An algorithmic technique for solving complex problems by breaking them down into simpler subproblems.
Dynamic Programming (DP) is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems and optimal substructure.
The key idea behind dynamic programming is to solve each subproblem only once and store the results in a table (memoization) to avoid redundant calculations. This significantly improves the efficiency of the algorithm.
Dynamic programming is typically used for optimization problems, where we want to find the best solution among many possible solutions. Examples include the knapsack problem, longest common subsequence, and shortest path problems.
The process of dynamic programming typically involves defining a state, establishing a recurrence relation, and determining the base cases. The solution can be implemented using either a top-down approach (recursion with memoization) or a bottom-up approach (tabulation).
Dynamic programming has applications in various fields, including computer science, mathematics, economics, and bioinformatics. It is particularly useful for problems that involve making a sequence of decisions over time.