22296번 - cubic 다국어언어 제한함수 구현

문제

Write a function P7:

• input parameter: integers a, b, c, d satisfying 1ドル\le\max(|$a$|,|$b$|,|$c$|,|$d$|)\le10^9$
• return value: a list of all rational roots of the equation a$x^3+$b$x^2+$c$x+$d$=0,ドル in any order (Each root should be included only once.)
  • Suppose that $[t_0,t_1,\cdots,t_{n-1}]$ is the exact answer and $[u_0,u_1,\cdots,u_{m-1}]$ is your output.
  • Let $r(k)=\{i\in\mathbb Z:0\le i<k\}=\{0,1,\cdots,k-1\}$ for every non-negative integer $k$.
  • Your answer will be graded correct iff there exists a bijective function $\sigma\colon r(n)\to r(m)$ such that \[\frac{|u_{\sigma(i)}-t_i|}{\max(1,|t_i|)}\le10^{-6}\qquad\text{for all }i\in r(n)\]
• Hint: The rational root theorem states the following:
  • Consider a polynomial function $f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_0$ with integer coefficients where $a_n$ and $a_0$ are nonzero.
  • If $\displaystyle f\left(\frac{p}{q}\right)=0,ドル where $|p|$ and $|q|$ are relatively prime positive integers, then $\displaystyle\frac{a_0}{p}$ and $\displaystyle\frac{a_n}{q}$ are integers.

입력

출력

제한

힌트

첨부

• B_P7_cubic.py