Valid Number

To solve this coding challenge, we need to determine if a given string represents a valid number according to specific rules. The problem can be divided into smaller components, each checking different aspects of the string to ensure it conforms to the criteria for a valid number. Here's a detailed explanation and step-by-step pseudocode to solve the problem.

Explanation

A number can be valid based on the following definitions:
  1. Integer : An optional sign (
    -
    or
    +
    ) followed by digits.
  2. Decimal : An optional sign (
    -
    or
    +
    ) and either:
    • Digits followed by a dot (
      .
      ).
    • Digits followed by a dot (
      .
      ) and more digits.
    • A dot (
      .
      ) followed by digits.
  3. Exponent : Defined with an exponent notation (
    e
    or
    E
    ) followed by an integer.
  4. The challenge involves parsing the string to check if it matches these definitions. We will break down the problem into manageable steps:
  5. Trim : Remove any leading or trailing whitespace.
  6. Sign : Check for an optional sign at the beginning.
  7. Digits and Dots : Validate the presence and placement of digits and dots.
  8. Exponent : If an
    e
    or
    E
    is present, ensure that it is followed by a valid signed integer.
  9. Here is the pseudocode:
                                                
    function is_valid_number(s):
    # Trim any whitespace from start and end
    strip_whitespace_from_edges(s)
    
    # Check if the string is empty after trimming
    if s is empty:
    return false
    
    # Initialize flags
    found_digit = false
    found_dot = false
    found_exponent = false
    found_digit_after_exponent = false
    
    # Define allowed characters
    digits = '0123456789'
    exponent_chars = 'eE'
    sign_chars = '+-'
    dot_char = '.'
    
    # Iterate over each character in the string
    for each character in s:
    if character is in digits:
    found_digit = true
    if found_exponent:
    found_digit_after_exponent = true
    
    elif character == dot_char:
    if found_dot or found_exponent:
    # Invalid if more than one dot or dot after exponent
    return false
    found_dot = true
    
    elif character is in exponent_chars:
    if found_exponent or not found_digit:
    # Invalid if more than one exponent or exponent before any digit
    return false
    found_exponent = true
    found_digit_after_exponent = false # Reset for exponent part
    
    elif character is in sign_chars:
    # Sign characters are allowed only at the beginning 
    # or immediately after an exponent
    if s_length_before_current_char_is_not(0_and_previous_char_is_not_in_exponent_chars):
    return false
    
    else:
    # Any other character is invalid
    return false
    
    # Final check: String must contain at least one digit
    # and if there's an exponent, it must have a valid number after it
    if not found_digit or (found_exponent and not found_digit_after_exponent):
    return false
    
    return true
    
                                            

    Detailed Steps in Pseudocode

  10. Trim Whitespace :
    • Strip leading and trailing whitespace.
    • Check if the resultant string is empty, return
      false
      if it is.
  11. Initialize Flags :
    • found_digit
      : Tracks if any digit has been encountered.
    • found_dot
      : Tracks if a decimal dot has been encountered.
    • found_exponent
      : Tracks if an exponent (
      e
      or
      E
      ) has been encountered.
    • found_digit_after_exponent
      : Tracks if a digit has been found after the exponent.
  12. Iterate Over String :
    • Loop through each character, updating flags based on character type.
    • For digits, set
      found_digit
      to
      true
      , and if after an exponent, set
      found_digit_after_exponent
      to
      true
      .
    • For a dot (
      .
      ), check if it's the first one and it appears before any exponent.
    • For an exponent (
      e
      or
      E
      ), ensure it's the first one, and follows a valid number.
    • For sign characters (
      +
      or
      -
      ), ensure they are at the start or immediately after an exponent.
  13. Final Validation :
    • Ensure at least one digit is present before and after any exponent.
By carefully following these steps, we can accurately determine if the input string is a valid number.