Poj [number theory/combination/Game Theory] Question list

Source: Internet
Author: User

From: http://hi.baidu.com/lydrainbowcat/item/f16e64103f8c5c088fbde44c

 

Poj [number theory/combination/Game Theory] Question list

The original list is relatively watery. Today I changed a difficult list and started to do it again ~

The red color indicates that the AC has passed, and the blue color indicates that the AC has passed. This sentence seems to have an amount in each list in my space.

Game Theory

Poj 2234 matches game
Poj 2975 Nim
Poj 2505 a multiplication game
Poj 1067 takes the stone game weizov game, the singular situation (must defeat) is ak = [K * (1 + SQRT (5)/2], BK = ak + K;
Poj 2484 a funny game
Poj 2425 a chess game
Poj 2960 S-nim SG Function
Poj 1704 Georgia and Bob transformed the tiered game into Nim. When n is an odd number, P [1] is bound to 0.
Poj 1740 A new stone game
Poj 2068 Nim
Poj 3480 John anti-SG question Jia Zhihao's thesis Chapter2

Poj 2348 Euclid's game
Poj 3710 Christmas game
Poj 3533 light switching game
Poj 3537 crosses and crosses

Number Theory/Combination

 

 

1. Burnside theorem, polyA notation
You can refer to brudildi's composite mathematics. This chapter of this book is very detailed and easy to understand. It is best to fully understand and understand the problem, rather than simply remembering a formula.
* Simple question: (you can simply use a set of formulas)
Pku2409 let it Bead
Pku2154 color
Pku1286 neckparts of beads
* Strongly recommended: (this question is very good, very clever)
Pku2888 magic bracelet
2. Replacement and replacement operations

The concept of replacement is quite understandable, as described in composite mathematics. For power operation of replacement, you can refer to Pan zhenhao's article research and discussion on Fast Power Operation of replacement groups, which is well written.
* Simple question: (you should understand the concept)
Pku3270 cow sorting
Pku1026 Cipher
* Power replacement operation:
Pku1721 cards
Pku3128 Leonardo's notebook
* Recommendation: (good applications)
Pku3590 the shuffle Problem
3. prime number, integer decomposition, Euler's Function

Prime numbers are the most permanent and classic problems in number theory (our team name is primemusic ^-^ ). The determination of prime numbers, the screening method for prime numbers, the determination of large prime numbers... there are many other problems that will use prime numbers.
* The most watery: (used to relieve boredom when you are in a bad mood)
Pku1365 prime land
Pku2034 anti-prime Sequences
Pku2739 sum of consecutive prime numbers
Pku3518 prime gap
Pku3126 prime path
Pku1595 prime cuts
Pku3641 Pseudo Prime Numbers
Pku2191 Mersenne composite numbers
Pku1730 perfect PTH powers
Pku2262 Goldbach's Conjecture
Pku2909 Goldbach's Conjecture
* Screening method:
Pku2689 prime distance (a good application)
* Inverse Prime Number:
Zoj2562 more Divisors
* Prime number judgment, integer decomposition:
Both of these questions need to be judged by miller_rabin's prime number and the integer decomposition of pollard_rock. There will be both in the algorithm book. It should be a template question, but you 'd better understand it and try it again.
Pku1811 prime test
Pku2429 GCD & LCM Inverse

* Euler's function:
Euler's function can be used in many places in number theory, which is very important.
Pku1284 primitive roots (theorem about the original root: the original root of P is Euler (p). In this question, when P is an odd prime number, therefore, the answer is ))
Pku2407 relatives (very watery)
Pku2773 happy 2006
Pku2478 farey sequence (quick Euler's function)
Pku3090 visible lattice points (farei Series)
* Recommendation: (Euler's function, ferma's theorem)
Pku3358 period of an infinite binary expansion
* Integer Decomposition
This is also very important, including the representation of large numbers.
Pku2992 Divisors
Pku3101 astpolicmy (minimum public multiple of the score)
4. Extended Euclidean, linear covariance, Chinese Remainder Theorem

This should be an important part of number theory. There are many such questions. You 'd better first look at the number theory book. I have also sorted out some of them for reference:
* Simple question:
Pku1006 biorhythms
Pku1061 frog appointment
Pku2891 strange way to express Integers
Pku2115 C looooops
Pku2142 the balance
* Strongly recommended:
Sgu106 the equation
Pku3708 recurrent function (Classic)
5. Joseph Ring

This problem is quite interesting, not very difficult.
* Simple question:
Pku3517 and then there was one
Pku1781 in danger
Pku1012 Joseph
Pku2244 eeny meeny moo
* Recommended:
Pku2886 who gets the most candies?
6. Gaussian elimination method for solving the equation

In fact, it is not very difficult to solve the equation, that is, to convert the coefficient matrix into an upper triangle matrix or a Number Matrix Based on Linear Algebra. However, there are some questions to judge whether there is a solution or to enumerate all solutions. However, I think it is more difficult to establish the equations. This understanding makes no big problem.
* Simple question:
Pku1222 extended lights out
Pku1681 painter's Problem
Pku1830 switch Problem
* Recommended:
Pku2947 widget Factory
Pku2065 SETI
* Strongly recommended:
Pku1753 flip game
Pku3185 the water bowls
* Abnormal questions:
Pku1487 single-player games

7. Matrix
It is really common to use matrices to solve problems, but I am not using them very well now, and I will not solve many problems yet. I suggest you go to matrix67's article on the ten questions about the Matrix. It's really classic, but it's not easy to understand.
* Simple:
Pku3070 maid
Pku3233 matrix Power Series
Pku3735 training little cats
8. High-Order homogeneous equation

I have no right to speak about this problem. A ^ B % C = D. Now I only want to ask D and B. I would like to recommend a few questions first. Here we have a baby-step and giant-step algorithm.
Pku3243 clever y
Pku2417 discrete Logging
9. Refresh principle and Pigeon nest Principle

Two useful theorems, but it seems that there are not many examples of these two theorems.
* Pigeon nest principle:
Pku2356 find a multiple
Pku3370 Halloween treats
* Refresh principle:
Hdu1695 GCD
Hdu2461 rectangles
10. Find the rule and push the formula

The design of such questions is generally very clever, and it is really difficult to come up with, but it is not difficult to find a rule or introduce a formula. Many of my tasks are based on others' ideas. It is really not easy to think about it by myself.
* I personally think it is quite good:
Pku3372 candy Distribution
Pku3244 difference between triplets
Pku1809 regetni
Pku1831 Indefinite Equations
Pku1737 Connected Graph
Pku2480 longge's Problem
Pku1792 hexagonal routes
11. permutation and combination, interval counting, and counting Sequence

These questions may require a combination of mathematical knowledge, which is sufficient for high learning. The interval count problem is generally not difficult, but it should be carefully written and considered in various situations. As for the catlan number and the differential sequence, it is quite interesting for the stringnumber. You can go and see composite mathematics.
* Simple question:
Pku1850 code
Pku1150 the last non-zero Digit
Pku1715 hexadecimal numbers
Pku2282 the counting problem
Pku3286 how between 0's?
* Recommended:
Pku3252 round numbers
* Counting sequence:
Pku1430 binary Stirling Numbers
Pku2515 birthday cake
Pku1707 sum of powers
12. bipartite

The idea of "two points" is still very important. Here we will simply recommend a few purely two points.
* Simple:
Pku3273 monthly expense
Pku3258 river hopscotch
Pku1905 expanding Rods
Pku3122 pie
* Recommended:
Pku1845 sumdiv
13. Stable marriage

It is quite interesting to come to this algorithm without notice. It is described in detail in composite mathematics.
Pku3487 the stable marriage problem
Zoj1576 marriage is stable
14. Digital statistics

This was the first time I encountered this kind of problem in the flight point month competition. I was advised to read a paper by scau Daniel little dragon. In, Liu Cong's "talking about digital statistics issues". This paper is quite brilliant, it is also quite detailed. Each question has a detailed analysis and the author's reference code. So I have nothing to say, and the Code for these questions will not be posted on my blog. Let's go directly to the paper.
Simple:
Ural1057 amount of degrees
Spoj1182 sorted bit squence
Hdu3271 snibb
Difficult:
Spoj2319 Sequence
Sgu390 tickets

 

 

 

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