Which of the following is/are property/properties of a dynamic programming problem?1 pointOptimal substructureOverlapping subproblemsGreedy approachBoth optimal substructure and overlapping subproblems

The properties of a dynamic programming problem are both optimal substructure and overlapping subproblems.

Step 1: Understanding the terms

• Optimal Substructure: A problem has optimal substructure if an optimal solution can be constructed from optimal solutions of its subproblems.
• Overlapping Subproblems: Overlapping subproblems means that a problem can be broken down into subproblems which are reused several times.

Step 2: Applying the terms to dynamic programming

• Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable when the subproblems are not independent, that is, when the solution to one subproblem overlaps with the solution to another (overlapping subproblems), and the optimal solution to the main problem can be found by the optimal solutions of its subproblems (optimal substructure).

Step 3: Conclusion

• Therefore, the properties of a dynamic programming problem are both optimal substructure and overlapping subproblems. The greedy approach is not a property of dynamic programming. The greedy approach makes the optimal choice at each step as it attempts to find the overall optimal way to solve the entire problem, which is not always applicable in dynamic programming problems.