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What is the difference between a heuristic and an algorithm?
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Algorithms and heuristics are different approaches to solving problems. Algorithms are comprehensive step-by-step procedures. They are exhaustive and guarantee the correct solution, but may be time-consuming and require a lot of mental effort. In contrast, heuristics are shortcut strategies or rules-of-thumb.
An algorithm is a methodical, logical rule or procedure that guarantees solving a particular problem. A heuristic is a simple thinking strategy that allows us to make judgements and solve problems efficiently. Generally, heuristics are speedier but more error-prone than algorithms.
Heuristic algorithms are used to solve NP problems and decrease the time complexity of problems by giving quick solutions. It's popularly utilized in artificial intelligence problems. One example is informed search, where additional information is available to determine the next step towards finding the solution.
While algorithms provide step-by-step procedures that can guarantee solutions, heuristics are faster and provide shortcuts for getting to solutions, though this has the potential to cause errors.
An algorithm is the description of an automated solution to a problem. What the algorithm does is precisely defined. The solution could or could not be the best possible one but you know from the start what kind of result you will get. You implement the algorithm using some programming language to get (a part of) a program.
Now, some problems are hard and you may not be able to get an acceptable solution in an acceptable time. In such cases you often can get a not too bad solution much faster, by applying some arbitrary choices (educated guesses): that's a heuristic.
A heuristic is still a kind of an algorithm, but one that will not explore all possible states of the problem, or will begin by exploring the most likely ones.
Typical examples are from games. When writing a chess game program you could imagine trying every possible move at some depth level and applying some evaluation function to the board. A heuristic would exclude full branches that begin with obviously bad moves.
In some cases you're not searching for the best solution, but for any solution fitting some constraint. A good heuristic would help to find a solution in a short time, but may also fail to find any if the only solutions are in the states it chose not to try.
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Many problems for which no efficient algorithm to find an optimal solution is known have heuristic approaches that yield near-optimal results very quickly.
There are some overlaps: "genetic algorithms" is an accepted term, but strictly speaking, those are heuristics, not algorithms.
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