Problem Description

You are given an array of alphanumeric strings and need to find the maximum value among all strings, where the value of each string is determined by specific rules.

For any alphanumeric string, its value is calculated as follows:

• If the string contains only digits (like "123" or "007"), its value is the numeric representation in base 10. For example, "123" has a value of 123, and "007" has a value of 7.
• If the string contains any non-digit characters (like "a1b2" or "hello"), its value is simply the length of the string. For example, "a1b2" has a value of 4, and "hello" has a value of 5.

Your task is to return the maximum value among all strings in the given array strs.

Example scenarios:

• For strs = ["5", "abc", "12"]:

  • "5" contains only digits → value = 5
  • "abc" contains letters → value = 3 (length)
  • "12" contains only digits → value = 12
  • Maximum value = 12

• For strs = ["a1", "999", "xy"]:

  • "a1" contains letters → value = 2 (length)
  • "999" contains only digits → value = 999
  • "xy" contains letters → value = 2 (length)
  • Maximum value = 999

The solution iterates through each string, applies the value calculation rule using a helper function f(s), and returns the maximum value found.

Intuition

The key insight is recognizing that we have two distinct types of strings with different valuation methods. We need a way to uniformly evaluate each string according to its type, then find the maximum among all these values.

When we look at any string, we first need to determine which category it falls into:

1. Pure numeric strings (like "123") - these should be converted to their integer value
2. Mixed or alphabetic strings (like "a1b" or "abc") - these should be evaluated by their length

The natural approach is to create a function that checks each character in the string. If all characters are digits, we treat it as a number and convert it using int(). Otherwise, we count its length using len().

Once we can evaluate any single string correctly, finding the maximum becomes straightforward - we just apply this evaluation function to every string in the array and pick the largest result.

The elegance of this solution lies in its simplicity: we use Python's built-in all() function with c.isdigit() to check if every character is a digit. This gives us a clean boolean condition to decide between int(s) and len(s). Then we leverage Python's max() function with a generator expression to efficiently find the maximum value without storing intermediate results.

This approach is optimal because we only need to traverse each string once to determine its type and calculate its value, giving us O(n*m) time complexity where n is the number of strings and m is the average string length.

Solution Approach

The implementation uses a helper function approach combined with Python's built-in functions for a clean and efficient solution.

Step 1: Define the evaluation function

We create a helper function f(s) that determines the value of a single string:

def f(s: str) -> int:
    return int(s) if all(c.isdigit() for c in s) else len(s)

This function works by:

• Using all(c.isdigit() for c in s) to check if every character in the string is a digit
• If true, converting the string to an integer with int(s)
• If false, returning the string's length with len(s)

Step 2: Apply the function to all strings and find maximum

We use a generator expression with max() to find the maximum value:

return max(f(s) for s in strs)

This approach:

• Iterates through each string s in the array strs
• Applies the evaluation function f(s) to get each string's value
• Uses max() to find and return the largest value

Algorithm walkthrough with example:

Given strs = ["5", "abc", "12"]:

1. Process "5": all(c.isdigit() for c in "5") returns True → value = int("5") = 5
2. Process "abc": all(c.isdigit() for c in "abc") returns False → value = len("abc") = 3
3. Process "12": all(c.isdigit() for c in "12") returns True → value = int("12") = 12
4. Return max(5, 3, 12) = 12

Time Complexity: O(n*m) where n is the number of strings and m is the average length of strings (for checking digits in each string)

Space Complexity: O(1) as we only use constant extra space (the generator expression doesn't create an intermediate list)

Example Walkthrough

Let's walk through the solution with strs = ["42", "a1b", "9", "xyz"]:

Step 1: Define our evaluation function

def f(s: str) -> int:
    return int(s) if all(c.isdigit() for c in s) else len(s)

Step 2: Process each string

For "42":

• Check each character: '4' is digit ✓, '2' is digit ✓
• all(c.isdigit() for c in "42") returns True
• Since all characters are digits, return int("42") = 42

For "a1b":

• Check each character: 'a' is NOT a digit ✗
• all(c.isdigit() for c in "a1b") returns False (stops early at 'a')
• Since it contains non-digits, return len("a1b") = 3

For "9":

• Check the character: '9' is digit ✓
• all(c.isdigit() for c in "9") returns True
• Since all characters are digits, return int("9") = 9

For "xyz":

• Check the first character: 'x' is NOT a digit ✗
• all(c.isdigit() for c in "xyz") returns False (stops early at 'x')
• Since it contains non-digits, return len("xyz") = 3

Step 3: Find the maximum

max(f(s) for s in strs)  # max(42, 3, 9, 3)

The values are: [42, 3, 9, 3]

The maximum value is 42.

Key observations:

• Pure digit strings get converted to their numeric value (potentially large)
• Mixed/alphabetic strings only count their length (typically small)
• The all() function short-circuits - it stops checking as soon as it finds a non-digit character, making the solution efficient

Solution Implementation

Time and Space Complexity

Time Complexity: O(n * m) where n is the number of strings in the list and m is the average length of the strings.

• The max() function iterates through all n strings in the list
• For each string s, the function f(s) is called
• Inside f(s), all(c.isdigit() for c in s) checks every character in the string, which takes O(m) time where m is the length of that string
• Converting a string to integer with int(s) also takes O(m) time
• Getting the length with len(s) takes O(1) time
• Therefore, processing each string takes O(m) time, and processing all n strings takes O(n * m) time

Space Complexity: O(1) auxiliary space

• The generator expression (f(s) for s in strs) uses O(1) space as it yields values one at a time rather than creating a list
• The function f(s) uses O(1) auxiliary space for its operations
• The all() function with generator expression also uses O(1) space
• No additional data structures are created that scale with input size
• Note: The input list itself takes O(n * m) space, but this is not counted as auxiliary space

Learn more about how to find time and space complexity quickly.

Common Pitfalls

1. Incorrect String Validation Using str.isdigit() Method

A common mistake is using str.isdigit() directly on the entire string instead of checking each character:

Incorrect approach:

def get_string_value(string: str) -> int:
    if string.isdigit():  # This won't work for leading zeros like "007"
        return int(string)
    else:
        return len(string)

Why it fails:

• The str.isdigit() method returns False for empty strings, which could cause issues
• More importantly, while this usually works, it's less explicit about what we're checking

Correct solution:

def get_string_value(string: str) -> int:
    if all(char.isdigit() for char in string):
        return int(string)
    else:
        return len(string)

2. Not Handling Empty Strings

The problem doesn't explicitly state whether empty strings are possible, but failing to consider them can cause runtime errors:

Problematic scenario:

strs = ["123", "", "abc"]
# An empty string would pass the digit check but fail on int("")

Solution with edge case handling:

def get_string_value(string: str) -> int:
    if string and all(char.isdigit() for char in string):
        return int(string)
    else:
        return len(string)  # Empty string returns 0

3. Using Regular Expressions Incorrectly

Some developers might try to use regex for digit checking but make pattern mistakes:

Incorrect regex approach:

import re

def get_string_value(string: str) -> int:
    if re.match(r'\d+', string):  # Wrong! This matches strings that START with digits
        return int(string)
    else:
        return len(string)

Why it fails:

• re.match(r'\d+', "123abc") would return a match, but int("123abc") would fail
• The pattern should be r'^\d+$' to match entire string of digits

Correct regex solution:

import re

def get_string_value(string: str) -> int:
    if re.match(r'^\d+$', string):  # Anchored to match entire string
        return int(string)
    else:
        return len(string)

4. Type Conversion Without Validation

Attempting to convert directly without checking can cause ValueError:

Incorrect approach:

def get_string_value(string: str) -> int:
    try:
        return int(string)
    except ValueError:
        return len(string)

Why it's problematic: While this works functionally, it uses exception handling for control flow, which is:

• Less efficient than checking beforehand
• Less readable and explicit about intent
• Against Python best practices for predictable conditions

The original solution using all(char.isdigit() for char in string) is cleaner and more efficient.