Do all dynamic programming algorithms satisfy an optimal substructure property?

1. Optimal substructure. “Optimal substructure” is a specific property of some problems and is not exclusive to dynamic programming. In other words, many problems actually have optimal substructures, but most of them do not have overlapping subproblems, so we cannot classify them dynamic programming problems.

Does dynamic programming have optimal substructure?

Typically, a greedy algorithm is used to solve a problem with optimal substructure if it can be proven by induction that this is optimal at each step. Otherwise, provided the problem exhibits overlapping subproblems as well, dynamic programming is used. This is an example of optimal substructure.

What are optimal substructure and overlapping sub-problems in dynamic programming?

To answer your main question: overlapping subproblems and optimal substructure are both different concepts/properties, a problem that has both these properties or conditions being met can be solved via Dynamic Programming.

What are optimal substructure and overlapping sub problems in Dynamic Programming?

Why optimal solution to the sub problems are stored in dynamic programming?

Dynamic Programming is mainly used when solutions of the same subproblems are needed again and again. In dynamic programming, computed solutions to subproblems are stored in a table so that these don’t have to be recomputed.

What are optimal substructure and overlapping sub problems in dynamic programming?

Why optimal solution to the sub problems are retained in dynamic programming?

1) Overlapping Subproblems: In dynamic programming, computed solutions to subproblems are stored in a table so that these don’t have to be recomputed. So Dynamic Programming is not useful when there are no common (overlapping) subproblems because there is no point storing the solutions if they are not needed again.