Dynamic Programming: A comprehensive review of Algorithms, Applications and Advances

Abstract

Dynamic Programming (DP) stands as a foundational optimization approach with vast programs
across numerous fields. This evaluate gives a comprehensive exploration of DP, encompassing
its ancient evolution, fundamental ideas, algorithmic strategies, and significant applications.
From conventional issues just like the Fibonacci series to complex optimization challenges in
economics, bioinformatics, and robotics, DP demonstrates its versatility. The paper examines
optimization strategies, compares memorization and tabulation, and delves into kingdom-area
reduction strategies. Applications in economics, bioinformatics, and robotics illustrate the realworld impact of DP. Advancing beyond conventional DP issues, the evaluation explores current
traits. Approximate DP and its connection to reinforcement learning, parallel and distributed
methods, and adaptive online variations imply the evolving landscape. The demanding situations
of scalability, reminiscence efficiency, and multi-goal optimization are addressed, dropping mild
on ability answers. The integration of DP with device learning opens new avenues for research
and application.