It is possible to simplify the equation to a*x1^2+b*x2^2=-(c*x3^2+d*x4^2) first.And then use a hash table to put the left side of the equation in a two-tiered loop to save the value.Finally, we find the number of values of the left function with the right side by two loops and accumulate the answerThe specific details of the reference code#include "Turn" hdu-1496-equations: skillfully use hash
"Reprint Please specify source" Http://www.cnblogs.com/mashiqi2015/09/08Today we focus on the following equation:$ $u ' =au, \textrm{where} (a > 0) $$Due to $a > 0$, $ (U '-\sqrt{a}u) ' + \sqrt{a} (U '-\sqrt{a}u) =0 \rightarrow \frac{d (U '-\sqrt{a}u)}{u '-\sqrt{a}u}=-\sqrt{ a}dx$. Therefore $u '-\sqrt{a}u = C e^{-\sqrt{a}x}$. This is a first-order linear ordinary differential equation.Let $u (x) = f (x) e^{-\sqrt{a}x}$, we can get $f ' -2\sqrt{a}f=c \rightarrow (F+\frac{c}{2\sqrt{a}}) ' =2\sqrt
Cycle-13. A positive integer solution for a special equation (15) time limit MS Memory limit 65536 KB code length limit 8000 B procedure StandardAuthor Zhang Tong Hongyu (Zhejiang University)The subject requires that all positive integer solutions of the equation x2+y2=n be obtained for any given positive integer n.Input format:The input gives a positive integer n (Output format:The output equation x2+y2=n all positive integer solutions, of which xInput Sample 1:884Output Example 1:10 2820 22Inp
Set A and B is a non-0 integer, G=GCD (A, a, a, a). The equation ax+by=g always has an integer solution (x1,y1) (which can be solved with the extended Euclidean algorithm), then each solution of the equation can be obtained by (x1+k*b/g,y1-k*a/g), where k can be any integer.Proof: The case of Ax+by=1 is first proved (GCD (A, b) =1). (1)if (x, y) is a solution of (1), then (X+kb,y-ka) is also (1) The solution, this is obvious.Of course, if (x1,y1) and (X2,y2) are both (1)-type solutions, thenAx1+
Newton Iteration#include #includestring.h>#includeusing namespacestd;floatFfloatx) { return(Pow (x,3)-5*pow (x,2)+ -*x+ the);}floatF1 (floatx) { return(3*pow (x,2)-5*x+ -);}intMain () {//x*x*x-5*x*x+16*x+80; floatx=1, X1,y1,y2; CIN>>x; Do{x1=x; Y1=f (x); Y2=F1 (x1); X=x1-y1/Y2; } while(Fabs (X-X1) >=0.000001); coutEndl; System ("Pause"); return 0;}If you want to calculate the root under 3, then the equation is x*x-3=0;Fabs the absolute value of floating-point numbersThe equation is sol
(Note the differences in the boundary conditions here)Using the standard solution of mathematical solution for ue=-0.5x2+0.5;clear All;close ALL;CLC;%method for overall central differencePercent forward difference to find out boundary u[0]=u[1]x1=linspace (0,1,7);d x=1/6; x0=linspace (0,1, -); UE=-0.5*x0.^2+0.5;%Exact solution plot (X0,ue,'k -'); hold On;e=ones (5,1); A=spdiags ([-E2*e-e],[-1 0 1],5,5);%a=toeplitz ([2,-1,0,0,0]); A (1,1)=1; A1=a/dx/DX;B1=ones (5,1); U10=a1\b1;u1=[U10 (1); U10;0]
Recently, in the model PRT processing, we need to use the least square method to optimize the fitting of sampling points. We may know the least square method (http://en.wikipedia.org/wiki/Least_squares ), in general, in order to facilitate the calculation of the target point, a matrix is usually introduced and the following matrix equation is obtained:Ax = BTheXIs a parameter column vector about the target point,BIs the corresponding observed vector, andAIs the data matrix obtained based on the
[Description]
A equations X1 + X2 +... + Xn = P.
X1> = A1, X2> = a2,..., xn> =.
Number of non-negative integer solutions of the equation is given in Series.
[Input description]
There are n + 2 rows of data. First Act N, followed by N Act a series. The last row is P.
[Output description]
The number of non-negative integer solutions.
[Example input]
2
1
1
6
[Sample output]
5
[Analysis]
Because each X has a lower limit, we set the sum of n1 = p-tot and t
Question
Is this a legendary deep search .... Uncertain, looks more like a simulation ,,,,
// I want to perform a deep search for questions. // I still simulate it. # include View code
HDU 2266 how many equations can you find (simulation, Deep Search)
Question address: http://acm.zju.edu.cn/onlinejudge/showProblem.do? Problemcode = 2678.
Question: 1 the answer to this question is gcd (m, n)
2. The point on the board is (I, j) 0
(A, B) forms a point set, making it possible for any I, j, 0
(A0 + k) % m, (b0 + k) % n) = (I, j)
This is a problem of homogeneous equations. It can be proved in number theory that the necessary and sufficient conditions for the solution of X = a (mod m) and X = B (mod n)
This article mainly introduces 97 kinds of curve equations commonly used in proe, the coordinate system used, and the legends for generating curves.
The curve types on each page are as follows:Page 1: disc spring, spiral, helical curve, butterfly curve, and Involute;Page 1: spiral, logarithm curve, spherical spiral, dual-arc external axis, and Xingxing line;Page 1: heart line, incircle spiral, sine curve, solar line, and ferma curve (a bit li
Typical problem and query set implementation
Question: A little, a few questions are analyzed, and there are analyses on the 81 pages of the black book. There are also many questions available on the Internet.
Note that WA will not be returned for some special cases. In addition, the description of the question is not accurate enough. The specific analysis section will be updated later.
1. Two equations may have different lengths and can be directly i
1. There is a soft uniform thin line, in the damping medium for small transverse vibration, the unit length chord resistance $F =-ru_t$. The vibration equation is deduced.Answer: $$\bex \rho u_{tt}=tu_{xx}-ru_t. \eex$$2. The three-dimensional heat conduction equation has the spherical symmetry form $u (x,y,z,t) =u (r,t) $ ($r =\sqrt{x^2+y^2+z^2}$) solution, trial: $$\bex U_t=a^2\sex{u_{rr}+\frac{2u_r}{r}}. \eex$$Proof: by $$\bex U_x=u_r\frac{x}{r},\quad u_{xx}=u_{rr}\frac{x^2}{r^2} +u_r\frac{r-x
2697: Iterative Method for Solving Equations
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Prompt
Question
Total time limit:
2000 ms
Memory limit:
65536kb
Description
For the Function Y = f (x) = x * x + a (where A is greater than 0 ). It is not easy to directly obtain the value of X when y = 0, but because Y is a monotonic increasing function, we can use this property t
2. Spherical equations and spherical coordinates
ISpherical Equation
1Definition: In the space Cartesian coordinate system, equation (X-a) ² + (Y-B) ² + (Z-C) ² = R (R is a real number)
The representation of the image is called a (generalized) sphere, where (a, B, c) is called its center.
It is called its radius.
It is not hard to see that the generalized sphere includes a common sphere, one point and a virtual sphere.
2Feature of the equa
{d} (\ Omega) \), \ (| v | _ k = \ sup _ {\ Omega} | V (X) |, \, V \ In \ mathcal {d} (\ Omega ). \) (you can prove it yourself)
$ \ Mit L ^ {p} (\ Omega) $ \ (\ subset \ mathcal {d'} (\ Omega )\), but $ \ mathcal {d'} (\ Omega) \ not \ subset \ mit L ^ {p} (\ Omega), p \ Ge, 1. $Step 1 proves that $ \ forall L \ In \ mit L ^ {p} (\ Omega) $ is a linear functional of \ (\ mathcal {d} (\ Omega;\ [\ Begin {Align *} l (v) = Step 2 proves that \ (L \) is continuous, that is, proof \ (| L (V) |
MATLAB solves the delayed differential equation. dde23 call format:
Sol = dde23 (ddefun, lags, history, tspan );
-- Ddefun function handle, solving the Differential EquationY' = f (t, y (t), y (t-Tau 1),..., y (t-Tau k ))
It must be written in the following format:
Dydt = ddefun (T, y, z );
T corresponds to the current time t, and Y is the column vector, which is similar to Y (t); Z (:, j) is similarY (t-Tau J)
-- LagsIs the delay time, positive constant.
For example, if the equation contains y1
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Strange way to express Integers
Descriptionelina is reading a book written by rujia Liu, which introduces a strange way to express non-negative integers. The way is described as following:Choose k different positive integers A1, A2 ,..., AK. For some non-negative M, divide it by every AI (1 ≤ I ≤ k) to find the remainder Ri. If A1, A2 ,..., AK are properly chosen, m can be determined, then the pairs (AI, RI) can be used to express M."It is easy to calc
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