You are given the following graph with nodes and weighted edges:

Edge Weights:

A to B: $2$

A to C: $3$

B to D: $4$

B to E: $1$

$C$ to $F$:$4$

$C$ to $G$:$2$

Tasks

Solve the Problem Using Uniform Cost Search $($UCS$)$

Apply UCS to find the least$-$cost path from node $A$ to the goal node $G.$

Show all steps and the final path with the total cost.

Solve the Problem Using A$*$ Search with Heuristic $1$

Use the following heuristic values:

A: $6$

B: $4$

C: $4$

D: $1$

$E$:$3$

$F$:$2$

G: $0($Goal$)$

$H$:$1$

Apply A$*$ Search to find the least$-$cost path from node $A$ to the goal node $G.$

Show all steps and the final path with the total cost.

Compare the result with the UCS result and explain any differences $($if any$).$

Solve the Problem Using A$*$ Search with Heuristic $2$

Use the following heuristic values:

A: $6$

B: $4$

C: $2$

D: $1$

E: $5$

$F$:$2$

G: $0($Goal$)$

$H$:$1$

Apply A$*$ Search to find the least$-$cost path from node $A$ to the goal node $G.$

Show all steps and the final path with the total cost.

Compare the result with the UCS result and explain any differences.