Dynamic programming is an optimization strategy used to solve complex problems by breaking them down into simpler subproblems, storing the results of these subproblems to avoid redundant computations. It is particularly effective for problems exhibiting overlapping subproblems and optimal substructure properties, such as the Fibonacci sequence or the shortest path in a graph.

Dynamic Programming

Dynamic programming

optimization strategy

complex problems

simpler subproblems

redundant computations

Overlapping subproblems is a property of a problem where the same subproblems are solved multiple times in a recursive algorithm. This characteristic is efficiently addressed using dynamic programming by storing the results of these subproblems to avoid redundant computations, thus optimizing the overall solution process.

overlapping subproblems

optimal substructure properties

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, often starting with 0 and 1. This sequence is significant in mathematics and nature, appearing in various phenomena such as the branching of trees, the arrangement of leaves, and the pattern of various fruits and flowers.

Fibonacci sequence

shortest path in a graph

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