2026年（2023级）考试题目汇总 笔试 大班离散。2小时，闭卷。 1. 给出一些自然语言表述，请用谓词逻辑刻画并用谓词逻辑的证明系统，证明某个自然语言表述。 2. 对于Sierpiński carpet 分型n次后的图形，用数学归纳法证明其面积等于某个表达式a_n，周长等于某个表达式b……

This is a hard version of Ep. 67. If you prefer an easier problem, please see OBCYSIO67. Meeting Point Given a directed graph G of n vertices and m edges. A single vertex S is called the starting point and a single vertex T is called the finish poi……

Solved! Difficulty: D2C Pretty basic exercise problem from FLA This is an easy version of Ep. 68. If you prefer harder problems, please visit here. Meeting Point Given a directed graph G of n vertices and m edges. A single vertex S is called ……

Solved! Difficulty: Div2C Classic 思考题 HP You are given a grid of n*m cells. You start from a starting cell S and can move up, down, left or right in one step without leaving the grid. Find: is it possible to visit each cell once and exactl……

Solved Difficulty: D2C 思考题 inspired by Saionji Video Channel Eastmost Eki There are n points on a 2D plane. You can select any real point as pivot in the rectangle bounded by (a,b) and (c,d) and rotate the entire plane by d degree clockwis……

思考题 inspired by car lanes Car Lane In Ryuto the capital of the Dragon Kingdom, there is an intersection with k+1 exits. On one lane of one exit, there is a queue of n cars. The i-th car in the queue wants to go in the direction d_i (1\leq d_i\le……

Solved Difficulty: D2C-D2D 思考题 inspired by Create Mod Assembly Line There is an assembly line consisting of n machines. The i-th machine on the line holds an infinitely long input queue and a processing time of t_i seconds. The machines wo……

short 思考题 A^B Problem Given two pattern strings A and B that consists of lower-case letters, ? (match a single character) and * (match zero or more characters) For example, abc?d*e matches abcfdppe and abcgde but not ae or abcdee. Find a string ……

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……

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……