Equal Rational Numbers - Practice Coding Problems

Equal Rational Numbers - Problem

Math String Hard

Given two strings s and t, each of which represents a non-negative rational number, return true if and only if they represent the same number. The strings may use parentheses to denote the repeating part of the rational number.

A rational number can be represented using up to three parts:

IntegerPart: For example, 12, 0, and 123.
IntegerPart.NonRepeatingPart: For example, 0.5, 1., 2.12, and 123.0001.
IntegerPart.NonRepeatingPart(RepeatingPart): For example, 0.1(6), 1.(9), 123.00(1212).

The repeating portion of a decimal expansion is conventionally denoted within a pair of round brackets. For example: 1/6 = 0.16666666... = 0.1(6) = 0.1666(6) = 0.166(66).

Input & Output

Example 1 — Same Rational Number

$ Input: s = "0.(52)", t = "0.5(25)"

› Output: true

💡 Note: Both represent the same repeating decimal 0.525252..., just with different groupings of the repeating part.

Example 2 — Different Numbers

$ Input: s = "0.1666(6)", t = "0.166(66)"

› Output: true

💡 Note: Both represent 1/6 = 0.16666..., showing different valid representations of the same repeating pattern.

Example 3 — No Repeating vs Repeating

$ Input: s = "0.9(9)", t = "1."

› Output: true

💡 Note: 0.9999... equals exactly 1.0, demonstrating the mathematical equivalence.

Constraints

Each string contains only digits, '.', '(', ')'
Both strings are valid representations of rational numbers
No leading zeros except for numbers less than 1
1 ≤ s.length, t.length ≤ 20

Visualization

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Understanding the Visualization

Input Strings

Two different string representations of rational numbers

Parse & Convert

Extract components and convert to exact fractions

Compare

Check if fractions are mathematically equal

Key Takeaway

🎯 Key Insight: Convert repeating decimals to exact fractions using mathematical formulas for precise comparison

Asked in

G Google 15 f Facebook 12 M Microsoft 8

The key insight is to convert repeating decimal representations to exact fraction form. The optimal approach uses mathematical formulas to convert repeating decimals to fractions, then compares the reduced fractions directly. Time: O(n), Space: O(1).

Common Approaches

Approach	Time	Space	Notes
✓ String Expansion and Comparison	O(n)	O(n)	Expand both numbers to long decimal strings and compare
Fraction Conversion	O(n)	O(1)	Convert both representations to exact fractions and compare

String Expansion and Comparison — Algorithm Steps

Parse each string to extract integer, non-repeating, and repeating parts
Expand repeating parts to create long decimal strings
Compare the expanded strings for equality

Visualization

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Step-by-Step Walkthrough

Parse Format

Extract integer, non-repeating, and repeating parts

Expand Repeating

Repeat the pattern many times

Compare

Check if expanded strings represent same value

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

double parseAndExpand(char* numStr) {
    char* openParen = strchr(numStr, '(');
    if (openParen == NULL) {
        return atof(numStr);
    }
    
    char* closeParen = strchr(numStr, ')');
    
    char beforeRepeat[1000] = {0};
    strncpy(beforeRepeat, numStr, openParen - numStr);
    
    char repeatPart[100] = {0};
    strncpy(repeatPart, openParen + 1, closeParen - openParen - 1);
    
    char expanded[2000] = {0};
    strcpy(expanded, beforeRepeat);
    
    for (int i = 0; i < 50; i++) {
        strcat(expanded, repeatPart);
    }
    
    return atof(expanded);
}

int solution(char* s, char* t) {
    double val1 = parseAndExpand(s);
    double val2 = parseAndExpand(t);
    return fabs(val1 - val2) < 1e-10;
}

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

Time & Space Complexity

Time Complexity

⏱️

O(n)

Linear time to parse strings and expand repeating parts

✓ Linear Growth

Space Complexity

O(n)

Space needed to store expanded decimal strings

⚡ Linearithmic Space

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

String Expansion and Comparison — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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