algorithm - Minimum cost of choosing items from n buckets -

i have n numbers of buckets. each bucket contains 3 items - i1, i2 & i3. each item has own cost associated. have pick items each bucket such items picked 2 consecutive buckets not same. algorithm find minimum cost of picking n items n such buckets?

i can think recursive brute force solution explore costs , find out minimum of them.

what can efficient algorithm solve problem?

the state space dynamic programming can defined follows.

c[i,j] = minimum cost attainable choosing items item each          bucket in {1,...,i} each item index different          item index in previous bucket , item in          last bucket j in {1,...,n} , j in {1,2,3} 

for state space, obtain following recurrence relation, i[j,k] each j in {1,...,n} , k in {1,2,3} denotes cost of k-th item in bucket k.

c[i,j] = min { min { c[i-1,2], c[i-1,3] } + i[i,1]: j = 1,                min { c[i-1,1], c[i-1,3] } + i[i,2]: j = 2,                min { c[i-1,1], c[i-1,2] } + i[i,3]: j = 3              } 

the initial states can filled assigning

c[1,1] = i[1,1], c[1,2] = i[1,2], c[1,3] = i[1,3] 

and after iteratively filling state space, desired value can found evaluating folowing expression.

min { c[n,1], c[n,2], c[n,3] }