In computer science and optimization a heuristic is a rule of thumb learned from experience but not always justified by an underlying theory. Heuristics are often used to improve efficiency or effectiveness of optimization algorithms, either by finding an approximate answer when the optimal answer would be prohibitively difficult or to make an algorithm faster. Usually, heuristics do not guarantee that an optimal solution is ever found. On the other hand, results about NP-hardness in theoretical computer science make heuristics the only viable alternative for many complex optimization problems which are significant in the real world.

An example of an approximation is one Jon Bentley described for solving the travelling salesman problem (TSP) where it was selecting the order to draw using a pen plotter. TSP is known to be NP-hard so an optimal solution for even moderate size problem is intractable. Instead the greedy algorithm can be used to to give a good but not optimal (it is an approximation to the optimal answer) in a short amount of time. The greedy algorithm heuristic says to pick whatever is currently the best next step regardless of whether that precludes good steps later. It is a heuristic in that practice says it is a good enough solution, theory says there are better solutions (and even can tell how much better in some cases).

Heuristic ( /hjʉˈrɪstɨk/; or heuristics; Greek: "Εὑρίσκω", "find" or "discover") refers to experience-based techniques for problem solving, learning, and discovery. Where an exhaustive search is impractical, heuristic methods are used to speed up the process of finding a satisfactory solution. Examples of this method include using a rule of thumb, an educated guess, an intuitive judgment, or common sense.

In more precise terms, heuristics are strategies using readily accessible, though loosely applicable, information to control problem solving in human beings and machines.

The most fundamental heuristic is trial and error, which can be used in everything from matching nuts and bolts to finding the values of variables in algebra problems.

Here are a few other commonly used heuristics, from George Pólya's 1945 book, How to Solve It:

In psychology, heuristics are simple, efficient rules, hard-coded by evolutionary processes or learned, which have been proposed to explain how people make decisions, come to judgments, and solve problems, typically when facing complex problems or incomplete information. These rules work well under most circumstances, but in certain cases lead to systematic errors or cognitive biases.^{[citation needed]}

Computer science or computing science (abbreviated CS or CompSci) designates the scientific and mathematical approach in information technology and its applications, notably computer software and sometimes hardware. A computer scientist is a scientist who specialises in the theory of computation and the design of computers.

Its subfields can be divided into practical techniques for its implementation and application in computer systems and purely theoretical areas. Some, such as computational complexity theory, which studies fundamental properties of computational problems, are highly abstract, while others, such as computer graphics, emphasize real-world applications. Still others focus on the challenges in implementing computations. For example, programming language theory studies approaches to description of computations, while the study of computer programming itself investigates various aspects of the use of programming languages and complex systems, and human-computer interaction focuses on the challenges in making computers and computations useful, usable, and universally accessible to humans.

A computer is a general purpose device which can be programmed to carry out a finite set of arithmetic or logical operations. Since a sequence of operations can be readily changed, the computer can solve more than one kind of problem. The essential point of a computer is to implement an idea, the terms of which are satisfied by Alan Turing's Universal Turing machine.

Conventionally, a computer consists of at least one processing element and some form of memory. The processing element carries out arithmetic and logic operations, and a sequencing and control unit that can change the order of operations based on stored information. Peripheral devices allow information to be retrieved from an external source, and the result of operations saved.

A computer's processing unit executes a series of instructions that make it read, manipulate and then store data. Conditional instructions change the sequence of instructions as a function of the current state of the machine or its environment.

In order to interact with such a machine, programmers and engineers developed the concept of a user interface in order to accept input from humans and return results for human consumption.

Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. In an older and closely related meaning (found, for example, in Aristotle), "science" refers to the body of reliable knowledge itself, of the type that can be logically and rationally explained (see History and philosophy below). Since classical antiquity science as a type of knowledge was closely linked to philosophy. In the early modern era the words "science" and "philosophy" were sometimes used interchangeably in the English language. By the 17th century, natural philosophy (which is today called "natural science") was considered a separate branch of philosophy. However, "science" continued to be used in a broad sense denoting reliable knowledge about a topic, in the same way it is still used in modern terms such as library science or political science.