From 9f52ddd6c280aaac1e649cbd047a236b666ba493 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Wed, 10 Sep 2014 11:07:02 -0400
Subject: [ps1] small typos

---
 ps1/main.tex | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

(limited to 'ps1/main.tex')

diff --git a/ps1/main.tex b/ps1/main.tex
index a2646e3..65c7707 100644
--- a/ps1/main.tex
+++ b/ps1/main.tex
@@ -44,6 +44,8 @@ necessarily equal to the number of elements. Indeed, inserting an element can
 possibly require creating a min pointer in its cluster and recursively
 inserting its cluster id into the summary.
 
+\paragraph{(b)} See \textbf{(c)}.
+
 \paragraph{(c)} Let us denote by $N(u)$ the number of min pointers created when
 inserting an element in a $u$-vEB tree. We have two cases:
 
@@ -210,9 +212,9 @@ c)) - 1}
 \end{center}
 
 Then, the least significant bit set to one of a word $x$ of length $w$ can be
-computed by first finding the rightmost non-empty cluster of length $w$ in $x$,
-then extract this cluster by shifting and masking, and then finding the least
-significant bit set to one in this cluster:
+computed by first finding the rightmost non-empty cluster of length $\sqrt{w}$
+in $x$, then extracting this cluster by shifting and masking, and then finding
+the least significant bit set to one in this cluster:
 
 \vspace{1em}
 
@@ -221,7 +223,7 @@ significant bit set to one in this cluster:
 \hspace*{1cm}\texttt{if z == -1:}\newline
 \hspace*{2cm}\texttt{return -1}\newline
 \hspace*{1cm}\texttt{return z * $\sqrt{\texttt{w}}$
-    + lsb-short((x >> z * $\sqrt{w}$) \& (1 << $\sqrt{w}$ - 1))}
++ lsb-short((x >> z * $\sqrt{\texttt{w}}$) \& (1 << $\sqrt{\texttt{w}}$ - 1))}
 
 Note that the above code only requires a constant number of multiplications and
 bitwise operations once the constants $m$, $a$, $b$ and $c$ have been
-- 
cgit v1.2.3-70-g09d2

