Codeforces 1741E Sending a Sequence - Defining the State and Base Case

Now I write the DP formally using the prefix idea.

$1.$ Define the state Let $dp[i]$ = can you split the prefix $b_1, b_2, \dots, b_i$ into valid blocks? This is a boolean state.

$2.$ Set the base case The empty prefix is always valid, so $dp[0] = \text{true}.$ All other values start as false: Now that you have your state definition and base case ready, the next step is to build the transition (how to compute dp[i] from earlier values). Without this stopping condition, the recursion would never terminate.