Strobogrammatic Number

Problem Statement

In computational problems involving strings and numbers, a unique and interesting category is that of the "strobogrammatic number". A number is considered strobogrammatic if it retains the same visual representation when rotated 180 degrees—effectively when it is turned upside down. The task is to determine whether a given string, that represents an integer, qualifies as a strobogrammatic number.

For instance, the number '69' when flipped appears as '96', which is the same set of digits but in reverse order. Thus, identifying whether a number is strobogrammatic involves examining its readability post this rotation.

Examples

Example 1

Input:

num = "69"

Output:

true

Example 2

Input:

num = "88"

Output:

true

Example 3

Input:

num = "962"

Output:

false

Constraints

• 1 <= num.length <= 50
• num consists of only digits.
• num does not contain any leading zeros except for zero itself.

Approach and Intuition

Let's dissect the nature and solution approach for this problem through the given examples and constraints:

1. Understanding strobogrammatic digits:

   • Only certain digits look like valid digits when rotated 180 degrees. These include: 0, 1, 8 which look the same, and pairs like 6 and 9 which transform into each other.
   • Digits such as 2, 3, 4, 5, 7 do not form valid digits upon being flipped and hence, cannot be part of a strobogrammatic number unless paired correctly (like 6 with 9).

2. Solution methodology using examples:

   • Example 1: '69'
     • '6' turns to '9', and '9' turns to '6'. When flipped, '69' becomes '96', which is the reverse of the original number. Hence, the output is true.
   • Example 2: '88'
     • Both '8's remain '8' when rotated. Thus, the flipped number is still '88', mirroring the original. Therefore, the output is true.
   • Example 3: '962'
     • While '9' turns to '6' and '6' turns to '9', '2' does not represent a valid strobogrammatic digit. Thus, the number cannot maintain its strobogrammatic nature. Therefore, the output is false.

3. Constraints review and edge cases:

   • The length of num can be up to 50, which means it's pertinent to consider performance, but the operation of checking pairs remains lightweight.
   • Inputs will not suffer from complications like non-digit characters or inappropriate leading zeros, avoiding unnecessary preprocessing.

In summary, to determine if a number represented as a string is strobogrammatic, one would:

• Check each digit and its corresponding opposite-end digit in the string.
• Verify if they are valid strobogrammatic pairs.
• Continue this across the string’s length; if all are valid pairs, then the string as a whole is strobogrammatic.

Solutions

class Solution {

    public boolean checkStrobogrammatic(String num) {
        
        Map<Character, Character> reversibleNumbers = new HashMap<> (
            Map.of('0', '0', '1', '1', '6', '9', '8', '8', '9', '6'));
         
        for (int start = 0, end = num.length() - 1; start <= end; start++, end--) {
            char startChar = num.charAt(start);
            char endChar = num.charAt(end);            
            if (!reversibleNumbers.containsKey(startChar) || reversibleNumbers.get(startChar) != endChar) {
                return false;
            }
        }
        return true;
        
    }
}

class Solution:
    def checkStrobogrammatic(self, number: str) -> bool:
        
        flip_mapping = {'0': '0', '1': '1', '8': '8', '6': '9', '9': '6'}
        
        start = 0 
        end = len(number) - 1
        
        while start <= end:
            if number[start] not in flip_mapping \
                    or flip_mapping[number[start]] != number[end]:
                return False
            start += 1
            end -= 1
        return True