2015CCPC南阳场 D - Pick The Sticks

本文介绍了2015年CCPC南阳站的D题-Pick The Sticks的解题思路,包括两种解决方案。第一种方案涉及处理小数体积问题,需要将所有体积乘2进行计算。第二种方案利用动态规划dp[i][M][k]表示使用前i种物品构造长度为M的大木块,两端放置k个小木棒,通过降维避免内存溢出。给出了具体的代码实现。

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D - Pick The Sticks
Time Limit:10000MS     Memory Limit:65535KB     64bit IO Format:%I64d & %I64u

Description

The story happened long long ago. One day, Cao Cao made a special order called "Chicken Rib" to his army. No one got his point and all became very panic. However, Cao Cao himself felt very proud of his interesting idea and enjoyed it. 

Xiu Yang, one of the cleverest counselors of Cao Cao, understood the command Rather than keep it to himself, he told the point to the whole army. Cao Cao got very angry at his cleverness and would like to punish Xiu Yang. But how can you punish someone because he's clever? By looking at the chicken rib, he finally got a new idea to punish Xiu Yang. 

He told Xiu Yang that as his reward of encrypting the special order, he could take as many gold sticks as possible from his desk. But he could only use one stick as the container. 

Formally, we can treat the container stick as an   length segment. And the gold sticks as segments too. There were many gold sticks with different length   and value  . Xiu Yang needed to put these gold segments onto the container segment. No gold segment was allowed to be overlapped. Luckily, Xiu Yang came up with a good idea. On the two sides of the container, he could make part of the gold sticks outside the container as long as the center of the gravity of each gold stick was still within the container. This could help him get more valuable gold sticks. 

As a result, Xiu Yang took too many gold sticks which made Cao Cao much more angry. Cao Cao killed Xiu Yang before he made himself home. So no one knows how many gold sticks Xiu Yang made it in the container. 

Can you help solve the mystery by finding out what's the maximum value of the gold sticks Xiu Yang could have taken?
 
### CCPC 2023 H题 解析 关于CCPC 2023 H题的具体题目描述尚未公开,但从以往的比赛惯例以及类似的题目解析可以推测其可能涉及的内容和技术要点。以下是基于已有参考资料和专业知识对该类问题的解答框架。 #### 1. **问题背景** CCPC(Chinese Collegiate Programming Contest)作为国内重要的编程竞赛之一,通常会设计具有挑战性的算法问题来测试参赛者的逻辑思维能力和编码技巧。H题通常是比赛中的难点之一,往往涉及到复杂的算法模型或数据结构的应用[^2]。 #### 2. **潜在的技术方向** 根据过往的经验,H题可能会覆盖以下几个方面: - 动态规划 (Dynamic Programming)[^1] - 构造性问题 (Construction Problems)[^4] - 数学优化 (Mathematical Optimization) 假设该题属于动态规划类别,则需关注状态转移方程的设计;如果是构造性问题,则重点在于如何通过有限操作达到目标条件。 #### 3. **通用解题策略** 无论具体主题为何种类型,在面对高难度赛题时可遵循如下方法论: ##### (1)深入理解题目需求 仔细阅读并反复确认输入输出的要求及其约束条件,确保不会遗漏任何细节信息[^3]。 ##### (2)选取合适的算法工具箱 依据实际景挑选最匹配的方法论,比如当存在重叠子问题且具备最优子结构性质时优先选用DP技术[^1]。 ##### (3)编写清晰易懂的代码实现 采用模块化的方式分步完成整个功能开发流程,并辅以充分注释说明每一部分的作用机制。 ```cpp // 示例伪代码片段展示基本框架布局 #include <bits/stdc++.h> using namespace std; int main(){ ios::sync_with_stdio(false); cin.tie(0); int n; cin >> n; // 输入规模参数 vector<long long> dp(n+1, INF); // 初始化dp数组,默认极大值表示未访问过 dp[0]=0; for(int i=1;i<=n;i++){ for(auto &coin : coins){ if(i >= coin && dp[i - coin]+costs[coin]<dp[i]){ dp[i]=dp[i - coin]+costs[coin]; } } } cout << (dp[n]==INF ? -1 : dp[n])<< "\n"; } ``` 上述例子仅作示意用途,真实情况下应严格依照官方给定的数据范围调整变量类型及边界处理方式。 #### 4. **复杂度考量** 对于大规模实例而言,效率至关重要。因此除了正确率之外还需兼顾运行时间和内存消耗指标。一般建议尽可能降低渐近时间开销至O(NlogN)甚至更低级别。 --- ###
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