BestCoder Round #54 (div.2) HDU5329 Geometric Progression

Geometric Progression

                                                    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
                                                                            Total Submission(s): 1040    Accepted Submission(s): 294

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 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.

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 ≠ 0 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≤20) which denotes the number of test cases. 

For each test case, there is an positive integer n(1≤n≤100) 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

41031 1 131 4 2516 8 4 2 1

 

Sample Output

YesYesNoYes

 

Source

BestCoder Round #54 (div.2)

出题人：判断是否为等比数列，可以检验对所有$1<i<n$

$A[i-1]\ast A[i+1]=A[i]\ast A[i]$ 是否都成立。

直接高精度也是资词的。比较简单的方法是选择若干质数

（保证乘积大于10^{200}10​200​​），在模意义下检验。

复杂度$O(k\ast n)$。$k$表示选取的质数个数。

1003：HDU5329 Geometric Progression

Geometric Progression

                                                    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
                                                                            Total Submission(s): 1040    Accepted Submission(s): 294

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 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.

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 ≠ 0 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≤20) which denotes the number of test cases. 

For each test case, there is an positive integer n(1≤n≤100) 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

41031 1 131 4 2516 8 4 2 1

 

Sample Output

YesYesNoYes

 

Source

BestCoder Round #54 (div.2)

出题人：判断是否为等比数列，可以检验对所有$1<i<n$

$A[i-1]\ast A[i+1]=A[i]\ast A[i]$ 是否都成立。直接高精度也是资词的。

比较简单的方法是选择若干质数（保证乘积大于10^{200}10​200​​），

在模意义下检验。复杂度$O(k\ast n)$。$k$表示选取的质数个数。