Q$-1(20$ pts$)$ Dynamic Programming. Consider a graph with $n+1$ nodes as given in the following figure.

A robot starts at node $0$ and aims to reach node $n.$ At each node, it can move to the next node or skip

one and proceed to the node after that. Each node i has an associated positive cost $C[i]$ for the robot,

except for nodes $0$ and $n,$ where the cost is zero. $($i$.$e$.C[0]=C[n]=0).$ The goal is to move from node

$0$ to node $n$ with minimum total cost.

For example, if $C=[0,10,15,20,0],$ then the robot will visit node $0,2$ and $4,$ and the minimum total

cost would be $15.$

If $C=[0,1,1,10,1,10,1,1,10,0],$ then the robot will visit nodes $0,2,4,6,7,$ and $9,$ and the

minimum total cost would be $4.$

Describe a dynamic programming algorithm for this problem. Apply your algorithm for the following

instance: $C=[0,10,5,20,15,25,30,0]$

Hint: Define $f[i]$ as the minimum total cost from node $i$ to node $n.$ Set up a recurrence relation for $f[i].$