Final answer:
Dynamic programming is a method in algorithm design used to solve complex problems efficiently by breaking them down into simpler subproblems.
Step-by-step explanation:
Dynamic programming (DP) is a method used in algorithm design and computer programming to solve complex problems by breaking them down into simpler subproblems. It is based on the principle of optimization, where an optimal solution is constructed from optimal solutions of its subproblems.
This technique is particularly effective when the problem has overlapping subproblems and optimal substructure, meaning that the same subproblems are solved multiple times and the optimal solution can be constructed from optimal solutions of its subproblems.
Dynamic programming can be implemented using two approaches: memoization and tabulation. Memoization is a top-down approach where we solve the problems recursively and store the results in some data structure (like an array or dictionary) to avoid redundant calculations.
Tabulation is a bottom-up approach where we solve all the related subproblems first, which typically involves filling up an n-dimensional table based on the results of smaller subproblems.
An example of a dynamic programming problem is the Fibonacci sequence, where each number is the sum of the two preceding ones. Instead of computing the Fibonacci numbers recursively, we can calculate them iteratively and store the results in an array, which is much more efficient and is an application of DP.