5:2, 6:9, 9:6}

        @cache
        def dp(pos, tight, rotated):
            if pos == N:
                return 1 if rotated else 0

            limit = digits[pos] if tight else 9
            res = 0

            for digit in range(0, limit + 1):
                if digit not in rotations: continue

                nextTight = tight and digit == digits[pos]
                nextRotated = rotated or rotations[digit] != digit

                res += dp(pos + 1, nextTight, nextRotated)    

            return res

        return dp(0, True, False)