POJ 1079 : Ratio - 分数逼近

题意：题意一目了然吧~分母从1到max，进行逼近

解法一：

#include<iostream>
#include<cstdio>
#include<cstdlib>
using namespace std;
int main(){
int i,p,q,pt,a,b;
while(~scanf("%d%d",&a,&b)){
p=1;
q=0;
for(i=1;i<=b;i++){
pt=(int)((double)(i*a)/(double)b+0.5);
if(q*abs(a*i-b*pt)<i*abs(a*q-b*p)){
p=pt;
q=i;
printf("%d/%d\n",p,q);
}
if(a*q==b*p) break;
}
puts("");
}
return 0;
}

解法二：

用分数套模板  ——  参考http://www.cnblogs.com/jiaohuang/archive/2010/09/18/1830434.html

代码
#include <cstdio>
#include <iostream>
#include <cmath>
 using namespace std;

typedef long long INT;
typedef struct{  // num/den
     INT num,den;
}frac;


int gcd(INT a,INT b){
    INT t;
    if (a<0)
        a=-a;
    if (b<0)
        b=-b;
    if (!b)
        return a;
    while (t=a%b)
        a=b,b=t;
    return b;
}

void simplify(frac& f){  //simplify
    int t;
    if (t=gcd(f.num,f.den))
        f.num/=t,f.den/=t;
    else
        f.den=1;  //num=0
}

frac f(INT n,INT d,INT s=1){ //init fraction
    frac ret;
    if (d<0)
        ret.num=-n,ret.den=-d;
    else
        ret.num=n,ret.den=d;
    if (s)
        simplify(ret);
    return ret;
}

int fraqcmp(frac a,frac b){
    int g1=gcd(a.den,b.den),g2=gcd(a.num,b.num);
    if (!g1||!g2)
        return 0;
    return b.den/g1*(a.num/g2)-a.den/g1*(b.num/g2);
}

frac add(frac a,frac b){
    INT g1=gcd(a.den,b.den),g2,t;
    if (!g1)
        return f(1,0,0);
    t=b.den/g1*a.num+a.den/g1*b.num;
    g2=gcd(g1,t);
    return f(t/g2,a.den/g1*(b.den/g2),0);
}

frac sub(frac a,frac b){
    return add(a,f(-b.num,b.den,0));
}

void printfra(frac a){
    printf("%INTd/%INTd\n",a.num , a.den);
}

int main(){
    frac fra_a , fra_t1,  dis , fsub;
    int na, nb;
    while( scanf("%d %d",&na,&nb) != EOF)
    {
        fra_a = f(na, nb , 1);
        dis.den = 1;
        dis.num = floor(fra_a.num * ( (double)(1 ) / fra_a.den) + 0.5);
        printfra( dis );
        dis = sub(fra_a , dis);
        if(dis.num < 0 )dis.num = -dis.num;

        for(int i=2 ; i<fra_a.den ; i++)
        {
            fra_t1.den = i;
            fra_t1.num =floor( fra_a.num *( (double)( i ) / fra_a.den)  + 0.5);
            
            INT ret ;
            fsub = sub(fra_t1, fra_a);
            if(fsub.num < 0)fsub.num = -fsub.num;
            
            ret = fraqcmp(dis , fsub);
            if( ret > 0)
            {
                printfra(fra_t1);
                dis = fsub;
            }
    
        }
        printfra(fra_a);
        puts("");
    }
    return 0;
}