Given a positive constant c, a sequence $S=〈s_1,s_2,\dots ,s_k〉$ of k numbers is said to be almost increasing if and only if $s_i>\underset{1\le j<i}{\max }{s}_j-c$ for all $1<i\le k$. A longest common almost-increasing subsequence (LCaIS) between two input sequences is a longest common subsequence that is also an almost increasing sequence. We found out that the existing algorithm proposed by Moosa et al. [1] to find an LCaIS of two sequences without repeated elements gives an incorrect result for some instances. In this work, we present a dynamic programming algorithm that can correctly compute an LCaIS between any two sequences with repeated elements in $O(nml)$ time and $O(nm)$ space, where n and m are the lengths of two input sequences and l is the length of the output LCaIS.

给定一个正常数c，一个序列$\mathrm{小号}=〈s_{\mathrm{1个}}，s_2，\dots ，s_{ķ}〉$当且仅当k个数的k几乎增加$s_{\mathrm{一世}}>\underset{\mathrm{1个}\le Ĵ<\mathrm{一世}}{\mathrm{最高}}{s}_{Ĵ}-C$ 对所有人 $\mathrm{1个}<\mathrm{一世}\le ķ$。两个输入序列之间的最长公共几乎增加子序列（LCaIS）是最长公共子序列，它也是几乎增加的序列。我们发现Moosa等人提出的现有算法。文献[1]发现两个序列的LCaIS没有重复的元素在某些情况下给出了错误的结果。在这项工作中，我们提出了一种动态编程算法，该算法可以正确计算任意两个具有重复元素的序列之间的LCaIS$Ø（ñ米升）$ 时间和 $Ø（ñ米）$空间，其中n和m是两个输入序列的长度，l是输出LCaIS的长度。