Problem

Given a string expression representing an expression of fraction addition and subtraction, return the calculation result in string format.

The final result should be an irreducible fraction. If your final result is an integer, change it to the format of a fraction that has a denominator 1. So in this case, 2 should be converted to 2/1.

Examples

Example 1:

Input: expression = "-1/2+1/2"
Output: "0/1"

Example 2:

Input: expression = "-1/2+1/2+1/3"
Output: "1/3"

Example 3:

Input: expression = "1/3-1/2"
Output: "-1/6"

Constraints:

  • The input string only contains '0' to '9', '/', '+' and '-'. So does the output.
  • Each fraction (input and output) has the format ±numerator/denominator. If the first input fraction or the output is positive, then '+' will be omitted.
  • The input only contains valid irreducible fractions, where the numerator and denominator of each fraction will always be in the range [1, 10]. If the denominator is 1, it means this fraction is actually an integer in a fraction format defined above.
  • The number of given fractions will be in the range [1, 10].
  • The numerator and denominator of the final result are guaranteed to be valid and in the range of 32-bit int.

Solution

Method 1 - Iteration

Here are the steps we can take to solve the problem:

  1. Parse the Input String: Split the expression into individual fractions and operators.
  2. Compute the Result: Use a loop to process each fraction and maintain a running sum.
  3. Simplify the Result: Reduce the resulting fraction to its irreducible form using the greatest common divisor (GCD).

Video Explanation

Here is the video explanation of the same:

Code

Java
public class Solution {
    public String fractionAddition(String expression) {
        int nr = 0;
        int dr = 1; // Start with a denominator of 1

        int i = 0;
        int n = expression.length();

        while (i < n) {
            // Read the numerator
            int sign = 1;
            if (expression.charAt(i) == '-' || expression.charAt(i) == '+') {
                sign = expression.charAt(i) == '-' ? -1 : 1;
                i++;
            }

            int currNr = 0;
            while (i < n && Character.isDigit(expression.charAt(i))) {
                currNr = currNr * 10 + (expression.charAt(i) - '0');
                i++;
            }
            currNr = currNr * sign;

            // Skip '/'
            i++;

            // Read the denominator
            int currDr = 0;
            while (i < n && Character.isDigit(expression.charAt(i))) {
                currDr = currDr * 10 + (expression.charAt(i) - '0');
                i++;
            }

            // Update the result fraction by calculating the common denominator
            nr = nr * currDr + currNr * dr;
            dr *= currDr;

            // Simplify the result
            int gcd = gcd(Math.abs(nr), Math.abs(dr));
            nr /= gcd;
            dr /= gcd;
        }

        // Format the result
        return nr + "/" + dr;
    }

    // Helper function to calculate the greatest common divisor
    public int gcd(int a, int b) {
        while (b != 0) {
            int temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }
}

Complexity

  • Time: O(n)
  • Space: O(1)