Dynamic Programming Questions
The key characteristics of problems that can be solved using Dynamic Programming are as follows:
1. Overlapping subproblems: The problem can be divided into smaller subproblems, and the solution to the main problem can be obtained by combining the solutions to these subproblems. These subproblems should have overlapping substructures, meaning that the same subproblem is solved multiple times.
2. Optimal substructure: The optimal solution to the main problem can be constructed from the optimal solutions of its subproblems. In other words, the optimal solution to the main problem can be obtained by making a sequence of locally optimal choices.
3. Memoization or tabulation: Dynamic Programming can be implemented using either memoization (top-down approach) or tabulation (bottom-up approach). Memoization involves storing the solutions to subproblems in a table or cache to avoid redundant calculations, while tabulation involves solving the subproblems in a bottom-up manner and storing their solutions in a table.
4. The problem exhibits the principle of optimality: The optimal solution to the main problem contains optimal solutions to its subproblems. This principle allows us to solve the problem by solving its subproblems and combining their solutions.
5. The problem can be solved using recursion or iteration: Dynamic Programming can be implemented using either recursive or iterative approaches. Recursive implementation is often used when using memoization, while iterative implementation is used when using tabulation.
Overall, problems that can be solved using Dynamic Programming have overlapping subproblems, exhibit optimal substructure, and can be solved using recursion or iteration with the help of memoization or tabulation techniques.