Problem Description
Given a string s, return whether s is a valid number. A valid number can be an integer or a decimal number, optionally followed by an exponent.
Key Insights
- A valid number can be an integer or a decimal with optional signs (+ or -).
- Integers consist of digits with an optional sign.
- Decimals can have digits before and/or after a decimal point, with optional signs.
- Exponents are indicated by 'e' or 'E' followed by an integer.
- Invalid cases include letters mixed with numbers, isolated 'e' or '.', and multiple signs.
Space and Time Complexity
Time Complexity: O(n), where n is the length of the input string s. Each character is processed once. Space Complexity: O(1), as no additional space proportional to the input size is used.
Solution
To determine if a string represents a valid number, we can use a state machine or regular expressions to validate the structure of the string against the defined rules. The algorithm involves checking for optional signs, digits, decimal points, and exponent notation systematically to ensure the string conforms to the valid number definitions.