LeetCode 592 - Fraction Addition and Subtraction

http://bookshadow.com/weblog/2017/05/21/leetcode-fraction-addition-and-subtraction/

Given a string representing an expression of fraction addition and subtraction, you need to return the calculation result in string format. The final result should be irreducible fraction. If your final result is an integer, say 2, you need to change it to the format of fraction that has denominator 1. So in this case, 2should be converted to 2/1.

Example 1:

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

Example 2:

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

Example 3:

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

Example 4:

Input:"5/3+1/3"
Output: "2/1"

Note:

1. The input string only contains '0' to '9', '/', '+' and '-'. So does the output.
2. Each fraction (input and output) has format ±numerator/denominator. If the first input fraction or the output is positive, then '+' will be omitted.
3. 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.
4. The number of given fractions will be in the range [1,10].
5. The numerator and denominator of the final result are guaranteed to be valid and in the range of 32-bit int.

https://discuss.leetcode.com/topic/90061/small-and-simple-c-and-java

public String fractionAddition(String expression) {
    Scanner sc = new Scanner(expression).useDelimiter("/|(?=[-+])");
    int A = 0, B = 1;
    while (sc.hasNext()) {
        int a = sc.nextInt(), b = sc.nextInt();
        A = A * b + a * B;
        B *= b;
        int g = gcd(A, B);
        A /= g;
        B /= g;
    }
    return A + "/" + B;
}

private int gcd(int a, int b) {
    return a != 0 ? gcd(b % a, a) : Math.abs(b);
}

https://discuss.leetcode.com/topic/89991/concise-java-solution

public String fractionAddition(String expression) {
    String[] fracs = expression.split("(?=[-,+])"); // splits input string into individual fractions
    String res = "0/1";
    for (String frac : fracs) res = add(res, frac);
    return res;
}

public String add(String frac1, String frac2) {
    int[] f1 = Stream.of(frac1.split("/")).mapToInt(Integer::parseInt).toArray(), 
          f2 = Stream.of(frac2.split("/")).mapToInt(Integer::parseInt).toArray();
    int lcm = f1[1]*f2[1]/gcd(f1[1], f2[1]);
    int numerator = lcm*f1[0]/f1[1] + lcm*f2[0]/f2[1];
    String sign = "";
    if (numerator < 0) {sign = "-"; numerator *= -1;}
    return sign + numerator/gcd(numerator, lcm) + "/" + lcm/gcd(numerator, lcm);
}

// Computes gcd using Euclidean algorithm
public int gcd(int x, int y) {
  if (x == 0 || y == 0) return x + y; 
  return gcd(y, x % y);
}

https://discuss.leetcode.com/topic/89993/java-solution-fraction-addition-and-gcd

    public String fractionAddition(String expression) {
        List<String> nums = new ArrayList<>();
        int i = 0, j = 0;
        while (j <= expression.length()) {
            if (j == expression.length() || j != i && (expression.charAt(j) == '+' || expression.charAt(j) == '-')) {
                if (expression.charAt(i) == '+') {
                    nums.add(expression.substring(i + 1, j));
                }
                else {
                    nums.add(expression.substring(i, j));
                }
                    
                i = j;
            }
            j++;
        }
        
        String result = "0/1";
        
        for (String num : nums) {
            result = add(result, num);
        }
        
        return result;
    }
    
    private String add(String s1, String s2) {
        String[] sa1 = s1.split("/");
        String[] sa2 = s2.split("/");
        int n1 = Integer.parseInt(sa1[0]);
        int d1 = Integer.parseInt(sa1[1]);
        int n2 = Integer.parseInt(sa2[0]);
        int d2 = Integer.parseInt(sa2[1]);
        
        int n = n1 * d2 + n2 * d1;
        int d = d1 * d2;
        
        if (n == 0) return "0/1";
        
        boolean isNegative = n * d < 0;
        n = Math.abs(n);
        d = Math.abs(d);
        int gcd = getGCD(n, d);
        
        return (isNegative ? "-" : "") + (n / gcd) + "/" + (d / gcd);
    }
    
    private int getGCD(int a, int b) {
        if (a == 0 || b == 0) return a + b; // base case
        return getGCD(b, a % b);
    }

求分母的最小公倍数，记为LO

将分子乘以 LO / 分母

对分子求和，记为HI

求LO和HI的最大公约数的绝对值，记为GCD

结果的分子分母分别为HI / GCD, LO / GCD