3365: Fixed Point
题目描述
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is a point that is mapped to itself by the function. That is to say, x is a fixed point of the function f if and only if f(x) = x. For example, if f is defined on the real numbers by f(x)=x*x-3*x+4.,then 2 is a fixed point of f, because f(2) = 2.
Not all functions have fixed points: for example, if f is a function defined on the real numbers as f(x) = x + 1, then it has no fixed points, since x is never equal to x + 1 for any real number. In graphical terms, a fixed point means the point (x, f(x)) is on the line y = x, or in other words the graph of f has a point in common with that line. The example f(x) = x + 1 is a case where the graph and the line are a pair of parallel lines.
------ http://en.wikipedia.org/wiki/Fixed_point_%28mathematics%29
Our problem is,for a defined on real number function:
f(x)=a*x*x*x+b*x*x+c*x+d,how many different fixed points does it have?输入
You can assume that -213<=a<=213, -213<=b<=213, -213<=c<=213, -213<=d<=213,and the number of the result is countable.
输出
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For each test case, output the answer in a single line. |
样例输入 复制
3 111 793 -3456
5 -135 811 0
-1 9 10 -81
样例输出 复制
3
3
3