reciprocity theorem

Description:Each edge has a probability of being present, asking the probability of the occurrence of a spanning tree. Solution:The probability that the probability of existence on the spanning tree does not exist by other edges.Matrix tree theorem can find the sum of the product of each spanning tree, then we turn the Benquan into Pi1−pi p i 1−p i \frac{p_i}{1-p_i}, make The Matrix tree theorem, and finall

set of integers of A*X+B*Y=GCD (A, B)Principle:When B = 0 o'clockx = 1,y = 0 is a set of solutions for the equation a*x+b*y=gcd (A, B).When b≠0A*x1+b*y1 = a*y2+b* (x2-a/b*y2)Proof Process:a*x1 + b*y1 = gcd (A, B)b*x2+ (a%b) *y2 = gcd (b,a%b)∵GCD (A, b) = gcd (b,a%b)∴a*x1 + b*y1 = b*x2+ (a%b) *y2=b*x2+ (A-[a/b]*b) *y2=b*x2+a*y2-[a/b]*b*y2=a*y2 + b (X2-[A/b]*y2)∴x1 = Y2,y1 = x2-[a/b]*y2The code is as follows:intEXGCD (intAintBintx,inty) { if(b = =0) {x=1, y =0; returnA; } intg = EXGCD (b,a%

block (the representative element of the original connected block). for(intx=1; xif(V[x].size () >1) {memset (A,0,sizeofA); for(intI=0, Lim=v[x].size (); i for(intA=v[x][i],b,j=i+1; jif(Tmp[a][b]) {//tmp[][] as the edge matrix can not be emptied, because the two connected blocks no longer appear at the same time. A[I][J]=A[J][I]=-TMP[A][B]; A[I][I]+=TMP[A][B], a[j][j]+=tmp[a][b]; }} Gauss (V[x].size ()); } for(intI=1; i//Calculate the end of a certain kind of edge

Lucas theorem Ans=c (n,0) +c (n,1) +......+c (n,k) =c (n/2333,0) *c (n%2333,0) +c (n/2333,0) *c (n%2333,1) +......+c (n/2333,0) *c (n%2333,2332) +c (/2333,1) *C (n%2333,0) +......+C (n/) 2333,k/2333) * (n%2333,k%2333) =∑c (N/2333,J) *sum[n%2333][2332] (0 Cal (N,k) =cal (n/2333,k/2333-1) *sum[n%2333][2332]+lucas (n/2333,k/2333) *sum[n%2333][k%2333] Attention to prefix and processing #include

Time limit:1000MS Memory Limit:32768KB 64bit IO Format:%lld %llu Submit Status Pra Ctice Lightoj 1214 Description Given integers, a and b, you should check whethera is divisible by b or not. We knowA integer a is divisible by an integer b if and only if there exists an integerC s Uch that a = b * C. Input Input starts with an integer T (≤525), denoting the number of test cases. Starts with a line containing-integers a ( -10200≤a≤10200) and B (|b| > 0, B fits into A + bit signed integer). Numbers

http://www.lydsy.com/JudgeOnline/problem.php?id=2467 Do not know why, see this problem decisively think of maxtrix-tree theorem, and then make Kirchhoff matrix. But first I need to understand the sample, test 3 kinds of situations to understand the sample. The example is that two Pentagon laps share an edge, all the points of the center polygon are in degrees 4, and the surrounding +1,-1 have edges and accumulate 1 (for 2 of cases do not write a spec

input consists of a sequence of lines, each containing an integer n. (n Output Print the word "yes" if 3 divide evenly into F (n).Print the word "no" if not.Sample Input 0 1 2 3 4 5 Sample Output No no yes no no no The thinking of solving problems: The application of congruence theorem. Reference Code: #include #include #include #include #include #include using namespace std; const int MAXN=1000000+10; int F[MAXN]; int ma

pair is the first instruction that gives the coordinates of the starting position. You may assume there is no more than instructions in each test case, and all the integer coordinates is in the range (-300, 300). The input is terminated if N is 0. Output for each test case there'll be one output line in the formatCase X:there is w pieces.,where x is the serial number starting from 1.Note:the figures below illustrate the and the sample input cases. Sample Input 5 0 0 0 1 1 1 1 0 0 0 7 1 1 1 5 2

The original topic see HDU 5768 In the [L,r] range is a multiple of 7 and does not satisfy the number of any given congruence. If the range is [1,100], does not meet the modulus of 3 to 2 or more than 3 of the modulus of 5 is 7,21,42,49,70,84,91, so the answer is 7.Where the divisor is a prime number other than 7 (≤105) (\le 10^5), the product of the divisor is less than 1018 10^{18}. The same redundancy has a maximum of 15. Analysis A multiple of 7 in all [L,r] range minus the number that sati

Test Instructions: T Group test data, each group of data one N, Beg (N-1)!%p? idea: Wilson's theorem: When and only if P is a prime number: (P-1)! ≡-1 (mod p), but 4 is an exception, (4-1). ≡2 (mod 4). The prime judgment is relatively slow and can be measured with miller_rabbin. #include

Friendship Link is the oldest Web site promotion method, in the Web site is very few initial stage of the Internet, the two more know the site through the exchange of links, making a "island" as the site effective contact, guide users can easily

Fifth chapter The law of large numbers and the central limit theorem Content Summary: The law of large numbers Theorem one (the special case of Chibi's law of large numbers) sets random variables to be independent of each other, with the same mean and variance: , for any given positive number, there are Set a random variable is a sequence of random variables, is a constant. For any given positive number,

has been painting Secret Garden recently, so the reverie of the four-color theorem has been aroused.Four-color theorem, also known as four-color conjecture, four-color problem, is one of the world's three major mathematical conjecture. The four-color theorem is a well-known mathematical theorem, and the popular saying

} \ times \ mathbb {R ^ n} \ rightarrow \ mathbb {R ^ n} :( V, W) \ rightarrow V \ times W. \] makes $ V \ times W $ linear for two components $ V and W $, and the product's norm is equal to the product of the norm: $ | V \ times w | = | v | \ cdot | w | $ (here $ | \ cdot | $ is a common European norm ), then we get an equation of the sum of squares of $ N $. Over the next 50 years, people have been trying to find a possible 16-square-sum equation, but all failed, so they began to wonder if s

Http://nathanmarz.com/blog/how-to-beat-the-cap-theorem.html Http://kb.cnblogs.com/page/124567/ The CAP theorem indicates that a database cannot satisfy consistency, availability, and partition fault tolerance at the same time ). However, partition fault tolerance cannot be sacrificed. Therefore, we can only make trade-offs on consistency and availability. How to handle such trade-offs is the core focus of nosql databases. However, there are many probl

Main content:1. Fourier analysis2. Shannon sampling theoremOne, Fourier transformReference:The strangled tutorial http://zhuanlan.zhihu.com/wille/19763358 Fourier analysisSecond, Shannon sampling theoremShannon's sampling theorem says that, as long as the sampling frequency is more than twice times the maximum frequency of the sampled signal, it can be fully recovered.Links: http://www.zhihu.com/question/24490634/answer/28430016Source: KnowNyquist sam

"Theorem Overview"The Chinese remainder theorem (Sun Tzu's theorem) is a method to solve the same-remainder group in ancient China. is an important theorem in number theory. One-element linear congruence Equation group problem was first seen in the Chinese Northern and Southern Dynasties (A.D. 5th century) of the mathe

Welcome to my Blog column "A detailed explanation of mathematical principles in image Processing"Full-text catalogs see mathematical Principles in Image Processing (master)http://blog.csdn.net/baimafujinji/article/details/48467225A detailed explanation of the mathematical Principles in image processing (part of the link has been posted)http://blog.csdn.net/baimafujinji/article/details/487510371.4.5 convolution theorem and its proofConvolution

Interface reconstruction theorem and Open-Close PrinciplesLink to related articles: module decomposition Principle Exploration module decomposition principle and three-Permission separation interface Relationship Stability Principle Exploration Interface Design theorem previous articles talked about the module decomposition principle and interface Relationship Stability principle, an Interface Design

This article is translated from @sevenson's article separating Axis theorem (SAT) explanation. The original author uses ActionScript to write the algorithm, but the main story is the algorithm principle, I think once the principle of the algorithm is mastered by us, choose what programming language to implement the algorithm is a secondary thing. I am not an English major, so the translation of the text is inappropriate or omissions, welcome you to co