[NOIP2014] solving equations, noip2014 Solving Equations3732 Solving Equations
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Description
Input description
Input Description
The input file name is equation. in.
Enter n + 2 rows in total.
The

Transferred from: http://silencethinking.blog.163.com/blog/static/911490562008928105813169/Ax=b or Xa=bIn MATLAB, when solving linear equations, the division operator "/" and "\" are mainly used in the previous chapters. Such as:
The x=a\b expresses the solution of the ax=b of the matrix equation;
X=B/A represents the solution of the matrix equation xa=b.
For the x=a\b of the

Solving Linear Equations Using MATLABAx = B or XA = BIn Matlab, the Division operators "/" and "\" described in the previous chapter are used to solve linear equations. For example:X = A \ B indicates the solution of the matrix equation Ax = B;X = B/A indicates the solution of matrix equation XA = B.For Equations x = A

Solving Linear Equations in C Language
Classical problems are solved using the Gaussian appointment algorithm. This requires proper processing of any form of linear equations. It cannot be used only when the number of equations is equal to the number of unknown equations.
Fi

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The progressive advanced method for solving recursive equations -- the Generation Method
The progressive advanced method for solving recursive equations -- the Generation Method
This method can be used to estimate both the upper and lower bounds. As mentioned above, the key step of the me

of Gamma MabThera in political activity was transferred to a private hospital where he fell in love with the Doctor's daughter. He was released one months later. But the doctor's daughter had an ex-boyfriend, so the two men were going to fight. The first night of the duel, he knew he was going to die, because he was a sharpshooter, and he tidied up his manuscript all Night long: "I have no time" on the side of the manuscript. Aged 21 years. This argument is too romantic for a general historian

Solving the equations of linear equation by the algorithm1) solving a modal linear equation ax = b (mod n)Equation ax = b (mod n), ax = b + NY->ax-ny = b-AX + N (-y) =b where a,n,b is known. A set of special solutions to this equation can be obtained by expanding Euclidean.Here are some theorems for solving the equatio

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An advanced method for solving recursive equations -- using the formula
An advanced method for solving recursive equations -- using the formula
This method is like:
T(N) =At(N/B) +F(N) (6.17)
Provides three applicable formulas for the gradual order of the solutions of recursive

Practical problems and unary one-time equations
General steps: 1. Trial and adjudication of test instructions,
2. Set and set unknown
3. Column, according to the equation of equal relations
4. Solving and solving equations
5. Answer and write the answers
The general steps to solve a one-dimensional equat

Steps:Where a is a n*n the coefficients of the square vectors x and b are the unknowns and the constant vectors respectively:The system may have 0, one, or infinitely multiple solutions, depending on the coefficients matrix A and vector B. There are many methods for solving linear systems, where a classical method-Gaussian elimination (https://zh.wikipedia.org/wiki/Gaussian elimination method) is used. First, we exchange A and B to make a into an uppe

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A progressive Method for Solving recursive equations -- Iterative Method
A progressive Method for Solving recursive equations -- Iterative Method
This method is used to estimate the approximate order of the Solution of recursive equations. It d

Solving equations with Python: 650) this.width=650; "Src=" Https://s2.51cto.com/wyfs02/M02/96/2C/wKiom1kdkrODRtWkAAAqvDlsKRM970.png " Title= "3333.png" alt= "Wkiom1kdkrodrtwkaaaqvdlskrm970.png"/>
From sympy Import *x = symbol (' x ') y = symbol (' y ') print solve ([x x y -3,3* × + y-7],[x, Y])2. Limit: 650) this.width=650; "src=" Https://s5.51cto.com/wyfs02/M00/96/2C/wKioL1kdkFGxXhMaAAAThVe1bmI131.png

/d) mod n for i=0 to D-1 Print (X0+i (n/d)) mod nelse print "No Solutions"2) solving the modular linear equation set x = A1 (mod m1) x = a2 (mod m2) x = a3 (mod m3) The first two equations of the equation group are solved. X=m1*k1+a1=m2*k2+a2m1*k1+m2* (-K2) =a2-a1This equation can be solved by Euclid to solve the k1 of the smallest positive integer x=m1*k1+a1 obviously x is the smallest posit

, instead get \ ({x}^{2}=4 \), there are two solutions.Why is that? Two numbers are equal, their squares should be equal, and there is no doubt that there is more than one root.This is because the squared on both sides of the equation is not equivalent to deformation. That is, \ (a=b \) can launch \ ({a}^{2}={b}^{2} \), \ ({a}^{2}={b}^{2} \) cannot be pushed out \ (a=b \). Only two equations can be introduced to each other, they are equivalent to each

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Definite Equations
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Computing process:
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Note:
Use of commas and semicolons in Matrix Coefficients
Backslash used for Matrix Division
The values in the matrix are extracted using parentheses. The number of rows and columns starts from 1.
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Indefinite Equations
The number of unknown numbers is greater than the number of equations.

Definition: If G (r) =r, then the real number r is a fixed point of function G.If we have an equation f (x) = 0, which is indicated as a fixed point problem, there is: g (x) =x (Note: f (x) =g (x)-X)The fixed point r is a root of the equation f (x) =0, which is the y=g (x) and the y=x of the intersection is the fixed point RAlgorithm Analysis: x0 = Initial Set valuex1 = g (x0)x2 = g (x1)x3 = g (x2)... ...X (k+1) = g (x (k))Until it converges to g (r) = g (Lim x (i)) = Lim X (i+1) = RMATLAB Code

at the same time. Instead of finding another iteration. Theta; 0 = Theta; 0- alpha;/m * sum; I (h (x (I)-y (I) x0 (I) Theta; 1 = Theta; 1- alpha;/m * sum; I (h (x (I)-y (I) x1 (I)Solution 2: Normal EquationsJ ( Theta;) about Theta; evaluate to 0, and solve the join column equations: Theta; = (XTX)-1XTY (where the row vector of X is x (I), and each element of Y is y (I ))Note: (XTX)-1 is not necessarily meaningful.Case 1: the dimension of each x

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