Is Your String A Valid Number? LeetCode Easy Guide

by Alex Johnson 51 views

Valid numbers can be tricky to define, can't they? One moment you're looking at a simple digit like "5", the next you're dealing with a complex scientific notation like "-123.456e789". The LeetCode problem "Valid Number" throws a bunch of these variations at you and asks: "Is this string a valid number?" It’s a fantastic challenge that tests your understanding of parsing and state management. Let's dive deep into what makes a number valid according to these rules and how we can systematically check if a given string fits the bill. We’ll break down the formal definitions, explore edge cases, and build a strategy to tackle this problem, ensuring you can confidently identify valid numerical representations.

Decoding the Anatomy of a Valid Number

At its core, a valid number string can be thought of as either an integer or a decimal, optionally followed by an exponent. This gives us a hierarchical structure to understand. Let's dissect each component: the optional sign, the digits, the decimal point, and the exponent. Understanding these building blocks is crucial for validating the entire string. We're not just looking for numbers; we're looking for correctly formatted numbers. This means the arrangement of signs, digits, and decimal points matters. For instance, a decimal point can appear in several ways: preceding digits (like ".9"), following digits (like "4."), or between digits (like "3.14"). Each of these sub-patterns needs to be accounted for.

Integers: The Foundation

An integer is the simplest form. It starts with an optional sign ('+' or '-') and is followed by one or more digits. Examples like "2", "0089", and "-90" fit this category. The leading zeros in "0089" are perfectly acceptable in this definition, which is a common point of confusion if you're used to strict numerical types in programming languages that might automatically strip leading zeros. The key here is that digits must be present after the optional sign. A string with just a sign, like "+" or "-", is not a valid integer (and therefore not a valid number).

Decimals: Adding the Fractional Part

A decimal number is a bit more elaborate. It also begins with an optional sign. After the sign, it can take one of three forms:

  1. Digits followed by a dot '.': Like "4.". This implies a whole number part but no fractional part explicitly written. The dot signifies it could have a fractional part, but it's empty.
  2. Digits followed by a dot '.' followed by digits: This is your standard decimal representation, like "+3.14" or "-123.456". Both the integer and fractional parts are present.
  3. A dot '.' followed by digits: Like "-.9". Here, there's no explicit integer part, but a fractional part is clearly defined. This is equivalent to "0.9" but represented more compactly.

Crucially, a string consisting of just a dot "." is not a valid decimal number according to these rules. It needs digits either before or after the dot (or both) to qualify. The presence of a decimal point always makes it a decimal number, even if it looks like an integer (e.g., "4.").

The Exponent: Scientific Notation

The exponent part is where things get really interesting. A valid number can be followed by an exponent, indicated by 'e' or 'E'. This exponent part must itself be an integer. So, the structure becomes (integer or decimal) + 'e'/'E' + (integer). Examples include "2e10", "-90E3", "3e+7", and "53.5e93".

Let's break down the exponent rules:

  • The exponent indicator: It must be 'e' or 'E'.
  • The exponent value: It must be an integer. This means it can have an optional sign ('+' or '-') followed by one or more digits. So, "99e2.5" is invalid because the exponent part (".5") is not an integer. "99e+" is also invalid because the exponent needs digits after the sign. "1e" is invalid because it lacks the integer part after 'e'.

When an exponent is present, the part before the 'e'/'E' must already be a valid number (either integer or decimal). The exponent itself, along with its sign and digits, forms a valid integer. Combining these two valid parts with 'e' or 'E' creates a new, larger valid number.

Navigating the Nuances: Edge Cases and Pitfalls

Understanding the formal definitions is a great start, but programming often involves dealing with the edge cases – those tricky inputs that seem to bend the rules or are easily overlooked. For the valid number problem, several such scenarios are common:

  • Multiple signs: Strings like "--6" or "-+" are invalid. A number can have at most one sign, and it must appear at the beginning of the number or immediately after an 'e'/'E'.
  • Misplaced decimal points: While "4." and ".9" are valid, ".." or "1.2.3" are not. Only one decimal point is allowed in the non-exponent part of the number.
  • Incomplete exponents: As mentioned, "1e" or "e3" are invalid. The 'e'/'E' needs a valid integer following it. Similarly, an exponent sign ('+' or '-') must be followed by digits. "3e+" is not a valid number.
  • Non-numeric characters: The most straightforward invalid cases are strings containing characters other than digits, '+', '-', '.', 'e', or 'E'. "abc", "1a", or "95a54e53" are clear examples of invalid inputs.
  • Empty or single-character strings: An empty string is generally not considered a valid number. Single characters like 'e', '.', or '+' are also invalid on their own.

It’s important to remember that the problem states s consists of only English letters (both uppercase and lowercase), digits (0-9), plus '+', minus '-', or dot '.'. This simplifies things slightly as we don't need to worry about arbitrary Unicode characters, but it still means letters can appear, making them inherently invalid numbers.

Crafting a Robust Validation Strategy

Given the complexity and the various components of a valid number, a common and effective approach is to use a state machine or a series of flags. The idea is to iterate through the string character by character, keeping track of what we've seen so far and what is still allowed. This avoids complex lookaheads or recursive parsing.

Let's outline a potential strategy using flags:

  1. Initialization: We'll need flags to track if we've seen a digit (hasDigit), a decimal point (hasDot), or an exponent (hasExponent). We also need to handle the sign carefully, ensuring it only appears at the beginning or after an 'e'/'E'.

  2. Iteration: Loop through each character c in the input string s.

    • Digit ('0'-'9'): If c is a digit, set hasDigit = true. This is generally always allowed, regardless of the current state, as long as it's not part of an invalid sequence (like appearing after a misplaced character).
    • Sign ('+' or '-'): A sign is only valid if it's the first character of the string, OR if it immediately follows an 'e' or 'E'. If we encounter a sign elsewhere, or if we've already seen a sign in the current segment (before 'e'/'E', or after 'e'/'E'), it's invalid. Be careful: a sign cannot follow a decimal point directly.
    • Decimal Point ('.'): A decimal point is only valid if we haven't seen one yet and we haven't seen an exponent yet. If hasDot is already true, or if hasExponent is true, encountering another '.' is invalid. If we see a '.', set hasDot = true.
    • Exponent ('e' or 'E'): An exponent is only valid if we haven't seen one yet AND we have seen at least one digit before it. If hasExponent is true, or if hasDigit is false when we see 'e'/'E', it's invalid. If it's valid, set hasExponent = true and importantly, reset hasDigit = false. This is because the exponent part must have its own digits, and we need to track if those follow.
    • Other Characters: If c is anything else (like a letter), the string is immediately invalid.

  3. Final Check: After iterating through the entire string, the number is valid only if we have seen at least one digit (hasDigit must be true). This handles cases like "+", "-", ".", "e", or "e+" which might pass intermediate checks but lack the essential digits.

This flag-based approach allows us to manage the state transitions implicitly. For example, encountering a sign after a digit is fine if we haven't hit 'e' yet, but encountering a sign after 'e' requires a separate check for valid exponent placement. The hasDigit flag is crucial for ensuring that components like the base number and the exponent part are not empty.

Advanced Considerations and State Transitions

While the flag-based approach is intuitive, some might prefer a more formal Finite State Machine (FSM). This involves defining a set of states and transitions based on the input characters. For instance, states could include:

  • START: Initial state.
  • SIGN: Saw a sign.
  • INTEGER: Saw digits (before decimal/exponent).
  • DOT_NO_INTEGER: Saw a dot without preceding digits.
  • DOT_WITH_INTEGER: Saw a dot after preceding digits.
  • DECIMAL: Saw digits after a dot.
  • EXPONENT: Saw 'e' or 'E'.
  • EXPONENT_SIGN: Saw a sign after 'e'/'E'.
  • EXPONENT_INTEGER: Saw digits after 'e'/'E'.
  • END: Valid end state.
  • INVALID: Any state leading to an invalid number.

Each character would cause a transition from the current state to a new state. For example, from START, seeing '+' or '-' transitions to SIGN. Seeing a digit transitions to INTEGER. Seeing '.' transitions to DOT_NO_INTEGER. Seeing 'e'/'E' from START or SIGN would be invalid. The power of an FSM is its clarity in defining all possible valid and invalid paths through the string. Some FSM implementations might use a 2D array (states x characters) to define transitions, making the logic very explicit and manageable.

Another common strategy is regular expressions (regex). A well-crafted regex can capture all the rules of a valid number in a single pattern. However, for this specific problem, the regex can become quite complex and hard to read and debug. The formal definition provided by LeetCode is quite intricate, and translating it directly into a regex might lead to a very long and potentially error-prone expression. For instance, a regex might look something like:

^[+-]?(\\d+(\\.\\d*)?|\\.\\d+)([eE][+-]?\\d+)?$

This regex attempts to cover: an optional sign, then either digits followed by an optional decimal part OR a decimal part starting with a dot, optionally followed by an exponent part. While powerful, understanding why a specific regex works or fails can be challenging compared to the step-by-step logic of an FSM or flag-based approach. Moreover, the constraints of the problem (like ensuring at least one digit in specific parts) can make a pure regex solution more cumbersome than an iterative approach.

When implementing the iterative or FSM approach, remember the crucial final check: at least one digit must be present overall. A string like . or + or e is invalid. This final check ensures that the string actually represents a numerical value, not just a symbolic representation of one.

Conclusion: Mastering Number Validation

Validating strings for numerical correctness, especially with complex rules like those for scientific notation, is a classic computer science problem. It requires careful attention to detail, understanding of both standard formats and edge cases, and a systematic approach to parsing. Whether you opt for a flag-based iteration, a formal Finite State Machine, or even a (potentially complex) regular expression, the key is to meticulously cover all the rules: optional signs, digits, decimal points, and the exponent part. The valid number problem on LeetCode is an excellent exercise for honing these parsing and validation skills. It teaches you to break down complex requirements into manageable steps and to handle the subtleties that make software robust.

For further exploration into string parsing and validation techniques, you might find resources on regular expressions and formal languages to be particularly enlightening. Understanding how these tools and concepts are applied in real-world scenarios, like input validation in web forms or parsing configuration files, can deepen your appreciation for these seemingly simple yet powerful techniques.

Check out the official LeetCode problem page for more examples and discussions: LeetCode Valid Number. And for a deeper dive into regular expressions, a fantastic resource is Regular-Expressions.info: Regular-Expressions.info.