algoadvance

You are given a digit string num. You need to determine if the count of each digit in the string matches its value. Specifically, for each digit at index i in the string, the count of digit i in the entire string should match the digit’s value at that index. Return ‘True’ if the string satisfies this condition, otherwise return ‘False’.

Clarifying Questions:

1. What is the range of the length of the string num?
   • The length of the string can be up to 10.
2. Can the string contain any non-digit characters?
   • No, the string contains only digits from ‘0’ to ‘9’.
3. Should the function be case-sensitive?
   • Since the string contains only digits, case sensitivity is not relevant.

Code:

def digit_count(num: str) -> bool:
    # Create a dictionary to hold the count of each digit
    from collections import Counter
    digit_counts = Counter(num)
    
    # Traverse through each digit
    for i in range(len(num)):
        # Check if the count of the digit i (converted to string) matches num[i] (converted to int)
        if digit_counts[str(i)] != int(num[i]):
            return False
    
    return True

# Example tests
print(digit_count("1210"))  # True
print(digit_count("030"))   # False

Strategy:

1. Use a Counter: Utilize the Counter from the collections module to count the instances of each character (digit) in the string num.
2. Iterate through String: Loop through each index i of the string num.
3. Compare Counts: For each index i, check if the count of the digit str(i) in the Counter equals the integer value of num[i].
4. Return Result: If all checks pass, return True. If any check fails, return False.

Time Complexity:

• Building the Counter: O(n), where n is the length of num, to count the frequency of each digit.
• Iterating and Checking: O(n), to loop through each index in the string and check the counts.
• Overall Complexity: O(n), since both the major operations (counting and checking) are linear in terms of the length of num.

The provided solution is efficient and well within the acceptable limits for the problem constraints.

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