# Search modes

## Heuristic

A*, Greedy and Beam search all use the following heuristic to select candidates to expand on the next layer of the graph

$$mult(n) = 
\begin{cases}
    4 &\text{if  $n$ is a neutron star} \\\\
    1.5 &\text{if $n$ is a white dwarf star} \\\\
    1 &\text{otherwise}
\end{cases}
$$

$$d(a,b) = \sqrt{(a_x-b_x)^2+(a_y-b_y)^2+(a_z-b_z)^2}$$

$$
h(\text{node},\text{goal})=
    \max(
        d(\text{node},\text{goal})-
        (
            \text{range}*mult(\text{node})
        ),0)
$$

potential new heuristic:

$$
h(\text{node},\text{next},\text{goal})=
1 - {\cos^{-1}(|(\text{next}-\text{node})| \cdot |(\text{goal}-\text{node})|)\over\pi}
$$