Valid Number

Valid Number - Problem

String Hard

Given a string s, return whether s is a valid number.

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".

Formally, a valid number is defined using one of the following definitions:

An integer number followed by an optional exponent.
A decimal number followed by an optional exponent.

An integer number is defined with an optional sign '-' or '+' followed by digits.

A decimal number is defined with an optional sign '-' or '+' followed by one of the following definitions:

Digits followed by a dot '.'.
Digits followed by a dot '.' followed by digits.
A dot '.' followed by digits.

An exponent is defined with an exponent notation 'e' or 'E' followed by an integer number.

The digits are defined as one or more digits.

Input & Output

Example 1 — Valid Scientific Notation

$ Input: s = "3.14e-2"

› Output: true

💡 Note: Valid decimal number 3.14 followed by valid exponent e-2, representing 3.14 × 10^(-2) = 0.0314

Example 2 — Invalid Letter Character

$ Input: s = "1a"

› Output: false

💡 Note: Contains invalid character 'a' - only digits, signs, decimal point, and e/E are allowed

Example 3 — Valid Decimal Only

$ Input: s = ".5"

› Output: true

💡 Note: Valid decimal number - decimal point followed by digits is allowed

Constraints

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

Visualization

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Asked in

F Facebook 35 G Google 28 a Amazon 22

Brief HTML summary: The key insight is to recognize that a valid number follows specific patterns that can be modeled as a finite state machine. Best approach is the state machine method which cleanly handles all transitions. Time: O(n), Space: O(1)

Common Approaches

✓ Character-by-Character Validation

⏱️ Time: O(n) Space: O(1)

Iterate through the string and validate each character based on its position and context. Track whether we've seen signs, digits, decimal points, and exponents.

State Machine Approach

⏱️ Time: O(n) Space: O(1)

Model the valid number as a state machine with states for initial, signed, integer part, decimal part, exponent, etc. Each character transitions between valid states.

Character-by-Character Validation — Algorithm Steps

Step 1: Initialize flags for sign, digits, decimal, exponent
Step 2: Check each character and update flags
Step 3: Validate final state has required components

Visualization

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Step-by-Step Walkthrough

Check Sign

Optional + or - at start

Process Digits/Decimal

Track digits and single decimal point

Handle Exponent

Optional e/E followed by integer

Code -

solution.c — C

#include <stdio.h>
#include <string.h>
#include <stdbool.h>
#include <ctype.h>

bool solution(char* s) {
    int len = strlen(s);
    if (len == 0) return false;
    
    int i = 0;
    
    // Check sign
    if (i < len && (s[i] == '+' || s[i] == '-')) {
        i++;
    }
    
    bool hasDigits = false;
    bool hasDot = false;
    
    // Check digits and decimal point
    while (i < len && (isdigit(s[i]) || s[i] == '.')) {
        if (s[i] == '.') {
            if (hasDot) return false;
            hasDot = true;
        } else {
            hasDigits = true;
        }
        i++;
    }
    
    if (!hasDigits) return false;
    
    // Check exponent
    if (i < len && (s[i] == 'e' || s[i] == 'E')) {
        i++;
        if (i < len && (s[i] == '+' || s[i] == '-')) {
            i++;
        }
        
        bool hasExpDigits = false;
        while (i < len && isdigit(s[i])) {
            hasExpDigits = true;
            i++;
        }
        
        if (!hasExpDigits) return false;
    }
    
    return i == len;
}

int main() {
    char s[1000];
    fgets(s, sizeof(s), stdin);
    s[strcspn(s, "\n")] = 0; // Remove newline
    
    bool result = solution(s);
    printf(result ? "true\n" : "false\n");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through the string of length n

✓ Linear Growth

Space Complexity

O(1)

Only using a few boolean variables

✓ Linear Space

28.0K Views

Medium Frequency

~25 min Avg. Time

892 Likes

Ln 1, Col 1

Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Character-by-Character Validation — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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