String to Integer (atoi)

 

  1. Clarify the problem:

    • The problem requires us to convert a given string to an integer.
    • The string may contain leading whitespace characters, an optional plus/minus sign, and a sequence of numerical digits.
    • We need to convert the string to an integer and handle overflow and underflow conditions.
    • If the string does not represent a valid integer, we should return 0.

  2. Analyze the problem:

    • Input: A string representing an integer.
    • Output: An integer value.
    • Constraints:
      • Ignore leading whitespace characters.
      • The string may contain an optional plus/minus sign before the numerical digits.
      • Ignore any trailing characters after the numerical digits.
      • Handle overflow and underflow conditions.

  3. Design an algorithm:

    • We can solve this problem by iterating over the characters of the string and converting them to an integer.
    • We need to handle various cases, including leading whitespace, sign, and numerical digits.
    • We can use a state machine approach to handle different states and transitions.
    • We initialize the result and sign variables to store the final integer value and the sign of the number, respectively.
    • We iterate over the characters of the string and process each character based on the current state.
    • The possible states are:
      • Start: The initial state.
      • Sign: The state after encountering a plus/minus sign.
      • Digit: The state after encountering a numerical digit.
      • End: The state after encountering a non-digit character or the end of the string.
    • We update the state and perform the necessary actions at each step.
    • We check for overflow and underflow conditions during the conversion.
    • Finally, we return the result with the appropriate sign.

  4. Explain your approach:

    • We will implement an iterative solution using a state machine approach to convert the string to an integer.
    • We initialize the result and sign variables as 0 and 1, respectively.
    • We define a dictionary to represent the state transitions and actions for each character.
    • We iterate over the characters of the string and process each character based on the current state.
    • We handle the following cases:
      • Start state:
        • Ignore leading whitespace characters.
        • Transition to the Sign state if a plus/minus sign is encountered.
        • Transition to the Digit state if a numerical digit is encountered.
      • Sign state:
        • Update the sign variable based on the encountered sign character.
        • Transition to the Digit state if a numerical digit is encountered.
        • Transition to the End state if a non-digit character is encountered.
      • Digit state:
        • Convert the numerical digit character to an integer and add it to the result.
        • Check for overflow and underflow conditions.
        • Transition to the Digit state if more numerical digits are encountered.
        • Transition to the End state if a non-digit character is encountered.
      • End state:
        • Break the loop and return the result with the appropriate sign.
    • We handle the edge cases of overflow and underflow by limiting the result to the range of a 32-bit signed integer.

  5. Write clean and readable code:

    python
  6. def atoi(s):
    result = 0
    sign = 1
    state = 'Start'

    transitions = {
        'Start': {'whitespace': 'Start', 'sign': 'Sign', 'digit': 'Digit', 'other': 'End'},
        'Sign': {'whitespace': 'End', 'sign': 'End', 'digit': 'Digit', 'other': 'End'},
        'Digit': {'whitespace': 'End', 'sign': 'End', 'digit': 'Digit', 'other': 'End'},
        'End': {'all': 'End'}
    }

    for char in s:
        if char.isspace():
            transition = transitions[state]['whitespace']
        elif char in '+-':
            transition = transitions[state]['sign']
            sign = 1 if char == '+' else -1
        elif char.isdigit():
            transition = transitions[state]['digit']
            result = result * 10 + int(char)
            result = min(result, 2**31 - 1) if sign == 1 else min(result, 2**31)
        else:
            transition = transitions[state]['other']

        state = transition

        if state == 'End':
            break

    return sign * result

  7. Test your code:

    • We can test the code with multiple test cases, including edge cases and corner cases, to ensure its correctness.
    • For example:
      python
    • # Example 1
s = "42"
print(atoi(s))
# Output: 42

# Example 2
s = "   -42"
print(atoi(s))
# Output: -42

# Example 3
s = "4193 with words"
print(atoi(s))
# Output: 4193

# Example 4
s = "words and 987"
print(atoi(s))
# Output: 0

# Example 5
s = "-91283472332"
print(atoi(s))
# Output: -2147483648

  9. Optimize if necessary:

    • The provided solution already has an optimal time complexity of O(n), where n is the length of the string.
    • The space complexity is O(1) since we only use a constant amount of extra space for variables.

  10. Handle error cases:

    • If the input string is empty (s = ""), we can return 0 since there are no characters to convert.
    • If the first non-whitespace character is not a plus/minus sign or a numerical digit, we can return 0 since the string does not represent a valid integer.

  11. Discuss complexity analysis:

    • The time complexity of the solution is O(n), where n is the length of the string.
    • This is because we iterate over each character of the string once.
    • The space complexity is O(1) since we only use a constant amount of extra space for variables.
    • The solution is efficient and optimal considering the requirements of the problem.
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