第七章数学 4 AcWing 1578. 有理数运算

小鱼儿 2024-03-31 10:20 110阅读 0赞

## 第七章 数学 4 AcWing 1578. 有理数运算 ##

### 原题链接 ###

[AcWing 1578. 有理数运算][AcWing 1578.]

### 算法标签 ###

数学 模拟

### 思路 ###

依题意模拟

### 代码 ###

#pragma GCC optimize(2)
    #pragma GCC optimize(3)
    #include<bits/stdc++.h>
    #define int long long
    #define x first
    #define y second
    #define ump unordered_map
    #define ums unordered_set
    #define pq priority_queue
    #define rep(i, a, b) for(int i=a;i<b;++i)
    #define Rep(i, a, b) for(int i=a;i>=b;--i)
    using namespace std;
    typedef pair<int, int> PII;
    const int N=10005, INF=0x3f3f3f3f3f3f3f3f;
    const double Exp=1e-8;
    //int t, n, m, cnt, ans;
    int a, b, c, d;
    inline int rd(){
       int s=0,w=1;
       char ch=getchar();
       while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
       while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
       return s*w;
    }
    void put(int x) {
        if(x<0) putchar('-'),x=-x;
        if(x>=10) put(x/10);
        putchar(x%10^48);
    }
    void print(int a, int b) {
        int t=__gcd(a, b);
        a/=t, b/=t;
        if(b<0){
            a*=-1, b*=-1; 
        }
        
        if(a<0){
            printf("(");
            if(abs(a)>=b){
                if(b==1){
                    printf("%lld", a);
                }else{
                    printf("%lld", a/b);
                    if(abs(a)%b){
                        printf(" %lld/%lld", abs(a-a/b*b), b);
                    }   
                }
            }else{
                printf("%lld/%lld", a, b);
            }
            printf(")");
        }else{
            if(abs(a)>=b){
                if(b==1){
                    printf("%lld", a);
                }else{
                    printf("%lld", a/b);
                    if(abs(a)%b){
                        printf(" %lld/%lld", a-a/b*b, b);
                    }else{
                        printf("%lld/%lld", a, b);
                    }
                }
            }else{
                if(a){
                    printf("%lld/%lld", a, b);
                }else{
                    printf("0");
                }
            }
        }
    }
    
    void add(int a, int b, int c, int d) {
        print(a, b), printf(" + "), print(c, d);
        a=a*d+c*b;
        b*=d;
        printf(" = "), print(a, b);
        puts("");
    }
    void sub(int a, int b, int c, int d) {
        print(a, b), printf(" - "), print(c, d);
        a=a*d-c*b;
        b*=d;
        printf(" = "), print(a, b);
        puts("");
    }
    void mul(int a, int b, int c, int d) {
        print(a, b), printf(" * "), print(c, d);
        a*=c;
        b*=d;
        printf(" = "), print(a, b);
        puts("");
    }
    void div(int a, int b, int c, int d) {
        print(a, b), printf(" / "), print(c, d);
        a*=d;
        b*=c;
        printf(" = ");
        if(!b||!d){
            printf("Inf");
        }else{
            print(a, b);    
        }
        puts("");
    }
    
    signed main(){
    	ios::sync_with_stdio(false);
    	cin.tie(0);
    	cout.tie(0);
    	scanf("%lld/%lld%lld/%lld", &a, &b, &c, &d);	
    	add(a, b, c, d);
    	sub(a, b, c, d);
    	mul(a, b, c, d);
    	div(a, b, c, d);
    	return 0;
    }

### 参考文献 ###

[AcWing 1578. 有理数运算（PAT甲级辅导课）y总视频讲解][AcWing 1578. _PAT_y]

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![在这里插入图片描述][9cb4cb80a18345158f8a69e2f196e5b9.png]

[AcWing 1578.]: https://www.acwing.com/problem/content/1580/
[AcWing 1578. _PAT_y]: https://www.acwing.com/video/1150/
[9cb4cb80a18345158f8a69e2f196e5b9.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/03/31/97f4a373ed484692ac2f7f84c28c5464.png