Problem

本文探讨了SpringBoot中使用Swagger 3.0遇到的404路径问题解决方案,并详细讲解了如何配置Druid数据源,同时涵盖了Log4j.properties配置。涉及技术包括XML映射、DTD引用、API文档生成和数据库连接池管理。
Dynamic programming is an algorithm suitable for solving the Knapsack problem. It avoids repeated calculations by decomposing complex problems into overlapping sub - problems and storing the solutions to the sub - problems. The core of dynamic programming is state definition and state transition equations [^1]. The general steps of using dynamic programming to solve the Knapsack problem are as follows: 1. **Define the state**: Usually, two - dimensional states are defined. For example, let `dp[i][j]` represent the maximum value that can be obtained when considering the first `i` items and the capacity of the knapsack is `j`. 2. **State transition equation**: For the 0 - 1 Knapsack problem, if the weight of the `i` - th item is `w[i]` and the value is `v[i]`, then the state transition equation is: - When `j < w[i]`, `dp[i][j]=dp[i - 1][j]` (the current item cannot be put into the knapsack). - When `j >= w[i]`, `dp[i][j]=max(dp[i - 1][j], dp[i - 1][j - w[i]]+v[i])` (choose whether to put the current item into the knapsack). Here is a simple Python code example for the 0 - 1 Knapsack problem: ```python def knapsack(weights, values, capacity): n = len(weights) dp = [[0 for _ in range(capacity + 1)] for _ in range(n + 1)] for i in range(1, n + 1): for j in range(1, capacity + 1): if j < weights[i - 1]: dp[i][j] = dp[i - 1][j] else: dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - weights[i - 1]] + values[i - 1]) return dp[n][capacity] weights = [2, 3, 4, 5] values = [3, 4, 5, 6] capacity = 8 print(knapsack(weights, values, capacity)) ``` ### Application scenarios - **Resource allocation**: In project management, given a limited amount of resources (such as time, budget, manpower), and different tasks with different resource requirements and benefits, the Knapsack problem can be used to select the most profitable combination of tasks. - **Stock selection**: When an investor has a certain amount of funds and there are multiple stocks with different prices and expected returns, the Knapsack problem can be used to select the most profitable stock portfolio.
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