Problem Statement:

A valid number can be split up into these components (in order):

1. A decimal number or an integer.
2. (Optional) An 'e' or 'E', followed by an integer.

A decimal number can be split up into these components (in order):

1. (Optional) A sign character (either '+' or '-').
2. One of the following formats:
   1. One or more digits, followed by a dot '.'.
   2. One or more digits, followed by a dot '.', followed by one or more digits.
   3. A dot '.', followed by one or more digits.

An integer can be split up into these components (in order):

1. (Optional) A sign character (either '+' or '-').
2. One or more digits.

For example, all the following are valid numbers: ["2", "0089", "-0.1", "+3.14", "4.", "-.9", "2e10", "-90E3", "3e+7", "+6e-1", "53.5e93", "-123.456e789"], while the following are not valid numbers: ["abc", "1a", "1e", "e3", "99e2.5", "--6", "-+3", "95a54e53"].

Given a string s, return true if s is a valid number.

Example 1

Input: s = "0"
Output: true

Example 2

Input: s = "e"
Output: false

Example 3

Input: s = "."
Output: false

Example 4

Input: s = ".1"
Output: true

Constraints

• 1 <= s.length <= 20
• s consists of only English letters (both uppercase and lowercase), digits (0-9), plus'+', minus '-', or dot '.'.

Problem Solving Approach

Seeing that this problem involves checking if an input follows a particular pattern, I thought of using good old regular expressions to solve this problem. In order to come up with a regular expression to solve the problem we must first get to know the repetitive portions of the pattern.

• We know that a string is a valid number if the first par tis either a decimal or an integer and both of them do start with a sign character optionally so we use the following pattern: [+-]?
• Now following the sign we can have a decimal or an integer:
  • For the decimal portion we can summarize all the three rules into one general rule. We need to have at zero or more digits followed by a dot followed by zero or more digits BUT it cannot be just a dot. This can be represented as the following pattern: (\\d+[.]\\d*) or (\\d*[.]\\d+))
  • For a valid integer we need to have an optional sign character followed by atleast one digit, giving the following pattern: (\\d+)
• once we finish the first part we need to follow that with an optional e/E character and a integer, this would look something like : ([eE][+-]?\\d+)?.

Summing up all the above observations we get the following pattern: ([+-]?)((\\d+[.]\\d*)|(\\d*[.]\\d+)) or ([+-]?\\d+) followed by ([eE][+-]?\\d+)?

Implementation

The following is my implementation of the above approach in Java:

import java.util.regex.*;

public class ValidNumber {
  public boolean isNumber(String s) {
    String pattern = "(([+-]?)((\\d+[.]\\d*)|(\\d*[.]\\d+))|([+-]?\\d+))([eE][+-]?\\d+)?";
    Pattern p = Pattern.compile(pattern);
    Matcher m = p.matcher(s);
    return m.matches();
  }
}