funny problem from model theory problem sheet 题面 Let L be a countable language, T a theory. Let c_1,c_2,... be new constants, L'=L\cup\lbrace c_1,...\rbrace, and let X be the set of all complete theories of L' with T\subset t. Enumerate the L' se……

前言 红黑树是一种复杂的平衡树，在大部分情况下都会使用父指针或者递归实现。假如我们一定要三无实现呢？ 本文必须配合OI-Wiki食用！！ 基础结构 #define BLK_COLOR 0 #define RED_COLOR 1 #define LEFT 0 #define RIGHT 1 #define Color(node) (node==NULL?BLK_COLO……

感谢XLH同学指出blog中的一些错误，本文已于2024/9/28更新 引入 AVL树有种种实现方式，其中最自然的是采用递归的写法，毕竟AVL树是递归定义的。但是，有的老师认为“递归时间常数大”，觉得应该用迭代。但是，还有老师认为迭代要用栈，“栈空间大（指占用了 O(\log n) ）……

Rotman algebraic topology上的题, 个人认为出的非常好, 极大增进了读者对\pi_1(S^1)计算过程的理解. 题面 A group G which is also a topology space is called a topological group if \mu:G\times G\to G:(x,y)\mapsto xy and i:G\to G:x\mapsto x^{-1} are contin……

Dieudonne的题, 真实难度不好说, 回顾一下发现其实挺简单的. 题面 Let E be a Hilbert space, F a dense linear subspace of E, distinct from E. (For example E space of l^2 sum of a suitable countable linear independent set and F space of finite sum of thi……

It's a well known fact that Euclidean domains are principal ideal domain by taking the element in a certain ideal with smallest \varphi value. Yet the converse is false, and one counterexample just lies among our familiar algebraic integer rings, \……

题目背景 为证一个非零吃大师 题面 Assuming AC, prove that for a integral domain R, if any nonzero prime ideal P contains a nonzero prime (p), R is UFD. 先想再看提示哦 提示 Let S be the set of elements that are prime factori……

This proof is due to Choudum. A sequence of nonnegative integers (d_1,...,d_n) is called graphic if there is a simple graph G with V(G)=\lbrace v_1,...,v_n\rbrace and d(v_i)=d_i. It's very easy to show that if a nonincreasing sequence, i.e. d_1\ge ……

飞机上半昏迷状态下以为无法调整, 暴力算出来的搞笑解答. 非常具有统计色彩 (nod) 题面 A simple graph G is called complete k-partite if there's a partion of V(G): A_1,..., A_k s.t. for all i there's no edge with both vertices in A_i , and for any v\in A……

高程复习 C++与C的关系 C++包含了C的所有成分 添加了： 更好的支持过程式编程，提高与类型相关的安全性 支持面向对象 支持泛型 带参数的宏定义的缺点： 需要加上很多括号 会出现重复计算 (e.g. ```max(x+1,y*2)```) 不进行类型检查和转换 不利于一些工具对程序……