Speculating Prices

Let $v(k,1)$ and $v(k,0)$ denote the maximum profit that can be gained starting from day $k$ onwards when currently I do have a car and don't have a car, respectively. Let the price vector be denoted by $\mathbf{p}$ the horizon length by $n$ . Then obviously, $v(n,1)=p(n), v(n,0)=0.$ Furthermore, for $1\leq m <n$ , we have the following DP recursions $v(m,0)=\max\{ -p(m)+v(m+1,1), v(m+1,0)\},$ and, $v(m,1)=\max \{p(m)+v(m+1,0), v(m+1,1) \}.$ The above gives an $O(n)$ Dynamic Programming Algorithm for computing the maximum profit starting from day 1 (i.e., $v(1,0)$ ), which turns out to be $13$ for the given example.