Problem Description
Determine whether a sequence is a Geometric progression or not. In mathematics, a **geometric progression**, also known as a **geometric sequence**, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence , , , , ... is a geometric progression with common ratio . Similarly , , 2.5, 1.25, ... is a geometric sequence with common ratio /. Examples of a geometric sequence are powers rk of a fixed number r, such as 2k and 3k. The general form of a geometric sequence is a, ar, ar2, ar3, ar4, … where r ≠ is the common ratio and a is a scale factor, equal to the sequence's start value.
Input
First line contains a single integer T(T≤) which denotes the number of test cases. For each test case, there is an positive integer n(≤n≤) which denotes the length of sequence,and next line has n nonnegative numbers Ai which allow leading zero.The digit's length of Ai no larger than 100.
Output
For each case, output "Yes" or "No".
Sample Input
Sample Output
Yes
Yes
No
Yes
Source
判定一个序列是否是等比数列。
坑点：
首项可以是0，此时其余项必须全为0才是等比数列
扒了个比较好用的大数模板，几乎可以和int一样使用。
#include <iostream>
#include <cstring>
using namespace std; #define DIGIT 4 //四位隔开,即万进制
#define DEPTH 10000 //万进制
#define MAX 251 //题目最大位数/4，要不大直接设为最大位数也行
typedef int bignum_t[MAX+]; /************************************************************************/
/* 读取操作数，对操作数进行处理存储在数组里 */
/************************************************************************/
int read(bignum_t a,istream&is=cin)
{
char buf[MAX*DIGIT+],ch ;
int i,j ;
memset((void*)a,,sizeof(bignum_t));
if(!(is>>buf))return ;
for(a[]=strlen(buf),i=a[]/-;i>=;i--)
ch=buf[i],buf[i]=buf[a[]--i],buf[a[]--i]=ch ;
for(a[]=(a[]+DIGIT-)/DIGIT,j=strlen(buf);j<a[]*DIGIT;buf[j++]='');
for(i=;i<=a[];i++)
for(a[i]=,j=;j<DIGIT;j++)
a[i]=a[i]*+buf[i*DIGIT--j]-'' ;
for(;!a[a[]]&&a[]>;a[]--);
return ;
} void write(const bignum_t a,ostream&os=cout)
{
int i,j ;
for(os<<a[i=a[]],i--;i;i--)
for(j=DEPTH/;j;j/=)
os<<a[i]/j% ;
} int comp(const bignum_t a,const bignum_t b)
{
int i ;
if(a[]!=b[])
return a[]-b[];
for(i=a[];i;i--)
if(a[i]!=b[i])
return a[i]-b[i];
return ;
} int comp(const bignum_t a,const int b)
{
int c[]=
{ }
;
for(c[]=b;c[c[]]>=DEPTH;c[c[]+]=c[c[]]/DEPTH,c[c[]]%=DEPTH,c[]++);
return comp(a,c);
} int comp(const bignum_t a,const int c,const int d,const bignum_t b)
{
int i,t=,O=-DEPTH* ;
if(b[]-a[]<d&&c)
return ;
for(i=b[];i>d;i--)
{
t=t*DEPTH+a[i-d]*c-b[i];
if(t>)return ;
if(t<O)return ;
}
for(i=d;i;i--)
{
t=t*DEPTH-b[i];
if(t>)return ;
if(t<O)return ;
}
return t> ;
}
/************************************************************************/
/* 大数与大数相加 */
/************************************************************************/
void add(bignum_t a,const bignum_t b)
{
int i ;
for(i=;i<=b[];i++)
if((a[i]+=b[i])>=DEPTH)
a[i]-=DEPTH,a[i+]++;
if(b[]>=a[])
a[]=b[];
else
for(;a[i]>=DEPTH&&i<a[];a[i]-=DEPTH,i++,a[i]++);
a[]+=(a[a[]+]>);
}
/************************************************************************/
/* 大数与小数相加 */
/************************************************************************/
void add(bignum_t a,const int b)
{
int i= ;
for(a[]+=b;a[i]>=DEPTH&&i<a[];a[i+]+=a[i]/DEPTH,a[i]%=DEPTH,i++);
for(;a[a[]]>=DEPTH;a[a[]+]=a[a[]]/DEPTH,a[a[]]%=DEPTH,a[]++);
}
/************************************************************************/
/* 大数相减(被减数>=减数) */
/************************************************************************/
void sub(bignum_t a,const bignum_t b)
{
int i ;
for(i=;i<=b[];i++)
if((a[i]-=b[i])<)
a[i+]--,a[i]+=DEPTH ;
for(;a[i]<;a[i]+=DEPTH,i++,a[i]--);
for(;!a[a[]]&&a[]>;a[]--);
}
/************************************************************************/
/* 大数减去小数(被减数>=减数) */
/************************************************************************/
void sub(bignum_t a,const int b)
{
int i= ;
for(a[]-=b;a[i]<;a[i+]+=(a[i]-DEPTH+)/DEPTH,a[i]-=(a[i]-DEPTH+)/DEPTH*DEPTH,i++);
for(;!a[a[]]&&a[]>;a[]--);
} void sub(bignum_t a,const bignum_t b,const int c,const int d)
{
int i,O=b[]+d ;
for(i=+d;i<=O;i++)
if((a[i]-=b[i-d]*c)<)
a[i+]+=(a[i]-DEPTH+)/DEPTH,a[i]-=(a[i]-DEPTH+)/DEPTH*DEPTH ;
for(;a[i]<;a[i+]+=(a[i]-DEPTH+)/DEPTH,a[i]-=(a[i]-DEPTH+)/DEPTH*DEPTH,i++);
for(;!a[a[]]&&a[]>;a[]--);
}
/************************************************************************/
/* 大数相乘，读入被乘数a，乘数b，结果保存在c[] */
/************************************************************************/
void mul(bignum_t c,const bignum_t a,const bignum_t b)
{
int i,j ;
memset((void*)c,,sizeof(bignum_t));
for(c[]=a[]+b[]-,i=;i<=a[];i++)
for(j=;j<=b[];j++)
if((c[i+j-]+=a[i]*b[j])>=DEPTH)
c[i+j]+=c[i+j-]/DEPTH,c[i+j-]%=DEPTH ;
for(c[]+=(c[c[]+]>);!c[c[]]&&c[]>;c[]--);
}
/************************************************************************/
/* 大数乘以小数，读入被乘数a，乘数b，结果保存在被乘数 */
/************************************************************************/
void mul(bignum_t a,const int b)
{
int i ;
for(a[]*=b,i=;i<=a[];i++)
{
a[i]*=b ;
if(a[i-]>=DEPTH)
a[i]+=a[i-]/DEPTH,a[i-]%=DEPTH ;
}
for(;a[a[]]>=DEPTH;a[a[]+]=a[a[]]/DEPTH,a[a[]]%=DEPTH,a[]++);
for(;!a[a[]]&&a[]>;a[]--);
} void mul(bignum_t b,const bignum_t a,const int c,const int d)
{
int i ;
memset((void*)b,,sizeof(bignum_t));
for(b[]=a[]+d,i=d+;i<=b[];i++)
if((b[i]+=a[i-d]*c)>=DEPTH)
b[i+]+=b[i]/DEPTH,b[i]%=DEPTH ;
for(;b[b[]+];b[]++,b[b[]+]=b[b[]]/DEPTH,b[b[]]%=DEPTH);
for(;!b[b[]]&&b[]>;b[]--);
}
/**************************************************************************/
/* 大数相除,读入被除数a，除数b，结果保存在c[]数组 */
/* 需要comp()函数 */
/**************************************************************************/
void div(bignum_t c,bignum_t a,const bignum_t b)
{
int h,l,m,i ;
memset((void*)c,,sizeof(bignum_t));
c[]=(b[]<a[]+)?(a[]-b[]+): ;
for(i=c[];i;sub(a,b,c[i]=m,i-),i--)
for(h=DEPTH-,l=,m=(h+l+)>>;h>l;m=(h+l+)>>)
if(comp(b,m,i-,a))h=m- ;
else l=m ;
for(;!c[c[]]&&c[]>;c[]--);
c[]=c[]>?c[]: ;
} void div(bignum_t a,const int b,int&c)
{
int i ;
for(c=,i=a[];i;c=c*DEPTH+a[i],a[i]=c/b,c%=b,i--);
for(;!a[a[]]&&a[]>;a[]--);
}
/************************************************************************/
/* 大数平方根，读入大数a，结果保存在b[]数组里 */
/* 需要comp()函数 */
/************************************************************************/
void sqrt(bignum_t b,bignum_t a)
{
int h,l,m,i ;
memset((void*)b,,sizeof(bignum_t));
for(i=b[]=(a[]+)>>;i;sub(a,b,m,i-),b[i]+=m,i--)
for(h=DEPTH-,l=,b[i]=m=(h+l+)>>;h>l;b[i]=m=(h+l+)>>)
if(comp(b,m,i-,a))h=m- ;
else l=m ;
for(;!b[b[]]&&b[]>;b[]--);
for(i=;i<=b[];b[i++]>>=);
}
/************************************************************************/
/* 返回大数的长度 */
/************************************************************************/
int length(const bignum_t a)
{
int t,ret ;
for(ret=(a[]-)*DIGIT,t=a[a[]];t;t/=,ret++);
return ret>?ret: ;
}
/************************************************************************/
/* 返回指定位置的数字，从低位开始数到第b位，返回b位上的数 */
/************************************************************************/
int digit(const bignum_t a,const int b)
{
int i,ret ;
for(ret=a[(b-)/DIGIT+],i=(b-)%DIGIT;i;ret/=,i--);
return ret% ;
}
/************************************************************************/
/* 返回大数末尾0的个数 */
/************************************************************************/
int zeronum(const bignum_t a)
{
int ret,t ;
for(ret=;!a[ret+];ret++);
for(t=a[ret+],ret*=DIGIT;!(t%);t/=,ret++);
return ret ;
} void comp(int*a,const int l,const int h,const int d)
{
int i,j,t ;
for(i=l;i<=h;i++)
for(t=i,j=;t>;j++)
while(!(t%j))
a[j]+=d,t/=j ;
} void convert(int*a,const int h,bignum_t b)
{
int i,j,t= ;
memset(b,,sizeof(bignum_t));
for(b[]=b[]=,i=;i<=h;i++)
if(a[i])
for(j=a[i];j;t*=i,j--)
if(t*i>DEPTH)
mul(b,t),t= ;
mul(b,t);
}
/************************************************************************/
/* 组合数 */
/************************************************************************/
void combination(bignum_t a,int m,int n)
{
int*t=new int[m+];
memset((void*)t,,sizeof(int)*(m+));
comp(t,n+,m,);
comp(t,,m-n,-);
convert(t,m,a);
delete[]t ;
}
/************************************************************************/
/* 排列数 */
/************************************************************************/
void permutation(bignum_t a,int m,int n)
{
int i,t= ;
memset(a,,sizeof(bignum_t));
a[]=a[]= ;
for(i=m-n+;i<=m;t*=i++)
if(t*i>DEPTH)
mul(a,t),t= ;
mul(a,t);
} #define SGN(x) ((x)>0?1:((x)<0?-1:0))
#define ABS(x) ((x)>0?(x):-(x)) int read(bignum_t a,int&sgn,istream&is=cin)
{
char str[MAX*DIGIT+],ch,*buf ;
int i,j ;
memset((void*)a,,sizeof(bignum_t));
if(!(is>>str))return ;
buf=str,sgn= ;
if(*buf=='-')sgn=-,buf++;
for(a[]=strlen(buf),i=a[]/-;i>=;i--)
ch=buf[i],buf[i]=buf[a[]--i],buf[a[]--i]=ch ;
for(a[]=(a[]+DIGIT-)/DIGIT,j=strlen(buf);j<a[]*DIGIT;buf[j++]='');
for(i=;i<=a[];i++)
for(a[i]=,j=;j<DIGIT;j++)
a[i]=a[i]*+buf[i*DIGIT--j]-'' ;
for(;!a[a[]]&&a[]>;a[]--);
if(a[]==&&!a[])sgn= ;
return ;
}
struct bignum
{
bignum_t num ;
int sgn ;
public :
inline bignum()
{
memset(num,,sizeof(bignum_t));
num[]= ;
sgn= ;
}
inline int operator!()
{
return num[]==&&!num[];
}
inline bignum&operator=(const bignum&a)
{
memcpy(num,a.num,sizeof(bignum_t));
sgn=a.sgn ;
return*this ;
}
inline bignum&operator=(const int a)
{
memset(num,,sizeof(bignum_t));
num[]= ;
sgn=SGN (a);
add(num,sgn*a);
return*this ;
}
;
inline bignum&operator+=(const bignum&a)
{
if(sgn==a.sgn)add(num,a.num);
else if
(sgn&&a.sgn)
{
int ret=comp(num,a.num);
if(ret>)sub(num,a.num);
else if(ret<)
{
bignum_t t ;
memcpy(t,num,sizeof(bignum_t));
memcpy(num,a.num,sizeof(bignum_t));
sub (num,t);
sgn=a.sgn ;
}
else memset(num,,sizeof(bignum_t)),num[]=,sgn= ;
}
else if(!sgn)
memcpy(num,a.num,sizeof(bignum_t)),sgn=a.sgn ;
return*this ;
}
inline bignum&operator+=(const int a)
{
if(sgn*a>)add(num,ABS(a));
else if(sgn&&a)
{
int ret=comp(num,ABS(a));
if(ret>)sub(num,ABS(a));
else if(ret<)
{
bignum_t t ;
memcpy(t,num,sizeof(bignum_t));
memset(num,,sizeof(bignum_t));
num[]= ;
add(num,ABS (a));
sgn=-sgn ;
sub(num,t);
}
else memset(num,,sizeof(bignum_t)),num[]=,sgn= ;
}
else if
(!sgn)sgn=SGN(a),add(num,ABS(a));
return*this ;
}
inline bignum operator+(const bignum&a)
{
bignum ret ;
memcpy(ret.num,num,sizeof (bignum_t));
ret.sgn=sgn ;
ret+=a ;
return ret ;
}
inline bignum operator+(const int a)
{
bignum ret ;
memcpy(ret.num,num,sizeof (bignum_t));
ret.sgn=sgn ;
ret+=a ;
return ret ;
}
inline bignum&operator-=(const bignum&a)
{
if(sgn*a.sgn<)add(num,a.num);
else if
(sgn&&a.sgn)
{
int ret=comp(num,a.num);
if(ret>)sub(num,a.num);
else if(ret<)
{
bignum_t t ;
memcpy(t,num,sizeof(bignum_t));
memcpy(num,a.num,sizeof(bignum_t));
sub(num,t);
sgn=-sgn ;
}
else memset(num,,sizeof(bignum_t)),num[]=,sgn= ;
}
else if(!sgn)add (num,a.num),sgn=-a.sgn ;
return*this ;
}
inline bignum&operator-=(const int a)
{
if(sgn*a<)add(num,ABS(a));
else if(sgn&&a)
{
int ret=comp(num,ABS(a));
if(ret>)sub(num,ABS(a));
else if(ret<)
{
bignum_t t ;
memcpy(t,num,sizeof(bignum_t));
memset(num,,sizeof(bignum_t));
num[]= ;
add(num,ABS(a));
sub(num,t);
sgn=-sgn ;
}
else memset(num,,sizeof(bignum_t)),num[]=,sgn= ;
}
else if
(!sgn)sgn=-SGN(a),add(num,ABS(a));
return*this ;
}
inline bignum operator-(const bignum&a)
{
bignum ret ;
memcpy(ret.num,num,sizeof(bignum_t));
ret.sgn=sgn ;
ret-=a ;
return ret ;
}
inline bignum operator-(const int a)
{
bignum ret ;
memcpy(ret.num,num,sizeof(bignum_t));
ret.sgn=sgn ;
ret-=a ;
return ret ;
}
inline bignum&operator*=(const bignum&a)
{
bignum_t t ;
mul(t,num,a.num);
memcpy(num,t,sizeof(bignum_t));
sgn*=a.sgn ;
return*this ;
}
inline bignum&operator*=(const int a)
{
mul(num,ABS(a));
sgn*=SGN(a);
return*this ;
}
inline bignum operator*(const bignum&a)
{
bignum ret ;
mul(ret.num,num,a.num);
ret.sgn=sgn*a.sgn ;
return ret ;
}
inline bignum operator*(const int a)
{
bignum ret ;
memcpy(ret.num,num,sizeof (bignum_t));
mul(ret.num,ABS(a));
ret.sgn=sgn*SGN(a);
return ret ;
}
inline bignum&operator/=(const bignum&a)
{
bignum_t t ;
div(t,num,a.num);
memcpy (num,t,sizeof(bignum_t));
sgn=(num[]==&&!num[])?:sgn*a.sgn ;
return*this ;
}
inline bignum&operator/=(const int a)
{
int t ;
div(num,ABS(a),t);
sgn=(num[]==&&!num [])?:sgn*SGN(a);
return*this ;
}
inline bignum operator/(const bignum&a)
{
bignum ret ;
bignum_t t ;
memcpy(t,num,sizeof(bignum_t));
div(ret.num,t,a.num);
ret.sgn=(ret.num[]==&&!ret.num[])?:sgn*a.sgn ;
return ret ;
}
inline bignum operator/(const int a)
{
bignum ret ;
int t ;
memcpy(ret.num,num,sizeof(bignum_t));
div(ret.num,ABS(a),t);
ret.sgn=(ret.num[]==&&!ret.num[])?:sgn*SGN(a);
return ret ;
}
inline bignum&operator%=(const bignum&a)
{
bignum_t t ;
div(t,num,a.num);
if(num[]==&&!num[])sgn= ;
return*this ;
}
inline int operator%=(const int a)
{
int t ;
div(num,ABS(a),t);
memset(num,,sizeof (bignum_t));
num[]= ;
add(num,t);
return t ;
}
inline bignum operator%(const bignum&a)
{
bignum ret ;
bignum_t t ;
memcpy(ret.num,num,sizeof(bignum_t));
div(t,ret.num,a.num);
ret.sgn=(ret.num[]==&&!ret.num [])?:sgn ;
return ret ;
}
inline int operator%(const int a)
{
bignum ret ;
int t ;
memcpy(ret.num,num,sizeof(bignum_t));
div(ret.num,ABS(a),t);
memset(ret.num,,sizeof(bignum_t));
ret.num[]= ;
add(ret.num,t);
return t ;
}
inline bignum&operator++()
{
*this+= ;
return*this ;
}
inline bignum&operator--()
{
*this-= ;
return*this ;
}
;
inline int operator>(const bignum&a)
{
return sgn>?(a.sgn>?comp(num,a.num)>:):(sgn<?(a.sgn<?comp(num,a.num)<:):a.sgn<);
}
inline int operator>(const int a)
{
return sgn>?(a>?comp(num,a)>:):(sgn<?(a<?comp(num,-a)<:):a<);
}
inline int operator>=(const bignum&a)
{
return sgn>?(a.sgn>?comp(num,a.num)>=:):(sgn<?(a.sgn<?comp(num,a.num)<=:):a.sgn<=);
}
inline int operator>=(const int a)
{
return sgn>?(a>?comp(num,a)>=:):(sgn<?(a<?comp(num,-a)<=:):a<=);
}
inline int operator<(const bignum&a)
{
return sgn<?(a.sgn<?comp(num,a.num)>:):(sgn>?(a.sgn>?comp(num,a.num)<:):a.sgn>);
}
inline int operator<(const int a)
{
return sgn<?(a<?comp(num,-a)>:):(sgn>?(a>?comp(num,a)<:):a>);
}
inline int operator<=(const bignum&a)
{
return sgn<?(a.sgn<?comp(num,a.num)>=:):(sgn>?(a.sgn>?comp(num,a.num)<=:):a.sgn>=);
}
inline int operator<=(const int a)
{
return sgn<?(a<?comp(num,-a)>=:):
(sgn>?(a>?comp(num,a)<=:):a>=);
}
inline int operator==(const bignum&a)
{
return(sgn==a.sgn)?!comp(num,a.num): ;
}
inline int operator==(const int a)
{
return(sgn*a>=)?!comp(num,ABS(a)): ;
}
inline int operator!=(const bignum&a)
{
return(sgn==a.sgn)?comp(num,a.num): ;
}
inline int operator!=(const int a)
{
return(sgn*a>=)?comp(num,ABS(a)): ;
}
inline int operator[](const int a)
{
return digit(num,a);
}
friend inline istream&operator>>(istream&is,bignum&a)
{
read(a.num,a.sgn,is);
return is ;
}
friend inline ostream&operator<<(ostream&os,const bignum&a)
{
if(a.sgn<)
os<<'-' ;
write(a.num,os);
return os ;
}
friend inline bignum sqrt(const bignum&a)
{
bignum ret ;
bignum_t t ;
memcpy(t,a.num,sizeof(bignum_t));
sqrt(ret.num,t);
ret.sgn=ret.num[]!=||ret.num[];
return ret ;
}
friend inline bignum sqrt(const bignum&a,bignum&b)
{
bignum ret ;
memcpy(b.num,a.num,sizeof(bignum_t));
sqrt(ret.num,b.num);
ret.sgn=ret.num[]!=||ret.num[];
b.sgn=b.num[]!=||ret.num[];
return ret ;
}
inline int length()
{
return :: length(num);
}
inline int zeronum()
{
return :: zeronum(num);
}
inline bignum C(const int m,const int n)
{
combination(num,m,n);
sgn= ;
return*this ;
}
inline bignum P(const int m,const int n)
{
permutation(num,m,n);
sgn= ;
return*this ;
}
};
bignum a[],zero;
int main()
{
int i,t,n;
zero=;
cin>>t;
while(t--)
{
cin>>n;
int cnt=;
for(i=;i<n;++i)
{
cin>>a[i];
if(a[i]==zero) ++cnt;
}
if(cnt&&cnt!=n) cout<<"No"<<endl;
else{
for(i=;i<n-;++i)
if(a[i]*a[i]!=a[i-]*a[i+]) break;
if(i<n-) cout<<"No"<<endl;
else cout<<"Yes"<<endl;
}
}
return ;
}