动态规划:PAT 1045 Favorite Color Stripe
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ADS的第7周作业,是一个动态规划算法题。
问题重现
Title: Favorite Color Stripe
Description:
Eva is trying to make her own color stripe out of a given one. She would like to keep only her favorite colors in her favorite order by cutting off those unwanted pieces and sewing the remaining parts together to form her favorite color stripe.
It is said that a normal human eye can distinguish about less than 200 different colors, so Eva’s favorite colors are limited. However the original stripe could be very long, and Eva would like to have the remaining favorite stripe with the maximum length. So she needs your help to find her the best result.
Note that the solution might not be unique, but you only have to tell her the maximum length. For example, given a stripe of colors {2 2 4 1 5 5 6 3 1 1 5 6}. If Eva’s favorite colors are given in her favorite order as {2 3 1 5 6}, then she has 4 possible best solutions {2 2 1 1 1 5 6}, {2 2 1 5 5 5 6}, {2 2 1 5 5 6 6}, and {2 2 3 1 1 5 6}.
Input Specification:
Each input file contains one test case. For each case, the first line contains a positive integer
Output Specification:
For each test case, simply print in a line the maximum length of Eva’s favorite stripe.
Sample Input:
65 2 3 1 5 612 2 2 4 1 5 5 6 3 1 1 5 6
Sample Output:
7
解法说明
设Eva喜欢的序列为
经过裁减,符合条件序列的最大长度(最大公共序列长度)的解为
对于状态空间
平凡态:
有状态转移方程:
平凡态比价容易理解:空序列的长度为0。
现在考虑当Eva喜欢的序列不变时,每当给出的条纹多了一个,即
最后考虑当这个新来的条纹不匹配时,它,或者Eva喜欢的最后一个颜色,两者之一总有一个没有卵用的:当新来的条纹不存在(
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