Consider a search space, where each state can be red, green, blue, yellow, or black. Multiple states may have the same color. The goal is to reach any black state. Here are some rules on the successors of different states, based on their color (these successor functions are unidirectional):
Any path between a red and a green state has cost >= 20.
Any path between a red and a blue state has cost >= 30.
Any path between a blue and a yellow state has cost >= 45.
Any path between a green and a yellow state has cost >= 50.
Any path between a red and a yellow state must go through a green or blue state.
Any path connecting a red, green, or blue state to a black state must go through a yellow state.
Define the best admissible heuristic H that you can, using the above information. H should assign a value to a node based on the color of that node's state. That value should be the highest possible value that still guarantees that H is admissible.
H(red) =
H(green) =
H(blue) =
H(yellow) =
H(black) =