POJ3101 大数+LCM

来源：互联网发布：脐带血公司知乎编辑：程序博客网时间：2024/06/05 23:50
不是很难，倒是写大数类用了很久，由于要考虑到中间过程会出现long long 的情况，大数类里面的东西要用long long 写，包括，除法，取模运算什么的。
N个分数的的最小公倍数是分子的最小公倍数，分母的最大公约数。
(1/2)/(1/t1-1/t2)得到时间间隔，化简得到t1*t2/(2*(t2-t1))
#include <string.h>#include <stdio.h>#include <math.h>#include <stdlib.h>#include <iostream>#include <algorithm>#define NNN cout<<'\n';using namespace std;long long a[1111],b[1111];long long que=0;long long absMy(long long aa){    if(aa<0)        return -aa;    else        return aa;}class BigInteger{public:    long long num[1000];    long long len;    BigInteger()    {        len=0;        memset(num,0,sizeof(num));    }    BigInteger(char* ss)    {        len=0;        memset(num,0,sizeof(num));        long long& i=this->len;        long long lenofss=strlen(ss);        char s[10]={0};        for(i=0;lenofss/4;lenofss-=4)        {            strncpy(s,ss+lenofss-4,4);            this->num[i++]=atoi(s);        }        if(lenofss)        {            memset(s,0,sizeof(s));            strncpy(s,ss,lenofss);            this->num[i++]=atoi(s);        }    }BigInteger(long long s){len=0;memset(num,0,sizeof(num));while(s>10000){num[len++]=s%10000;s/=10000;}if(s){num[len++]=s;}if(s==0)            len=1;}    void Print()    {        long long i;        printf("%lld",num[len-1]);        for(i=this->len-2;i>=0;i--)        {            printf("%04lld",this->num[i]);        }//printf("\n");    }    BigInteger Times(BigInteger sec)//该数本身没有变化，只是返回了结果    {        long long i,j,jw;        BigInteger ans;        for(i=0;i<len;i++)        {            jw=0;            ans.len=i;            for(j=0;j<sec.len;j++)            {                jw+=this->num[i]*sec.num[j]+ans.num[ans.len];                ans.num[ans.len++]=jw%10000;                jw/=10000;            }            while(jw)            {                jw+=ans.num[ans.len];                ans.num[ans.len++]=jw%10000;                jw/=10000;            }        }        return ans;    }    BigInteger plusone()    {        long long i=0;        do        {            num[i]++;            num[i+1]+=num[i]/10000;            num[i]%=10000;            i++;        }while(num[i]<9999);        return *this;    }BigInteger operator+(const BigInteger& sec){bool isUp=false;BigInteger tmp=*this;for(long long i=0;i<this->len;i++){if(isUp){tmp.num[i]++;if(tmp.num[i]>=10000){tmp.num[i]=0;isUp=true;}}if(tmp.num[i]+sec.num[i]<=9999){tmp.num[i]+=sec.num[i];isUp=false;}else{tmp.num[i]=tmp.num[i]+sec.num[i]-10000;isUp=true;}}long long maxn=tmp.len>sec.len?tmp.len:sec.len;if(tmp.num[maxn]!=0)            tmp.len++;        else            tmp.len=maxn;return tmp;}BigInteger operator-(const BigInteger& sec)//big-small{bool isBorrow=false;BigInteger tmp=*this;for(long long i=0;i<this->len;i++){if(isBorrow){tmp.num[i]-=1;if(tmp.num[i]<0)tmp.num[i]=9999;}if(tmp.num[i]<sec.num[i]){tmp.num[i]=tmp.num[i]+10000-sec.num[i];isBorrow=true;}else{tmp.num[i]-=sec.num[i];isBorrow=false;}}long long i=0;for(i=999;i>=0;i--)        {            if(tmp.num[i]!=0)                break;        }        if(i==-1)            tmp.len=1;        else            tmp.len=i+1;return tmp;}    BigInteger operator*(const BigInteger sec)    {        return this->Times(sec);    }BigInteger operator/(long long sec)//big/small{    /*if(sec==1)            return *this;*/        BigInteger ret;        long long i,down=0;for(i=len-1;i>=0;i--)        {            ret.num[i]=(num[i]+down*10000)/sec;            down=num[i]+down*10000-ret.num[i]*sec;        }        ret.len=len;        while(ret.num[ret.len-1]==0&&ret.len>1)            ret.len--;        return ret;}BigInteger operator%(long long sec){BigInteger tmp=*this;BigInteger shang=tmp/sec;BigInteger big_sec=BigInteger(sec);BigInteger ans=tmp-shang*big_sec;return ans;}BigInteger& operator++()    {        this->plusone();        return *this;    }bool operator<=(const BigInteger& sec){if(len<sec.len)return true;for(long long i=len-1;i>=0;i--){if(num[i]>sec.num[i])return false;}return true;}bool operator>=(const BigInteger& sec){if(len>sec.len)return true;for(long long i=len-1;i>=0;i--){if(num[i]<sec.num[i])return false;}return true;}bool operator==(const BigInteger& sec){if(len!=sec.len)return false;for(long long i=len-1;i>=0;i--){if(num[i]!=sec.num[i])return false;}return true;}bool operator==(const long long& sec){if(len!=1)return false;if(num[0]==sec)return true;elsereturn false;}bool operator<(const BigInteger& sec){if(len<sec.len)return true;for(long long i=len-1;i>=0;i--){if(num[i]>sec.num[i])return false;else if(num[i]<sec.num[i])return true;}return false;}bool operator>(const BigInteger& sec){if(len>sec.len)return true;for(long long i=len-1;i>=0;i--){if(num[i]<sec.num[i])return false;else if(num[i]>sec.num[i])return true;}return false;}bool operator!=(const BigInteger& sec){if(len!=sec.len)return true;for(long long i=len-1;i>=0;i--){if(num[i]!=sec.num[i])return true;}return false;}/*BigInteger GCD(const BigInteger& first,const BigInteger& sec){return first%sec==0?sec:GCD(sec,first%sec);}BigInteger LCM(const BigInteger& first,const BigInteger& sec){return first/GCD(first,sec)*sec;}*/};long long gcd(long long a,long long b){    if(a<b)        swap(a,b);    return b==0?a:gcd(b,a%b);}long long lcm(long long a,long long b){    return a/gcd(a,b)*b;}int main(){    //freopen("D:/1.txt","r",stdin);//freopen("D:/my.txt","w",stdout);    long long n;    long long first;    cin>>n;    for(long long i=0;i<n;i++)    {        long long time;        cin>>time;        if(!i)            first=time;        else if(first!=time)        {            long long tmp=gcd(first*time,2*absMy(first-time));            a[que]=first*time/tmp;            b[que++]=2*absMy(first-time)/tmp;            first=time;        }    }    if(que==1)    {        printf("%lld %lld\n",a[0],b[0]);    }    else    {        long long gcdnum;        gcdnum=gcd(b[0],b[1]);        for(long long i=2;i<que;i++)        {            gcdnum=gcd(gcdnum,b[i]);        }        long long ans2=gcdnum;        BigInteger a0=BigInteger(a[0]);        BigInteger a1=BigInteger(a[1]);        BigInteger lcmnum=a0*a1/gcd(a[0],a[1]);        BigInteger bigai;        BigInteger modn_big;        long long tmpgcd;        for(long long i=2;i<que;i++)        {            modn_big=lcmnum%a[i];            long long modn=modn_big.num[1]*10000+modn_big.num[0];            tmpgcd=gcd(a[i],modn);            bigai=BigInteger(a[i]);            lcmnum=bigai*lcmnum/tmpgcd;            /*cout<<"TMPGCDis: ";            lcmnum.Print();            NNN            cout<<"lcmis: ";            lcmnum.Print();            NNN            cout<<"lcmis: ";            lcmnum.Print();            NNN*/        }        lcmnum.Print();        printf(" %lld\n",ans2);    }}
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