For coding interviews, the most common types of DP problems are:
1. Knapsack
- 0-1
- Bounded
- Unbounded
2. LCS
3. LIS
4. Matrix chain multiplication
5. DP on grid
6. Kadane's algorithm
etc
Advanced Dynamic Programming
1. Kth lexicographical string
2. DP on Tree
3. DP + bitmasking
4. DP + BIT/Segment tree
5. DP + convex hull
Mostly, this is for competitive programming.