Problem $6.$

Figure $3$ represents a map of the connected C$-$space, where each path now has an associated cost to travel this path, indicated by a number next to each path. This cost represents the paths distance.

Using A$*$ search and the cost function, $f(n)=g(n)+h(n),$ find a path to the goal. $g(n)$ represents the total cost of the path so far, represented on the path.

$h(n)$ is the estimate cost to the goal, represented next to each node. This can be thought of the distance to the goal ignoring obstacles.