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Commit 240db80a authored by Martin Mareš's avatar Martin Mareš
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Merge branch 'master' of gitlab.kam.mff.cuni.cz:mj/dsbook

parents a68fca94 f54ac383
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...@@ -134,7 +134,7 @@ ${\cal L} = \{ h_{a,b} \mid a,b\in [p] \}$ from $[p]$ to $[m]$, where ...@@ -134,7 +134,7 @@ ${\cal L} = \{ h_{a,b} \mid a,b\in [p] \}$ from $[p]$ to $[m]$, where
$h_{a,b}(x) = ((ax+b) \bmod p) \bmod m$. $h_{a,b}(x) = ((ax+b) \bmod p) \bmod m$.
} }
\theorem{The family~$\cal L$ is 1-universal.} \theorem{The family~$\cal L$ is 2-universal.}
\proof \proof
Let $x,y$ be two distinct numbers in $[p]$. Let $x,y$ be two distinct numbers in $[p]$.
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...@@ -20,7 +20,7 @@ ...@@ -20,7 +20,7 @@
are indexed starting with~0. are indexed starting with~0.
\:$\alpha[i:j]$ is the \em{substring} $\alpha[i]\alpha[i+1]\ldots\alpha[j-1]$; \:$\alpha[i:j]$ is the \em{substring} $\alpha[i]\alpha[i+1]\ldots\alpha[j-1]$;
note that $\alpha[j]$ is the first character \em{behind} the substring, note that $\alpha[j]$ is the first character \em{behind} the substring,
so we have $|\alpha[i:j]| = j-i$. If $i>j$, the substring is empty. so we have $|\alpha[i:j]| = j-i$. If $i\ge j$, the substring is empty.
Either $i$ or~$j$ can be omitted, the beginning or the end of~$\alpha$ Either $i$ or~$j$ can be omitted, the beginning or the end of~$\alpha$
is used instead. is used instead.
\:$\alpha[{}:j]$ is the \em{prefix} of~$\alpha$ formed by the first~$j$ characters. \:$\alpha[{}:j]$ is the \em{prefix} of~$\alpha$ formed by the first~$j$ characters.
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