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The puzzles in the book cover a wide range of difficulty, and in general do not require more than a high school level of mathematical background. [3] William Gasarch notes that grouping the puzzles only by their difficulty and not by their themes is actually an advantage, as it provides readers with fewer clues about their solutions.
NC = P problem The P vs NP problem is a major unsolved question in computer science that asks whether every problem whose solution can be quickly verified by a computer (NP) can also be quickly solved by a computer (P). This question has profound implications for fields such as cryptography, algorithm design, and computational theory. [1]
The history of computational thinking as a concept dates back at least to the 1950s but most ideas are much older. [6] [3] Computational thinking involves ideas like abstraction, data representation, and logically organizing data, which are also prevalent in other kinds of thinking, such as scientific thinking, engineering thinking, systems thinking, design thinking, model-based thinking, and ...
Some hobbyists have developed computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a type of brute force search. [3] Backtracking is a depth-first search (in contrast to a breadth-first search), because it will completely explore one branch to a possible solution before moving to another branch.
David Marr proposed that cognitive processes have three levels of description: the computational level, which describes that computational problem solved by the cognitive process; the algorithmic level, which presents the algorithm used for computing the problem postulated at the computational level; and the implementational level, which ...
The development of formal logic played a big role in the field of automated reasoning, which itself led to the development of artificial intelligence.A formal proof is a proof in which every logical inference has been checked back to the fundamental axioms of mathematics.
The question then is, whether there exists an algorithm that maps instances to solutions. For example, in the factoring problem, the instances are the integers n, and solutions are prime numbers p that are the nontrivial prime factors of n. An example of a computational problem without a solution is the Halting problem. Computational problems ...
For looking up a given entry in a given ordered list, both the binary and the linear search algorithm (which ignores ordering) can be used. The analysis of the former and the latter algorithm shows that it takes at most log 2 n and n check steps, respectively, for a list of size n.