Prefix function

... $p[i]$ is the length of the longest prefix of $s[i, |s|]$, which is also a prefix of $s$.

... $p[i]$ is the length of the longest prefix of $s[1, i]$, which is also a suffix of $s$.

... $p[i]$ is the length of the longest prefix of $s[1, i]$, which is also a suffix of $s[1, i]$.

... $p[i]$ is the length of the longest prefix of $s[i, |s|]$, which is also a suffix of $s[i, |s|]$.