Codeforces 455A Boredom - Defining the DP

$1.$ Define the states

Let $dp[i]$ = maximum points out of values from $1$ to $i$. You want to compute $dp[M]$, where $M = \max(a_1, a_2, \dots, a_n).$ If you define your dp like this, the base case is simple. **

Now think of the transition (how to compute dp[i] from earlier values). Work through examples by hand before coding. Understanding the pattern makes implementation simple. Practice with similar problems to reinforce your understanding.