★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★
➤ micro-channel public number: Shan Wing Chi ( shanqingyongzhi)
➤ blog Park address: San-ching Wing Chi ( https://www.cnblogs.com/strengthen/ )
➤GitHub address: https://github.com/strengthen/LeetCode
➤ original address: HTTPS: // the WWW. cnblogs.com/strengthen/p/10994773.html
➤ If the link is not the blog Chi Wing Shan Park address, it may be crawling author of the article.
➤ text has been modified update! Click strongly recommended that the original address read! Support authors! Support the original!
★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★
Monomial (monomial): algebraic expression of numbers or letters that is the product called monomials, a single letter or number, also called monomials. This term is a translation of the Qing Dynasty mathematician Li Shan-Ian finished the book in accordance with the original concept of the word. Digital single factor in the formula is called the monomial coefficients (Coefficient), a single formula, and all the letters of the index number is called the monomial (Degree of a monomial). Individual style is several times, several times called individual style.
Polynomial (Polynomial) Definition: it refers to a variable, and adding coefficient between them, subtraction, multiplication, exponentiation (non-negative integer power) obtained expression.
Generalized polynomials: 1 or 0 and are also considered monomial polynomial. By broad definition, a polynomial is Zhengshi. In fact, there is not a polynomial function of only narrow, Theorem monomials ineffective. 0 as a polynomial, is defined as the number of negative infinity (or 0). Monomial and polynomial collectively referred to as Zhengshi. Polynomial term, no letter is called a constant term. Continuous function is a simple polynomial, which is smooth, it must also be differential polynomial.
Polynomial function: the form f (x) = an · x ^ n + an-1 · x ^ (n-1) + ... + a2 · x ^ function 2 + a1 · x + a0, called polynomial function, which is a constant argument x after a limited number of multiplication and addition operations obtained. When n = 1, which is a linear function y = kx + b, when n = 2, which is a quadratic function.
Question: is known a polynomial function f (x) on the x, f (x) coefficients are positive integers, enter a positive integer N, the black box return value f (N) in a black box, will enter at least the number of times the coefficient of each item can be obtained polynomial f (x), that is obtained polynomial function f (x)?
Thought process:
The band is essentially based on the binary variable polynomial coefficients.
Example: Decimal
4321=4*10^3+3*10^2+2*10^1+1*10^0
Answer: The black box only needs to be entered twice, you can get polynomial coefficients.
First: input 1, to ensure that the factor for any
Black box returns f (1): that the whole polynomial and coefficients. Referred to as S = f (1).
Second: the input is greater than the value of S S + N, where N is a positive integer. The black box output value F (S + N) S + N into binary, that is, the polynomial coefficients (S + N) binary digital representation.
Such as: Input S + 1, the black box output value F (S + 1) S + 1 into binary. which is:
f(S+1)=
Is the coefficient corresponding to f (x) coefficients:
test:
Black box polynomial function: f (x) = 2 * x ^ 2 + 3 * x ^ 1 + 4 * x ^ 0
f(1)=9
f(9+1)=234
Intuitive to convert to decimal 234 234: 234 = 10 ^ 2 * 2 + 3 + 4 * 10 * 10 ^ 1 ^ 0
So coefficients of the polynomial function of the original order of 2,3,4.
Continue to test the polynomial function.
f(1)=9
f(9+2)=279
Short division 11 converts the hexadecimal 234 to 279: 279 = 11 ^ 2 * 2 + 3 + 4 * 11 * 11 ^ 1 ^ 0
So coefficients of the polynomial function of the original order of 2,3,4.
