From 465e17ee4aebf34696b3d38c8d986f058e967085 Mon Sep 17 00:00:00 2001
From: Martin Mares <mj@ucw.cz>
Date: Mon, 9 Dec 2019 10:30:11 +0100
Subject: [PATCH] Hashing: Typos
---
06-hash/hash.tex | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/06-hash/hash.tex b/06-hash/hash.tex
index 593478f..55675d6 100644
--- a/06-hash/hash.tex
+++ b/06-hash/hash.tex
@@ -815,7 +815,7 @@ Bloom filters are a~family of data structures for approximate representation of
in a~small amount of memory. A~Bloom filter starts with an empty set. Then it supports
insertion of new elements and membership queries. Sometimes, the filter gives a~\em{false
positive} answer: it answers {\csc yes} even though the element is not in the set.
-We will calculate the probability of false positves and decrease it at the expense of
+We will calculate the probability of false positives and decrease it at the expense of
making the structure slightly larger. False negatives will never occur.
\subsection{A trivial example}
@@ -900,7 +900,7 @@ If we set~$p$, it follows that $m \approx -n / \ln p$. Since all bands must fit
of memory, we want to use $k = \lfloor M/m\rfloor \approx -M/n \cdot \ln p$ bands. False
positives occur if we find~1 in all bands, which has probability
$$
- (1-p)^k \approx
+ (1-p)^k =
\e^{k\ln(1-p)} \approx
\e^{-M/n \cdot \ln p \cdot \ln(1-p)}.
$$
--
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