From 119a4676ff267db48d5a684bb1332965f736f619 Mon Sep 17 00:00:00 2001
From: Martin Mares <mj@ucw.cz>
Date: Fri, 21 Feb 2020 17:50:29 +0100
Subject: [PATCH] Splay: Fixed English
---
02-splay/splay.tex | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/02-splay/splay.tex b/02-splay/splay.tex
index d7018ac..5b8b9ce 100644
--- a/02-splay/splay.tex
+++ b/02-splay/splay.tex
@@ -73,7 +73,7 @@ The amortized cost of the full \alg{Splay} is a~sum of amortized costs of the in
Let $r_1(x),\ldots,r_t(x)$ denote the rank of~$x$ after each step and $r_0(x)$ the rank
before the first step.
-We will use the following claim, which will be proved in the rest of this section:
+We will use the following claim, which will be proven in the rest of this section:
{\narrower\claim{
The amortized cost of the $i$-th step is at most $3r_i(x) - 3r_{i-1}(x)$,
@@ -385,7 +385,7 @@ number of nodes in the tree during the sequence.}
\def\rmin{r_{\rm min}}
Splay trees have surprisingly many interesting properties. Some of them can be
-proved quite easily by generalizing the analysis of \em{Splay} by putting different
+proven quite easily by generalizing the analysis of \em{Splay} by putting different
weights on different nodes.
We will assign a~positive real \em{weight} $w(v)$ to each node~$v$. The size of
--
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