問題:git
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, 2
should be converted to 2/1
.express
Example 1:this
Input:"-1/2+1/2" Output: "0/1"
Example 2:spa
Input:"-1/2+1/2+1/3" Output: "1/3"
Example 3:code
Input:"1/3-1/2" Output: "-1/6"
Example 4:orm
Input:"5/3+1/3" Output: "2/1"
Note:ip
'0'
to '9'
, '/'
, '+'
and '-'
. So does the output.±numerator/denominator
. If the first input fraction or the output is positive, then '+'
will be omitted.解決:ci
① 實現分數的加減。直接計算:A / B + a / b = (Ab + aB) / Bbget
class Solution{ //105ms
public String fractionAddition(String expression) {
Scanner sc = new Scanner(expression).useDelimiter("/|(?=[-+])");
int A = 0;
int B = 1;
while(sc.hasNext()){
int a = sc.nextInt();
int b = sc.nextInt();
A = A * b + a * B;
B *= b;
int g = gcd(A,B);
A /= g;
B /= g;
}
return A + "/" + B;
}
public int gcd(int a,int b){
return a != 0 ? gcd(b % a,a) : Math.abs(b);
}
}input
② 直接遍歷計算。
class Solution{//11ms
public String fractionAddition(String expression) {
int i = 0;
int A = 0;
int B = 1;
while(i < expression.length()){
int sign = 1;
if (expression.charAt(i) == '-'){
sign = -1;
i ++;
}else if (expression.charAt(i) == '+'){
sign = 1;
i ++;
}
int a = 0;
while(Character.isDigit(expression.charAt(i))){
a = a * 10 + expression.charAt(i) - '0';
i ++;
}
a *= sign;
i ++;//跳過操做符
int b = 0;
while(i < expression.length() && Character.isDigit(expression.charAt(i))){
b = b * 10 + expression.charAt(i) - '0';
i ++;
}
int m = lcm(B,b);
A = A * m / B;
a = a * m / b;
A += a;
B = m;
}
int g = gcd(Math.abs(A),Math.abs(B));
A /= g;
B /= g;
return A + "/" + B;
}
public int lcm(int a,int b){
return a * b / gcd(a,b);
}
public int gcd(int a,int b){
return a != 0 ? gcd(b % a,a) : Math.abs(b);
}
}
③ 利用jdk1.8的新特性
class Solution {//113ms
public String fractionAddition(String expression) {//"(?=[-+])"表示匹配-或者+中的任意一個前面的字符。
String[] fractions = expression.split("(?=[-+])");
String res = "0/1";
for (String frac : fractions){
res = add(res,frac);
}
return res;
}
public String add(String frac1,String frac2){
int[] f1 = Stream.of(frac1.split("/")).mapToInt(Integer :: parseInt).toArray();
int[] f2 = Stream.of(frac2.split("/")).mapToInt(Integer :: parseInt).toArray();
int num = f1[0] * f2[1] + f1[1] * f2[0];
int den = f1[1] * f2[1];
String sign = "";
if (num < 0){
sign = "-";
num *= -1;
}
return sign + num / gcd(num,den) + "/" + den / gcd(num,den);
}
public int gcd(int x,int y){
return x == 0 || y == 0 ? x + y : gcd(y,x % y);
}
}
【注】