Explain the concept of dynamic programming and the relation between dynamic and linear programming approach.

Dynamic programming (DP) is a mathematical optimization technique used to solve problems by breaking them down into simpler subproblems. It is particularly useful for problems that exhibit the properties of overlapping subproblems and optimal substructure. These properties ensure that the solution to the problem can be constructed efficiently by solving each subproblem only once and storing its solution for reuse in future computations, thus avoiding redundant calculations.

The core idea behind dynamic programming is to solve complex problems by solving smaller, simpler subproblems and combining their solutions. This is done in a sequential manner, usually from the simplest subproblem to __________ _______ ___ ______ _______ ________ _____.
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