Dynamic programming is a technique used to solve problems by breaking them down into simpler subproblems and storing the results of these subproblems to avoid redundant computations.

Dynamic programming is a powerful technique for solving problems by breaking them down into smaller, overlapping subproblems. Instead of solving the same subproblem multiple times, dynamic programming stores the results of subproblems in a table (often called memoization or tabulation) and reuses these results whenever needed. This approach can significantly reduce the time complexity of an algorithm, making it much more efficient than a naive recursive solution. Problems that are well-suited for dynamic programming typically have two properties: overlapping subproblems and optimal substructure. Overlapping subproblems mean that the problem can be divided into smaller problems that are solved multiple times, while optimal substructure means that an optimal solution to the problem can be constructed from optimal solutions to its subproblems. A classic example of dynamic programming is the Fibonacci sequence, where each term is the sum of the two preceding ones. Without dynamic programming, a naive recursive solution would have exponential time complexity, but by storing previous results in an array or table, the time complexity can be reduced to O(n). Dynamic programming is also commonly used in algorithms like the knapsack problem, longest common subsequence, and matrix chain multiplication. Mastering dynamic programming is essential for solving complex problems efficiently, especially in competitive programming and technical interviews.