PAT甲级(Advanced Level)练习题 Rational Sum

PAT甲级(Advanced Level)练习题 Rational Sum

题目描述

Given N rational numbers in the form “numerator/denominator”, you are supposed to calculate their sum.

输入描述

Each input file contains one test case. Each case starts with a positive integer N (<=100), followed in the next line N rational numbers “a1/b1 a2/b2 …” where all the numerators and denominators are in the range of “long int”. If there is a negative number, then the sign must appear in front of the numerator.

输出描述:

For each test case, output the sum in the simplest form “integer numerator/denominator” where “integer” is the integer part of the sum, “numerator” < “denominator”, and the numerator and the denominator have no common factor. You must output only the fractional part if the integer part is 0.

输入例子:

5
2/5 4/15 1/30 -2/60 8/3

题目分析及实现

本题要实现分数的相加，分数相加考虑的是通分，寻找到最小公约数，然后分子分母同时相除即可。难点在于对字符串的分割处理，以及string和int之间的各种转换。

代码实现（C++版本）

// An highlighted block
#include <iostream>
#include <string>
#include <cstdlib>
#include <cmath>
#include <sstream>
using namespace std;

bool getSign(string str);
int getFenzi(string str);
int getFenmu(string str);
int strToint(string str);
int getfenshuIndex(string str);
int getGcd(int a,int b);

int getGcd(int a,int b){
    a = abs(a);
    b = abs(b);
    int minab = min(a,b);
    for(int i =minab ;i>=1;i--){
        if(a%i==0 && b%i==0)
            return i;
    }
    return 1;
}

bool getSign(string str){
    if(str[0]=='-'){
        return false;
    }
    return true;
}

int getFenzi(string str){
    string fenzi="";

    for(unsigned long i = 0; i < str.length();i++){
        if(str[i] == '/'){
            return strToint(fenzi);
        }else{
            fenzi += str[i];
        }
    }
    return strToint(fenzi);

}

int getfenshuIndex(string str){
    for(unsigned long i = 0; i < str.length();i++){
        if(str[i]=='/')
            return i;
    }
    return 0;
}

int getFenmu(string str){
    int length = getfenshuIndex(str)+1;
    string fenmu = "";
    for(unsigned long i =length; i < str.length();i++){
        fenmu += str[i];
    }
    return strToint(fenmu);
}

string calucute(string a, string b){
    int bnum = getFenzi(a);
    int anum = getFenmu(a);
    int d = getFenzi(b);
    int c = getFenmu(b);
    int fenzi = bnum*c + anum*d;
    int fenmu = anum*c;
    int gcd = getGcd(fenzi,fenmu);
    fenzi = fenzi /gcd;
    fenmu = fenmu / gcd;

    stringstream ss;
    ss<<fenzi<<"/"<<fenmu;
    string s1 = ss.str();
    string ans = s1;
    return ans;
}


int strToint(string str){
    bool fuhao = getSign(str);
    int ans = 0;
    if(fuhao){
        for(unsigned long i = 0; i<str.length();i++){
            int weishu = str.length()-1 -i;
            ans += (str[i] - '0') * pow(10,weishu);
        }
        return ans;
    }else{
        for(unsigned long i =1 ; i< str.length();i++){
            int weishu = str.length()-i -1;
            ans+= (str[i] -'0') * pow(10,weishu);
        }
        return -ans;
    }
}

int main()
{
    int n;
    cin >> n;
    string ans = "";
    for(int i = 0; i< n; i++){
        string input[n];
        cin >> input[i];
        if(i ==0){
            ans = input[i];
        }else if(input[i][0]!='0'){
            ans = calucute(ans,input[i]);
        }

    }

    int fenzi = getFenzi(ans);
    int fenmu = getFenmu(ans);
    if(ans == "1/1"){
        cout<<"1"<<endl;
    }else if(fenzi%fenmu == 0){
        cout<<fenzi/fenmu<<endl;
    }
    else if (getFenzi(ans)>getFenmu(ans)){
        int shang = fenzi / fenmu;
        int shenyu = fenzi - shang * fenmu;
        cout<< shang << " "<<shenyu<<"/"<<fenmu<<endl;
    }else if (fenzi<fenmu){
        cout<<fenzi <<"/"<<fenmu<<endl;
    }
    return 0;
}

运行结果