dynamic programming

简明释义

动态规划

英英释义

例句

1.The Fibonacci sequence can be calculated efficiently using dynamic programming techniques.

斐波那契数列可以使用动态规划技术高效计算。

2.When learning about algorithms, understanding dynamic programming is crucial for tackling many coding challenges.

在学习算法时，理解动态规划对解决许多编码挑战至关重要。

3.In game development, dynamic programming can help optimize resource management and AI behavior.

在游戏开发中，动态规划可以帮助优化资源管理和人工智能行为。

4.In computer science, dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems.

在计算机科学中，动态规划是一种通过将复杂问题分解为更简单的子问题来解决复杂问题的方法。

5.Many algorithms for optimization problems use dynamic programming to improve efficiency.

许多优化问题的算法使用动态规划来提高效率。

作文

Dynamic programming is a powerful algorithmic technique used in computer science and mathematics to solve complex problems by breaking them down into simpler subproblems. This method is particularly effective for optimization problems, where the goal is to find the best solution from a set of feasible solutions. The concept of dynamic programming (动态规划) was introduced by Richard Bellman in the 1950s and has since become a fundamental approach in various fields, including operations research, economics, and artificial intelligence.One of the key characteristics of dynamic programming (动态规划) is its ability to utilize overlapping subproblems. In many cases, a problem can be divided into smaller problems that are solved independently. However, these smaller problems often share common subproblems, which means that solving them repeatedly can lead to inefficiencies. Dynamic programming (动态规划) addresses this issue by storing the results of these subproblems in a table or an array, allowing for quick retrieval when needed. This process is known as 'memoization.'To illustrate the concept of dynamic programming (动态规划), consider the classic Fibonacci sequence problem. The Fibonacci sequence is defined as follows: F(0) = 0, F(1) = 1, and F(n) = F(n-1) + F(n-2) for n > 1. A naive recursive solution would involve recalculating the Fibonacci numbers multiple times, leading to an exponential time complexity. However, by applying dynamic programming (动态规划), we can store the results of previous calculations in an array, reducing the time complexity to linear, O(n).Another well-known example of dynamic programming (动态规划) is the Knapsack problem. In this problem, we have a set of items, each with a weight and a value, and we want to determine the maximum value we can carry in a knapsack of a given capacity. A naive approach would involve checking all combinations of items, which is computationally expensive. By using dynamic programming (动态规划), we can build a table that represents the maximum value achievable for every possible weight up to the capacity of the knapsack. This allows us to systematically find the optimal solution without redundant calculations.The applications of dynamic programming (动态规划) extend beyond theoretical problems. In real-world scenarios, it is widely used in resource allocation, financial modeling, and even in machine learning algorithms. For instance, in reinforcement learning, dynamic programming (动态规划) techniques are employed to optimize decision-making processes by evaluating the expected rewards of different actions over time.In conclusion, dynamic programming (动态规划) is an essential concept in problem-solving that emphasizes efficiency and optimization. By breaking problems into manageable subproblems and storing their solutions, it allows for significant reductions in computational time and resources. Whether applied to theoretical challenges or practical applications, understanding dynamic programming (动态规划) is crucial for anyone looking to excel in fields related to computer science and mathematics. As technology continues to advance, the relevance of dynamic programming (动态规划) will only grow, making it a vital skill for future problem solvers.

动态规划是一种强大的算法技术，广泛应用于计算机科学和数学中，通过将复杂问题分解为更简单的子问题来解决。这种方法特别适用于优化问题，其目标是从一组可行解中找到最佳解。动态规划（dynamic programming）的概念是由理查德·贝尔曼在20世纪50年代提出的，此后已成为运用在多个领域的基本方法，包括运筹学、经济学和人工智能。动态规划（dynamic programming）的一个关键特征是它能够利用重叠子问题。在许多情况下，一个问题可以被分解为独立解决的小问题。然而，这些小问题通常共享共同的子问题，这意味着重复解决它们会导致效率低下。动态规划（dynamic programming）通过将这些子问题的结果存储在表或数组中来解决这个问题，从而在需要时快速检索。这一过程称为“备忘录化”。为了说明动态规划（dynamic programming）的概念，考虑经典的斐波那契数列问题。斐波那契数列定义如下：F(0) = 0，F(1) = 1，并且对于n > 1，F(n) = F(n-1) + F(n-2)。一种简单的递归解决方案将涉及多次重新计算斐波那契数，导致指数时间复杂度。然而，通过应用动态规划（dynamic programming），我们可以将之前计算的结果存储在数组中，从而将时间复杂度降低到线性O(n)。另一个著名的动态规划（dynamic programming）示例是背包问题。在这个问题中，我们有一组物品，每个物品都有重量和价值，我们想要确定在给定容量的背包中可以携带的最大价值。简单的方法将涉及检查所有物品组合，这在计算上是昂贵的。通过使用动态规划（dynamic programming），我们可以构建一个表，表示在背包容量内每个可能重量的最大可实现价值。这使我们能够系统地找到最佳解决方案，而无需冗余计算。动态规划（dynamic programming）的应用超越了理论问题。在现实世界的场景中，它广泛应用于资源分配、金融建模，甚至机器学习算法。例如，在强化学习中，使用动态规划（dynamic programming）技术来优化决策过程，通过评估不同动作随时间的预期奖励。总之，动态规划（dynamic programming）是解决问题中的一个重要概念，强调效率和优化。通过将问题分解为可管理的子问题并存储其解决方案，它允许在计算时间和资源上显著减少。无论是应用于理论挑战还是实际应用，理解动态规划（dynamic programming）对任何希望在计算机科学和数学相关领域取得成功的人来说都是至关重要的。随着技术的不断进步，动态规划（dynamic programming）的相关性只会增加，使其成为未来问题解决者的重要技能。