IntroductionMany developers encounter dynamic programming for the first time through "grid walking" problems: navigating a two-dimensional grid from start to finish with limited movement options, seeking to count paths, minimize cost, or maximize收益 (gain).These problems elegantly encapsulate dynamic programming's core concepts. Let's explore them systematically.Problem 1: Minimum Path SumProblem Statement: Given an n × m grid of non-negative integers, start from the top-left corner and reach the bottom-right corner, moving only right or down...