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Which of the following is/are property/properties of a dynamic programming problem?a.Both optimal substructure and overlapping subproblemsb.Overlapping subproblemsc.Optimal substructured.Greedy approach

Question

Which of the following is/are property/properties of a dynamic programming problem?a.Both optimal substructure and overlapping subproblemsb.Overlapping subproblemsc.Optimal substructured.Greedy approach

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Solution

The properties of a dynamic programming problem are:

a. Both optimal substructure and overlapping subproblems: This is true. Dynamic programming problems typically have an optimal substructure, meaning the optimal solution to the problem can be computed by the optimal solutions of its subproblems. They also have overlapping subproblems, meaning the problem can be broken down into subproblems which are reused several times.

b. Overlapping subproblems: This is true. As mentioned above, dynamic programming problems often involve solving overlapping subproblems, where the same subproblem is solved multiple times.

c. Optimal substructure: This is true. Dynamic programming problems usually have an optimal substructure, which allows the problem to be broken down into smaller, simpler subproblems.

d. Greedy approach: This is false. A greedy approach, where the best or optimal choice is made at each decision point with the hope that these local optimums will lead to a global optimum, is not a property of dynamic programming. While some problems may be solved using both dynamic programming and a greedy approach, not all dynamic programming problems can be solved using a greedy approach.

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