From e010fb27e8571bb36fdc90ef454c5ce7534273d1 Mon Sep 17 00:00:00 2001
From: Antti H S Laaksonen <ahslaaks@cs.helsinki.fi>
Date: Mon, 17 Apr 2017 11:23:40 +0300
Subject: [PATCH] Better definition for function f [closes #31]

---
 chapter18.tex | 9 ++++-----
 1 file changed, 4 insertions(+), 5 deletions(-)

diff --git a/chapter18.tex b/chapter18.tex
index 81c7ab3..ca06440 100644
--- a/chapter18.tex
+++ b/chapter18.tex
@@ -21,8 +21,10 @@ For example, such queries are:
 The $k$th \key{ancestor} of a node $x$ in a rooted tree
 is the node that we will reach if we move $k$
 levels up from $x$.
-Let $f(x,k)$ denote the $k$th ancestor of $x$.
-For example, in the following tree, $f(2,1)=1$ and $f(8,2)=4$.
+Let $f(x,k)$ denote the $k$th ancestor of a node $x$
+(or $0$ if there is no such an ancestor).
+For example, in the following tree, $f(2,1)=1$, $f(8,2)=4$
+and $f(5,2)=0$.
 
 \begin{center}
 \begin{tikzpicture}[scale=0.9]
@@ -74,9 +76,6 @@ $\cdots$ \\
 \end{tabular}
 \end{center}
 
-The value $0$ means that the $k$th ancestor
-of a node does not exist.
-
 The preprocessing takes $O(n \log n)$ time,
 because each node can have at most $n$ ancestors.
 After this, any value of $f(x,k)$ can be calculated