Consider the search space below, where $S$ is the start node and G$1$ and G$2$ are goal nodes. Arcs are labeled with the value of a cost function; the number gives the cost of traversing the arc. Above each node is the value of a heuristic function. Assume that search algorithms always choose alphabetically when there is a tie, and expand the older node if two nodes are still tied.

A$-$ Give the solution by each one of the following search strategies to reach a goal

state.

$1-$ Greedy$-$best$-$First Search:

$2-$ Depth first search:

$3-$ A$*$ Search with testing at expanding: