In the graph below, nodes can be expanded based on different search strategies. The first node is labeled $"$S$"($Start$),$ and edges between nodes are numbered according to their path cost $($i$.$e$.$ distance to the next node$).$ Additionally, each node is associated with a heuristic value, denoted as $"$h$($n$),"$ representing an estimate of the effort that needs to be made to reach the next node from that node. The heuristic values are provided below:

$h(S)=7$

$h(A)=6$

$h(B)=4$

$h(C)=5$

$h(D)=2$

$h(E)=3$

$h(F)=1$

The graph structure is as follows:

If you apply the following search strategies, what node will be expanded next? Show your calculations for each node when needed or you will not receive credit for your solution.

In the graph below, nodes can be expanded based on different search strategies. The first node is labeled $"$S$"($Start$),$ and edges between nodes are numbered according to their path cost $($i$.$e$.$ distance to the next node$).$ Additionally, each node is associated with a heuristic value, denoted as $h(n),$ representing an estimate of the effort that needs to be made to reach the next node from that node. The heuristic values are provided below:

$h(S)=7$

$h(A)=6$

$h(B)=4$

$h(C)=5$

$h(D)=2$

$h(E)=3$

$h(F)=1$

The graph structure is as follows:

If you apply the following search strategies, what node will be expanded next? Show your calculations for each node when needed or you will not receive credit for your solution.

A$)$ A$*[10$ Points$]$

B$)$ Greedy Best$-$First Search $[5$ Points$]$

C$)$ Depth$-$First Search $[5$ Points$]$