In this note, we first introduce a new problem called the longest common subsequence and substring problem. Let $X$ and $Y$ be two strings over an alphabet $\Sigma$. The longest common subsequence and substring problem for $X$ and $Y$ is to find the longest string which is a subsequence of $X$ and a substring of $Y$. We propose an algorithm to solve the problem.

翻译：本文首先引入了一个新问题，称为最长公共子序列与子串问题。设$X$和$Y$为字母表$\Sigma$上的两个字符串。$X$与$Y$的最长公共子序列与子串问题旨在找出既是$X$的子序列又是$Y$的子串的最长字符串。我们提出了一种解决该问题的算法。