Summary of Game Theory-reprinted

Source http://blog.csdn.net/ACM_cxlove? Viewmode = contents by --- cxlove

 

First of all, you must provide some excellent learning materials:

Summary of basic game: http://blog.csdn.net/acm_cxlove/article/details/7854530

Classic coin game summary: http://blog.csdn.net/acm_cxlove/article/details/7854534

Classic edge deletion Game Summary: http://blog.csdn.net/acm_cxlove/article/details/7854532

Five national training team papers:

Zhang Yifei: from perceptual knowledge to rational understanding-analysis of the answer process of a class of Combat Games Wang Xiaoke:

Fang zhanpeng: There seems to be another question about a type of combined games starting from "K times dynamic subtraction game", which cannot be found. I have not studied this paper very deeply. Many of the proofs are very detailed and I have not studied it carefully.

We recommend that you thoroughly understand the significance of SG functions from the basic Nim game.

 

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Hdoj1079 & poj1082 & zoj1024 calendar game [regular game searching]
Find the rule based on the variation of parity, special considerations under special circumstances
Http://blog.csdn.net/acm_cxlove/article/details/7834004


Hdoj1525 & poj2348 Euclid's game [regular game searching]
Make decisions based on the inevitability and selectivity of each step
Http://blog.csdn.net/acm_cxlove/article/details/7834336


Hdoj1564 play a game [finding Rules]
Create tables to discover parity rules

Hdoj1846 brave game [finding Rules]
In a simple Bashi game, when n is m + 1, the latter wins; otherwise, the former wins. Because if it is m + 1, no matter how the former is obtained, the latter can win.


Hdoj1847 good luck in CET-4 everybody! [Finding Rules]
Basic SG function construction


Hdoj2147 Kiki's game [Search rules]
You can create a PN table, but you can find the rule directly. If one of N and M is an even number, it will win.


Hdoj2516 stone game [finding Rules]
FIB game model, http://blog.csdn.net/acm_cxlove/article/details/7834336


Hdoj2897 click [find rules] SG to create a table
Similar to the Bashi game, finding the interval [1-p] must fail. [p + 1, p + q] Must win (take a Q to enter the first interval) [p + q + * p + q] defeat: [2 * p + q + * P + 2 * q] victory


Hdoj3032 Nim or not Nim? [Query rules] SG tables
Lasker's Nim game, by playing a table, you can find the rule
Http://blog.csdn.net/acm_cxlove/article/details/7835178


Hdoj3389 game [Search rules]
1. Divide the image into two parts.
If you can get a card from A to B, connect a side from A to B. Satisfy all box numbers x (X %


3 = 0 & X % 2 = 1) | x % 3 = 1) Place the condition on the left and the other places on the right.
A) only the left-to-right side or the right-to-left side.
B) all the boxes that cannot take the cards out are on the left.
2. Verify that the box on the left does not affect the result. Assume that the current situation on the right shows that the loser
To get rid of this situation, I took n cards from a box on the left to B, because B must have an edge.
The N cards will be removed from B to the left. The situation remains unchanged.
3. This is equivalent to playing all the boxes on the right in Nim.


Hdoj3537 daizhenyang's coin [finding rules] SG table
Trigger coin game: Mock Turtles game
Http://blog.csdn.net/acm_cxlove/article/details/7854181

Hdoj3544 Alice's game [finding Rules]
The question is still a bit incomprehensible. Find the optimal strategy, and divide it into two points each time ..

Hdoj3863 no gambling [finding rules] Simple Dual game
The first is a winner, which is easy to find and cannot be blocked.

Hdoj3951 coin game [finding Rules]

As long as the first step is not completed, it becomes a chain, so the opponent can take it from the middle and divide it into equal two piles of stones to solve problems using symmetry.




Hdoj2188 mourn the victims of the 512 Wenchuan earthquake-selecting volunteers
[Bashi Game]

Hdoj2149 public sale [Bashi Game] Output Method
Obviously, if the requirements can be met in one step, the solution is m ...... N
If n is the number of m + 1 steps, it will be defeated. No matter how much you add, if a, the other party will add m + 1-A
Otherwise, the price is controlled at N % (m + 1 ).

Hdoj1850 being a good boy in Spring Festival [basic Nim Game]
You need to output the number of feasible solutions, indicating that the NIM product is 0 after the first step, and determine whether the number is greater than the number to be removed.

Hdoj2176 get (M heap) Stone game
[Basic Nim Game] Step 1 of output


Hdoj1527 & poj1067 game of stone acquisition [weizov Game]
Wythoff game, judge whether it is a = K * (SQRT (5) + 1)/2, B = a + k

Hdoj2177 (2 heap) Stone game [weizov Game]
You need to output a scheme, create a table, and then find
Http://blog.csdn.net/acm_cxlove/article/details/7836150

Hdoj1517 & poj2505 a multiplication game [K (2 ~ 9) times Game]
In the same way, the first hand wins from 1 to 9, and the first hand wins from 10 to 18. No matter what the first hand does, the latter wins. In the same way, 19-162 wins first. Rule discovery

Hdoj2486 & hdoj2580 & poj3922 a simple stone game [K times dynamic subtraction Game]
Magic structure Series
Http://blog.csdn.net/acm_cxlove/article/details/7836544

Hdoj4315 climbing the hill [tiered Game]
Step Nim: use odd digits as Nim. Even digits are not affected.

Hdoj1538 a puzzle for pirates [Pirate gold issue]
Detailed reasoning and proof of pirate money
Http://blog.csdn.net/acm_cxlove/article/details/7853916

Hdoj3404 switch lights [Nim product]
Http://blog.csdn.net/acm_cxlove/article/details/7836764

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Hdoj1404 digital deletions [SG Game]
Since the string length is only 6, it is integrated into an integer and the SG table is violent. From the P state, the N state can be reached in one step.

Hdoj1536 & hdoj1944 & poj2960 & zoj3084 S-nim [SG Game]
SG function. For each set, obtain the SG function.

Hdoj1729 stone game [SG Game]
SG function, http://blog.csdn.net/acm_cxlove/article/details/7838563


Hdoj1730 Northcott game [SG Game]
Convert to a distance Nim game

Hdoj1760 a new Tetris game [SG Game] Two-dimensional state
DFS game.

Hdoj1848 Fibonacci again and again [SG Game]
SG tables

Hdoj1849 rabbit and Grass [SG Game]
Convert to Nim

Hdoj1851 a simple game [SG Game]
Small Scope: directly construct the SG function, or convert it into a combination of Nim and Bashi games.

Hdoj1907 & poj3480 & zoj3113 John [SG Game]
ANTI-SG, see Jia Zhihao's paper
Http://blog.csdn.net/acm_cxlove/article/details/7839276

Hdoj2509 be the winner [SG Game] can be divided into two heap operations
ANTI-SG, same as above

Hdoj2873 bomb game [SG Game]
SG functions are used to create tables, similar to Nim.

Hdoj2999 stone game, why are you always there? [SG Game]
Construction SG, http://blog.csdn.net/acm_cxlove/article/details/7840042

Hdoj3595 Gg and mm [SG Game]
Every-SG problem, http://blog.csdn.net/acm_cxlove/article/details/7840427

Hdoj3980 paint chain [SG Game]
It was originally a ring, first dyed a segment, then chained, and the first step is fixed. The ring status is not easy to handle.
We do not care about the first step. Starting from the chain, one chain may be cut into two segments by dyeing in the middle, and then it will become two sub-segments.
Problem. See later http://blog.csdn.net/acm_cxlove/article/details/7840042
Finally, let's take the first step into consideration.

Hdoj4111 Alice and Bob [SG Game] DP + gravel merge
Http://blog.csdn.net/acm_cxlove/article/details/7841115

Hdoj3165 & zoj1827 the game of 31 [SG Game] memory-based search
Search, 5 ^ 6

Hdoj4203 doubloon game [finding rules] [SG Game]
Although it is an ordinary SG game, but the data is too big, there is no way to create a SG table, you can only find rules in small data.

Hdoj1524 a chess game [directed acyclic graph SG Game]
Similar to the general SG game, the SG value of the successor node is obtained recursively.
Http://blog.csdn.net/acm_cxlove/article/details/7842242

Hdoj3094 a tree game [directed to Wuhuan shujia SG Game]
Tree edge deletion game http://blog.csdn.net/acm_cxlove/article/details/7842586

Hdoj3590 PP and QQ [tree SG Game] Anti-game, tree cutting
Tree edge deletion games + ANTI-SG,
Http://blog.csdn.net/acm_cxlove/article/details/7842743

Hdoj3197 game [tree SG Game] tree cutting
Tree deletion game, just remove the root of multiple trees

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Poj1740 a new stone game [finding Rules]

Poj2484 a funny game [finding Rules]
As long as the first step is not completed, it becomes a chain, so the opponent can take it from the center and divide it
Two equal stones

Poj2234 matches game [basic Nim Game]

Poj2975 & zoj3067 Nim [basic Nim Game] Output Method

Poj2368 buttons [deformation of bus Game]
To understand the Bashi game, you only need to find the factor of the total number-1. However, because it cannot be 1
Start from 3, and pay special attention to the even number.

Poj2311 cutting game [SG Game]
For a status N * m, find the successor status, SG game
Http://blog.csdn.net/acm_cxlove/article/details/7845904


Poj2425 a chess game [SG Game]
Tree-like, undirected acyclic graph game

Poj1678 I love this game! [Dynamic Game] dynamic game + game
Game DP, memory-based search
Http://blog.csdn.net/acm_cxlove/article/details/7846480

Poj2068 Nim [SG Game] dual game
Two-dimensional game DP, http://blog.csdn.net/acm_cxlove/article/details/7846793


Poj3537 crosses and crosses [SG Game]
After you select a position to move it down, the left and right sides of the 4 adjacent positions do not take the initiative to put down the pawns. Length: N
The Board, if in position I put down the pawns, is divided into the left I-3 position and the right N-I-2 position of the sub game

Poj2599 a funny game [tree SG Game] memory
Search, status transition of n/P
Http://blog.csdn.net/acm_cxlove/article/details/7847347

Poj3710 Christmas game [graph Game] undirected graph edge Deletion
The Tarjan algorithm finds the ring. After processing the ring, it is a classic edge deletion game.
The ring with an odd edge can be simplified to an edge, and the ring with an even edge can be simplified to a node.
Http://blog.csdn.net/acm_cxlove/article/details/7848001

Poj1704 Georgia and Bob [tiered Game]
The distance is used as a stone heap. For a tiered game, the even heap does not affect the distance, which is equivalent to the NIM of the odd heap.

Poj2931 procrastination [unequal Game]
The subject cannot be understood, and the thesis cannot be understood.
If you are interested, you can refer to Fang Zhan Peng's paper, "talking about how to solve the unequal game problem".

Poj3533 light switching game [Nim product]
3D Nim Product

 

Triangle war (large shard search + alpha_beta pruning)

Http://blog.csdn.net/acm_cxlove/article/details/7997246

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Zoj2290 game [Search rules]
FIB game

Zoj2686 cycle game [finding rules] DFS search
Direct Search times out. We make some optimizations and find that if there are consecutive odd numbers not 0 in a certain direction
First, you can get all the data in that direction. If the opponent also gets the data, keep going first.
Hand wins. If the opponent does not finish, the first hand wins in reverse order.
Http://blog.csdn.net/acm_cxlove/article/details/7850050

Zoj2725 digital deletions [query rules] Table
Same as HDU 1404

Zoj2083 win the game [SG Game]
SG game, the length of N line segments, divided into two parts, I, n-i-2. Retrieve Mex operation after XOR

Zoj2507 let's play a game [anti-nim, SG Game]
ANTI-SG game, see http://blog.csdn.net/acm_cxlove/article/details/7839276

Zoj3513 human or pig [SG recurrence]
Recursion: All the successors of the P state are the H state; otherwise, the P state is the H state.

Zoj3529 a game between Alice and Bob [SG Game]
In the SG game, we can find that the SG value is the number of quality factors and is converted to Nim.
Http://blog.csdn.net/acm_cxlove/article/details/7850798

Zoj3591 Nim [Nim Game] + bitwise operation
In sequence, Nim [I] indicates the exclusive or value of the first I heap. If Nim [I] = Nim [J], it indicates
I + 1, I + 2 ...... The exception or value of J is 0, which means defeat.
Http://blog.csdn.net/acm_cxlove/article/details/7851099

Zoj3057 beans game [DP Game]
3D save status, game DP. Pay attention to the card memory
Http://blog.csdn.net/acm_cxlove/article/details/7851904

Zoj1039 number game [Pressure + game tree] memory-based search
Status compression: compresses 19 digits to make full use of bitwise operations. Each time you find a successor set, you can perform a memory-based search.
Http://blog.csdn.net/acm_cxlove/article/details/7852347

Zoj3599 game [K times Game]
Similar to HDU 2486,
Http://blog.csdn.net/acm_cxlove/article/details/7836544

Zoj2804 funny games [do not know what type]
I cannot understand the question ....
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Uva12350 queen game [kneeling Game]
I cannot understand the question ....