Solution Explanation

This problem requires reconstructing the original digits from their English spellings present in a scrambled string. The solution leverages the unique characteristics of the spellings of certain digits to deduce their counts first, then iteratively determines the counts of the remaining digits.

Approach:

The core idea is to identify digits with unique letters in their spellings. We can then subtract the counts of these unique letters from the counts of letters shared by multiple digits to find the counts of the remaining digits. The algorithm proceeds as follows:

1. Count Character Frequencies: First, count the occurrences of each character in the input string s.

2. Unique Digit Identification: The following digits are identified based on their unique letters:

   • 0 (z)
   • 2 (w)
   • 4 (u)
   • 6 (x)
   • 8 (g)

3. Iterative Deduction: The counts of remaining digits are found using the counts of unique digits:

   • 3 (h - 8)
   • 5 (f - 4)
   • 7 (s - 6)

4. Deduction using Shared Letters: Finally, the counts of 1 and 9 are calculated by subtracting the counts of other digits from the characters they share:

   • 1 (o - 0 - 2 - 4)
   • 9 (i - 5 - 6 - 8)

5. Construct Result: After obtaining the counts of all digits (0-9), construct the final string with digits in ascending order.

Time Complexity: O(N), where N is the length of the input string s. This is because counting character frequencies and constructing the final string takes linear time.

Space Complexity: O(1). The space used by the counters and other variables is constant regardless of the input string length.

Code Explanation (Python):

from collections import Counter
 
class Solution:
    def originalDigits(self, s: str) -> str:
        counter = Counter(s)  # Count character frequencies
        cnt = [0] * 10       # Initialize digit counts
 
        # Unique digits
        cnt[0] = counter['z']
        cnt[2] = counter['w']
        cnt[4] = counter['u']
        cnt[6] = counter['x']
        cnt[8] = counter['g']
 
        # Iterative deduction
        cnt[3] = counter['h'] - cnt[8]
        cnt[5] = counter['f'] - cnt[4]
        cnt[7] = counter['s'] - cnt[6]
 
        # Deduction using shared letters
        cnt[1] = counter['o'] - cnt[0] - cnt[2] - cnt[4]
        cnt[9] = counter['i'] - cnt[5] - cnt[6] - cnt[8]
 
        return ''.join(str(i) * cnt[i] for i in range(10)) #Construct result string
 

The other languages (Java, C++, Go) follow the same logic, with minor syntax differences. The key is the efficient use of character counting and the careful deduction of digit counts based on unique and shared letter patterns.