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Irrespective of the problem category, the process of solving a problem can be divided into two broad steps: constructing an efficient algorithm, and implementing the algorithm in a suitable programming language (the set of programming languages allowed varies from contest to contest). These are the two most commonly tested skills in programming ...
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance.
The evolution graph of the game of nim with three heaps is the same as three branches of the evolution graph of the Ulam–Warburton automaton. [9] Nim has been mathematically solved for any number of initial heaps and objects, and there is an easily calculated way to determine which player will win and which winning moves are open to that player.
In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which chance does not affect the decision making process. It says that if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. can force a win).
General game playing (GGP) is the design of artificial intelligence programs to be able to play more than one game successfully. [1] [2] [3] For many games like chess, computers are programmed to play these games using a specially designed algorithm, which cannot be transferred to another context.
Algorithmic game theory (AGT) is an area in the intersection of game theory and computer science, with the objective of understanding and design of algorithms in strategic environments. Typically, in Algorithmic Game Theory problems, the input to a given algorithm is distributed among many players who have a personal interest in the output.
For the purposes of the Sprague–Grundy theorem, a game is a two-player sequential game of perfect information satisfying the ending condition (all games come to an end: there are no infinite lines of play) and the normal play condition (a player who cannot move loses).
The game with a single cop, and the cop-win graphs defined from it, were introduced by Quilliot (1978). [25] [26] Another early reference is the work of Nowakowski & Winkler (1983), who were introduced to the game by G. Gabor. [2] [26] The game with multiple cops, and the cop number defined from it, were first studied by Aigner & Fromme (1984 ...