5366: Calculus
内存限制：256 MB
时间限制：1.000 S
评测方式：文本比较
命题人：
提交：3
解决：3
题目描述
This summer, ZXyang became so tired when doing the problems of Multi-University contests. So he decided to attend the Unified National Graduate Entrance Examination. This day, he sees a problem of series.
Let S(x) be a function with x as the independent variable. S(x) can be represented by the formula as follow.
C is a constant integer ranging from 0 to 109.
ZXyang wonders if S(x) is convergent. S(x) is convergent if and only if ${\lim_{x\to+\infty}}$S(x)=c, where c is a constant.
Let S(x) be a function with x as the independent variable. S(x) can be represented by the formula as follow.
f(x)=$\sum_{i=0}^n$fi(x)
S(x)=$\sum_{j=0}^x$f(j)
fi(x) is a function with x as the independent variable. Furthermore. fi(x) belongs to the function set F.
F={C, $\frac{C}{x}$ ,Csinx,Ccosx, C/$\sin x$ ,C/$\cos x$ ,Cx,Cx}
C is a constant integer ranging from 0 to 109.
ZXyang wonders if S(x) is convergent. S(x) is convergent if and only if ${\lim_{x\to+\infty}}$S(x)=c, where c is a constant.
输入
The first line of input contains a single integer t (1≤t≤104) --- the number of test cases.
The first and the only line of each test case contains a single string s (1≤|s|≤100), indicating the formula of f(x). Fraction is presented as a/b. Cx is presented as C^x. It's guaranteed that the constant C won't be left out when C=1. f(x) consists of functions from F connected with +.
The first and the only line of each test case contains a single string s (1≤|s|≤100), indicating the formula of f(x). Fraction is presented as a/b. Cx is presented as C^x. It's guaranteed that the constant C won't be left out when C=1. f(x) consists of functions from F connected with +.
输出
For each test case, print YES in one line if S(x) is a convergent sequence, or print NO in one line if not.
样例输入 复制
2
1sinx+0cosx+3x+6/sinx
0样例输出 复制
NO
YES