Dynamic Programming (DP) is a computational problem-solving technique that breaks down complex problems into simpler overlapping subproblems. It efficiently solves problems by storing and reusing solutions to avoid redundant computations. DP is widely used in disciplines like computer science, mathematics, and economics.
DP involves solving a problem by dividing it into smaller subproblems, solving each subproblem only once, and storing the solution for future use. This approach minimizes the time complexity of the overall problem, making it more efficient than brute-force methods.
In DP, the key idea is to recognize the overlapping subproblems and optimal substructure property. Overlapping subproblems imply that the solution to a larger problem can be obtained by combining solutions to smaller subproblems. The optimal substructure property states that an optimal solution to the problem contains optimal solutions to its subproblems.
To implement DP, one needs to identify the recurrence relation, which expresses the solution to a given subproblem in terms of solutions to smaller subproblems. The solutions to these smaller subproblems are stored in a table or array, allowing for efficient computation of the solution to the larger problem.
Overall, DP is a powerful technique that efficiently solves problems by breaking them down into smaller subproblems and utilizing the optimal substructure property. By storing and reusing solutions, DP reduces redundant computations and improves the runtime efficiency of solving complex problems.
