题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=6152 题意:判定一个无向图是否有三个点的团或者三个点的独立集. 解法:Ramsey theorem,n >= 6 直接输出 Bad 否则暴力.我是直接暴力,加个break优化就好了. #include <bits/stdc++.h> using namespace std; typedef long long LL; const int maxn = 3e3+3; bool w[maxn][…
w https://en.wikipedia.org/wiki/Ramsey's_theorem https://zh.wikipedia.org/wiki/拉姆齐定理 在组合数学上,拉姆齐(Ramsey)定理,又称拉姆齐二染色定理,是要解决以下的问题:要找这样一个最小的数n,使得n个人中必定有 k 个人相识或 l 个人互不相识. 这个定理以弗兰克·普伦普顿·拉姆齐命名,1930年他在论文On a Problem in Formal Logic(<形式逻辑上的一个问题>)证明了R(3,3)=6…
Source: wiki: Parseval's theorem As for signal processing, the power within certain frequency band = the sum of (power spectrum at all frequencies within the frequency band)^2.…
Stat2.2x Probability(概率)课程由加州大学伯克利分校(University of California, Berkeley)于2014年在edX平台讲授. PDF笔记下载(Academia.edu) Summary Standard Error The standard error of a random variable $X$ is defined by $$SE(X)=\sqrt{E((X-E(X))^2)}$$ $SE$ measures the rough size…
http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2119 11178 - Morley's Theorem Time limit: 3.000 seconds Problem DMorley’s TheoremInput: Standard Input Output: Standard Output Morley’s theorem stat…
Dirichlet's Theorem on Arithmetic Progressions Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 16733 Accepted: 8427 Description If a and d are relatively prime positive integers, the arithmetic sequence beginning with a and increasing…
Kaushik Sathupadi Programmer. Creator. Co-Founder. Dad. See all my projects and blogs → A plain english introduction to CAP Theorem You’ll often hear about the CAP theorem which specifies some kind of an upper limit when designing distributed systems…
Problem D Morley's Theorem Input: Standard Input Output: Standard Output Morley's theorem states that that the lines trisecting the angles of an arbitrary plane triangle meet at the vertices of an equilateral triangle. For example in the figure below…
Master theorem provides a solution in asymptotic terms to solve time complexity problem of most divide and conquer algorithms. Recurrence relations of the form: T(n) = a T(n/b) + f(n) where a >= 1 and b > 1 Case 1: f(n) = O(nc) where c < logb a T…
Morley’s Theorem Input: Standard Input Output: Standard Output Morley’s theorem states that that the lines trisecting the angles of an arbitrary plane triangle meet at the vertices of an equilateral triangle. For example in the figure below the tri-s…
Fermat's Chirstmas Theorem Time Limit: 1000ms Memory limit: 65536K 有疑问?点这里^_^ 题目描写叙述 In a letter dated December 25, 1640; the great mathematician Pierre de Fermat wrote to Marin Mersenne that he just proved that an odd prime p is expressible as p…
The Central Limit Theorem (CLT), and the concept of the sampling distribution, are critical for understanding why statistical inference works. There are at least a handful of problems that require you to invoke the Central Limit Theorem on every ASQ…
Infinite monkey theorem Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 1702 Accepted Submission(s): 882 Problem Description Could you imaging a monkey writing computer programs? Surely monkeys are…
Proof of Theorem 20.3 Theorem 20.3 The topologies on \(\mathbb{R}^n\) induced by the euclidean metric \(d\) and the square metric \(\rho\) are the same as the product topology on \(\mathbb{R}^n\). Proof: a) Prove the two metrics can mutually limit ea…
Theorem 20.4 The uniform topology on \(\mathbb{R}^J\) is finer than the product topology and coarser than the box topology; these three topologies are all different if \(J\) is infinite. Proof: a) Prove the uniform topology is finer than the product…
Theorem 19.6 Let \(f: A \rightarrow \prod_{\alpha \in J} X_{\alpha}\) be given by the equation \[ f(a) = (f_{\alpha}(a))_{\alpha \in J}, \] where \(f_{\alpha}: A \rightarrow X_{\alpha}\) for each \(\alpha\). Let \(\prod X_{\alpha}\) have the product…
Theorem 16.3 If \(A\) is a subspace of \(X\) and \(B\) is a subspace of \(Y\), then the product topology on \(A \times B\) is the same as the topology \(A \times B\) inherits as a subspace of \(X \times Y\). Comment: To prove the identity of two topo…
(Remark: The proof presented in this post is a reorganization and interpretation of that given by James Munkres in his book "Topology".) Theorem 37.3 (Tychonov Theorem) The product of arbitrary number of compact spaces is compact in the product…
确界原理 supremum and infimum principle 戴德金定理 Dedekind theorem http://www.math.ubc.ca/~cass/courses/m446-05b/dedekind-book.pdf#page=15 continulity and irrational numbersthe nature and meaning of numbers…
