abbr.数据处理(data processing ) ，防潮的（Damp Proofing），民主党（Democratic Party），难民（Displaced Person）

Dynamic Programming (DP) is a problem-solving approach that breaks down a complex problem into simpler sub-problems in a recursive manner.
动态规划（DP）是一种解决问题的方法，它以递归的方式将复杂问题分解为更简单的子问题。
The knapsack problem can be solved efficiently using dynamic programming, where we create a table to store the maximum value achievable with each weight capacity.
背包问题可以通过动态规划有效地解决，我们创建一个表格来存储每种重量容量可达到的最大价值。
In dynamic programming, the Bellman equation is used to find the optimal solution by iteratively updating the values of subproblems.
在动态规划中，使用贝尔曼方程通过迭代更新子问题的值来找到最优解。
Fibonacci sequence calculation is an example of bottom-up dynamic programming, where we compute the sequence from the base cases upwards.
斐波那契数列计算是一个自底向上的动态规划示例，我们从基本情况开始向上计算序列。
The shortest path problem in graphs can be solved using Dijkstra's algorithm or dynamic programming techniques like Floyd-Warshall algorithm.
图中最短路径问题可以使用Dijkstra算法或Floyd-Warshall这样的动态规划技术求解。
The use of memoization in dynamic programming helps avoid redundant computations by storing and reusing previously computed results.
动态规划中的记忆化方法通过存储并重用先前计算的结果来避免冗余计算。
The rod cutting problem, where a bar of metal needs to be cut into smaller pieces to maximize profit, can be modeled and solved using dynamic programming.
金属棒切割问题，需要将其切成小段以实现利润最大化，可以用动态规划进行建模和求解。
The Viterbi algorithm, used in Hidden Markov Models, employs dynamic programming to determine the most likely sequence of states given observations.
维特比算法，在隐马尔科夫模型中使用，利用动态规划来确定给定观测结果时最可能的状态序列。
Optimal binary search tree construction is another application of dynamic programming, where the cost of different search paths is minimized.
最优二叉搜索树构建是动态规划的另一个应用，旨在最小化不同搜索路径的成本。
The traveling salesman problem, which involves finding the shortest possible route visiting all cities exactly once, is a well-known NP-hard problem that can be approached using approximation algorithms or heuristics based on dynamic programming concepts.
旅行商问题，涉及寻找恰好访问所有城市一次的最短路线，是一个著名的NP难问题，可以采用基于动态规划概念的近似算法或启发式方法进行求解。