What does heuristic h: {1, ... , N} --> R mean?

Question

I want to know what does a heuristic h: {1, ... , N} --> R with the goal state always being 1 mean?

The state are represented as points in a 2D Cartesian system, with coordinates (x,y).

Answer 1

Wikipedia describes this notation of a function. In your specific case:

h: {1, ..., N] --> R

we have:

• h: The function's symbol (h for heuristic)
• {1, ..., N}: the domain of your function, in this case the set of all integers from 1 up to and including N. This is the ''input'' that your function can take. Note that this means that your function h(x) is not, for example, defined for x = 1.5. It can only take integers between 1 and N (both inclusive) as input.
• R: The codomain of your functions, in this case the set R which is probably supposed to denote the set of all real numbers. Your function can produce any real number as output.