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Can someone explain in very simple words what it is? Also, provide an example. So for example, if u have to find the heuristic function of something how is it supposed to look like?

Take as an example of the problem:

For the water-jug problem http://www.math.tamu.edu/~dallen/hollywood/diehard/diehard.htm

Devise and explain an admissible heuristic function (h) [not the trivial h(n) = 0]. The cost of an action is defined as 1 unit for performing the action, an additional 1 unit for moving each gallon of water (fill, empty, pour), and an additional 1 unit for wasting each gallon of water (empty). The path cost (g) is the sum of the cost of all the actions.

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A heuristic is a function that outlines from problem state description to measures desirability, usually represented as number weights. The value of a heuristic function at a given node in the search process gives a good estimate of that node being on the desired path to the solution. Well-designed heuristic functions can provide a fairly good estimate of whether a path is good or not. Let us say that the total of all the distances covered so far is a simple heuristic function in the traveling salesman problem. The main objective of a heuristic function is to guide the search process in the most profitable directions, by suggesting which path to follow first when more than one path is available.

For example, the query might be finding the shortest driving distance to a position. A heuristic cost would be the straight line distance to that particular position. It is simple and fast to calculate, an important feature of most heuristics. The actual distance would likely be higher as we have to stick to roads and is much harder to calculate.

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