Codeforces 977F Consecutive Subsequence - State Definition - 1

I again follow the four step dynamic programming pattern.

1. Define the state (what information dp[$v$] tracks)

You want a subsequence that forms: $\left[ x, x+1, x+2, \dots, x+k-1 \right]$ Let: $dp[v]$ = The maximum length of a good subsequence that ends with value $v$.

That means: among all subsequences you can pick from the array that end in value v, dp[v] stores the longest length achievable. Since values in the array can be as large as $10^9$, dp must be implemented as a map/hash map, not an array. Before moving to the next unit, think that only DP can't solve the whole problem; something else is also required.