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.
The challenge involves parsing the string to check if it matches these definitions. We will break down the problem into manageable steps:
4. Trim : Remove any leading or trailing whitespace.
5. Sign : Check for an optional sign at the beginning.
6. Digits and Dots : Validate the presence and placement of digits and dots.
7. Exponent : If an
   e
   or
   E
   is present, ensure that it is followed by a valid signed integer.
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

8. Trim Whitespace :
• Strip leading and trailing whitespace.
• Check if the resultant string is empty, return
  false
  if it is.
9. 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.
10. 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.
11. 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.