uva1451 - Average 单调队列维护下凸曲线

最新推荐文章于 2019-02-15 23:33:15 发布

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最新推荐文章于 2019-02-15 23:33:15 发布 · 1.8k 阅读

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给定一个DNA序列，通过将其转换为二进制序列，寻找长度至少为L且GC-ratio（即1的平均比例）最大的子序列。当有多个子序列具有相同最大平均值时，选择最短的；若存在多个最短子序列，则选取起始位置最小的。利用单调队列优化算法，维护下凸曲线，以高效找到满足条件的子序列。

A DNA sequence consists of four letters, A, C, G, and T. The GC-ratio of a DNA sequence is the number of Cs and Gs of the sequence divided by the length of the sequence. GC-ratio is important in gene finding because DNA sequences with relatively high GC-ratios might be good candidates for the starting parts of genes. Given a very long DNA sequence, researchers are usually interested in locating a subsequence whose GC-ratio is maximum over all subsequences of the sequence. Since short subsequences with high GC-ratios are sometimes meaningless in gene finding, a length lower bound is given to ensure that a long subsequence with high GC-ratio could be found. If, in a DNA sequence, a 0 is assigned to every A and T and a 1 to every C and G, the DNA sequence is transformed into a binary sequence of the same length. GC-ratios in the DNA sequence are now equivalent to averages in the binary sequence.