Dynamic Programming (DP) is a powerful algorithmic technique used to solve optimization problems by breaking them down into smaller, manageable subproblems. The essence of DP lies in its ability to store the results of these subproblems, which helps avoid redundant calculations when the same subproblems arise multiple times. This method is particularly effective for problems that exhibit overlapping subproblems and optimal substructure properties.

Mathematically, dynamic programming can be viewed as a structured approach to problem-solving, rooted in recursion, combinatorics, and optimization theory. It contrasts with divide and conquer strategies, where subproblems are independent and solutions are not reused. The typical process in DP involves defining the structure of the optimal solution, solving each overlapping subproblem just once, and storing their solutions for future reference ³⁴.

DP is widely applicable in various fields, including computer science, operations research, and economics, making it a fundamental concept for anyone looking to tackle complex problems efficiently.