【JOISC 2020】D1T1 building4

最新推荐文章于 2020-08-03 11:07:00 发布

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最新推荐文章于 2020-08-03 11:07:00 发布 · 472 阅读

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#算法 #动态规划

本文介绍了JOISC 2020比赛中的一个问题，涉及如何在两个装饰计划A和B中公平地选择建筑物装饰方案，使得从机场到住宿的路上豪华级别递增。提出了暴力求解方法和优化策略，通过动态规划求解合法的装饰方案，并给出了构造解决方案的思路。

题面及数据范围

The Olympic Games will be held in JOI Kingdom soon. In order to welcome participants from all over the world, the buildings on the way from the airport to the accommodation will be decorated. There are $2 N$ buildings, numbered from $1$ to $2 N$ from the airport.
President K is in charge of the decoration project. He asked the public to make decoration plans. After examining them, he finally chose two plans, the plan A and the plan B. In the plan A, the luxury level of the building $i$ ( $\leqslant i \leqslant 2N$ ) is $A_i$ . In the plan B, the luxury level of the building $i$ ( $\leqslant i \leqslant 2N$ ) is $B_i$ .
Both plans are very good, and it is difficult to choose one of them. He decided to decorate the buildings in the following way: for each building, one of the plan A or B will be chosen. In order to decorate the buildings in a fair way, the plan A will be chosen for N buildings, and the plan B will be chosen for the remaining N buildings.
Moreover, since the participants will be excited if the luxury levels are increasing on the way from the airport to the accommodation, the following condition should be satisfied: $Ci⩽Ci+1C_i \leqslant C_{i+1}$ for every $i$ with $\leqslant i \leqslant 2N - 1$ , where $C_i$ is the luxury level of the building