# NumberSolitaire

This page discusses different solutions to the problem NumberSolitaire presented by Codility in the lesson 17 “ Dynamic Programming”.

One simple solution is to distinguish between the length of A being less or more than 6.

```def solution(A):
N = len(A)
dp = [A] + *(N-1)
for i in xrange(1,min(N,6)):
dp[i] = max(dp[:i]) +A[i]
for j in xrange(6,N):
dp[j] = max(dp[j-6:j]) +A[j]
return dp[-1]
```

The solution above might have the best performance for large inputs of the three solutions on this page. However, the two for-loops could be joined together into one making the solution look neater:

```def solution(A):
N = len(A)
dp = [A] + *(N-1)
for j in xrange(1,N):
dp[j] = max(dp[max(0,j-6):j]) +A[j]
return dp[-1]
```

Moreover, if we assume that the input array can be modified, then there is no need to create a new list:

```def solution(A):
for j in xrange(1,len(A)):
A[j] += max(A[max(0,j-6):j])
return A[-1]
```

In any case, all three solutions on this page have the same worst-case time complexity of O(N) and score 100% under Codility’s test.