Patience Sort sorts a sequence of numbers with a minimal number of queues that work according to the First-In-First-Out (FIFO) principle. More precisely, if the length of the longest descreasing subsequence of the input sequence is $L$, then Patience Sort uses $L$ queues. We ask how much one can improve order with $k$ queues, where $k < L$? We address this question for two measures of sortedness: number of down-steps and length of the longest descreasing subsequence. For the first measure, we give an optimal algorithm. For the second measure, we give some partial results. The research was inspired by a problem arising in car manufacturing.
翻译:耐心根据第一出一出( FIFO) 原则, 以最小数量的队列排序一组数字。 更准确地说, 如果输入序列中最长时间消失的次序列的长度是 $L $, 那么耐心排序使用 $L 的队列。 我们询问, $k < L$ 能够用 $k 来改进队列的顺序, 在那里, $k < L$? 我们用两种分级尺度来解决这个问题: 下步数和最长消失的次序列的长度。 首先, 我们给出一个最佳算法。 对于第二个尺度, 我们给出部分结果。 这项研究是由汽车制造中出现的问题所启发的 。