Interview Question - Samsung for Senior Software Engineer

You have to pull out all of n stones.
You can only pull out one at a time.
The cost to pull out the ith stone is as follows(0<=i<N):

• The cost is 0 if there is no (i-1)th stone and (i+1) th stone
• The cost is A[i] if either the (i-1)th stone and (i+1)th stone is left.
• The cost is B[i] if both (i-1)th stone and (i+1) the stone are left.
  You are requested to find the minimum total sum of the necessary cost.

Example:
n=5
A[i]=[1,5,3,4,3]
B[i]=[0,2,1,5,0]
Answer:5

If stones are pulled out in the order of 0->2->4->1->3
1+1+3+0+0=5

n=4
a[]=[3,3,2,0]
B[]=[0,2,3,0]
Answer:2

If the stones are pulled out in the order of 1->3->0->2
2+0+0+0=2

Constraints

1<= N <= 50000

Any ideas on how this can be solved?