From 91304e190124a63ba165aa0393025d69b64ca6f8 Mon Sep 17 00:00:00 2001
From: Martin Mares <mj@ucw.cz>
Date: Mon, 22 Jan 2007 00:47:38 +0100
Subject: [PATCH] Pridany dva obrazky. Druhy mi vrr pri saveovani znicilo,
 takze od nej existuje jen EPS.

---
 5-mst/5-mst.tex |    6 +-
 5-mst/mst1.eps  | 3736 +++++++++++++++++++++++++++++++++++++++++++++++
 5-mst/mst1.vrr  |   64 +
 5-mst/mst2.eps  | 3602 +++++++++++++++++++++++++++++++++++++++++++++
 4 files changed, 7406 insertions(+), 2 deletions(-)
 create mode 100644 5-mst/mst1.eps
 create mode 100644 5-mst/mst1.vrr
 create mode 100644 5-mst/mst2.eps

diff --git a/5-mst/5-mst.tex b/5-mst/5-mst.tex
index 44a8e33..06fdb61 100644
--- a/5-mst/5-mst.tex
+++ b/5-mst/5-mst.tex
@@ -8,8 +8,6 @@ algoritmy na~hled
 z~knihy~\cite{tarjan:dsna}. V¹echny grafy v~této kapitole budou neorientované multigrafy
 a jejich hrany budou ohodnoceny vahami $w: E \to {\bb R}$.
 
-\todo{Chybí zde obrázky, znaènì by hutný text projasnily.}
-
 \h{Minimální kostry a jejich vlastnosti}
 
 \s{Definice:}
@@ -38,6 +36,8 @@ Bu
   Ostatním hranám nele¾ícím v~kostøe budeme øíkat {\I tì¾ké.}
 \endlist
 
+\figure{mst2.eps}{Kostra $T$, cesta $T[e]$ a výsledek operace $\<swap>(T,e,e')$}{\epsfxsize}
+
 \s{Vìta:} Kostra~$T$ je minimální $\Leftrightarrow$ neexistuje hrana lehká vzhledem k~$T$.
 
 Tato vìta nám dává pìknou alternativní definici MST, která místo sèítání vah váhy
@@ -65,6 +65,8 @@ pro kterou $\vert \check{T} \symdiff T' \vert = \vert T \symdiff T' \vert -2$.
 Po~koneèném poètu tìchto krokù tedy musíme dojít k~$T'$.
 \qed
 
+\figure{mst1.eps}{Jeden krok dùkazu swapovacího lemmatu}{\epsfxsize}
+
 \s{Monotónní lemma o~swapování:}
 Je-li $T$ kostra, k~ní¾ neexistují ¾ádné lehké hrany, a~$T'$ libovolná kostra,
 pak lze od~$T$ k~$T'$ pøejít posloupností swapù, pøi které váha kostry neklesá.
diff --git a/5-mst/mst1.eps b/5-mst/mst1.eps
new file mode 100644
index 0000000..0c47044
--- /dev/null
+++ b/5-mst/mst1.eps
@@ -0,0 +1,3736 @@
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+%%BeginResource: font CMMI10
+%!PS-AdobeFont-1.1: CMMI10 1.100
+%%CreationDate: 1996 Jul 23 07:53:57
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
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+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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+dup 168 /Upsilon put
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+%%BeginResource: font CMSY7
+%!PS-AdobeFont-1.1: CMSY7 1.0
+%%CreationDate: 1991 Aug 15 07:21:52
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMSY7) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.035 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMSY7 def
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+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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+%%EndResource
+%%BeginResource: font CMSY7
+%!PS-AdobeFont-1.1: CMSY7 1.0
+%%CreationDate: 1991 Aug 15 07:21:52
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMSY7) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.035 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMSY7 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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+dup 122 /daggerdbl put
+dup 123 /paragraph put
+dup 124 /club put
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+
+%%EndResource
+%%BeginResource: font CMR10
+%!PS-AdobeFont-1.1: CMR10 1.00B
+%%CreationDate: 1992 Feb 19 19:54:52
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.00B) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMR10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMR10 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 161 /Gamma put
+dup 162 /Delta put
+dup 163 /Theta put
+dup 164 /Lambda put
+dup 165 /Xi put
+dup 166 /Pi put
+dup 167 /Sigma put
+dup 168 /Upsilon put
+dup 169 /Phi put
+dup 170 /Psi put
+dup 173 /Omega put
+dup 174 /ff put
+dup 175 /fi put
+dup 176 /fl put
+dup 177 /ffi put
+dup 178 /ffl put
+dup 179 /dotlessi put
+dup 180 /dotlessj put
+dup 181 /grave put
+dup 182 /acute put
+dup 183 /caron put
+dup 184 /breve put
+dup 185 /macron put
+dup 186 /ring put
+dup 187 /cedilla put
+dup 188 /germandbls put
+dup 189 /ae put
+dup 190 /oe put
+dup 191 /oslash put
+dup 192 /AE put
+dup 193 /OE put
+dup 194 /Oslash put
+dup 195 /suppress put
+dup 196 /dieresis put
+dup 0 /Gamma put
+dup 1 /Delta put
+dup 2 /Theta put
+dup 3 /Lambda put
+dup 4 /Xi put
+dup 5 /Pi put
+dup 6 /Sigma put
+dup 7 /Upsilon put
+dup 8 /Phi put
+dup 9 /Psi put
+dup 10 /Omega put
+dup 11 /ff put
+dup 12 /fi put
+dup 13 /fl put
+dup 14 /ffi put
+dup 15 /ffl put
+dup 16 /dotlessi put
+dup 17 /dotlessj put
+dup 18 /grave put
+dup 19 /acute put
+dup 20 /caron put
+dup 21 /breve put
+dup 22 /macron put
+dup 23 /ring put
+dup 24 /cedilla put
+dup 25 /germandbls put
+dup 26 /ae put
+dup 27 /oe put
+dup 28 /oslash put
+dup 29 /AE put
+dup 30 /OE put
+dup 31 /Oslash put
+dup 32 /suppress put
+dup 33 /exclam put
+dup 34 /quotedblright put
+dup 35 /numbersign put
+dup 36 /dollar put
+dup 37 /percent put
+dup 38 /ampersand put
+dup 39 /quoteright put
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 42 /asterisk put
+dup 43 /plus put
+dup 44 /comma put
+dup 45 /hyphen put
+dup 46 /period put
+dup 47 /slash put
+dup 48 /zero put
+dup 49 /one put
+dup 50 /two put
+dup 51 /three put
+dup 52 /four put
+dup 53 /five put
+dup 54 /six put
+dup 55 /seven put
+dup 56 /eight put
+dup 57 /nine put
+dup 58 /colon put
+dup 59 /semicolon put
+dup 60 /exclamdown put
+dup 61 /equal put
+dup 62 /questiondown put
+dup 63 /question put
+dup 64 /at put
+dup 65 /A put
+dup 66 /B put
+dup 67 /C put
+dup 68 /D put
+dup 69 /E put
+dup 70 /F put
+dup 71 /G put
+dup 72 /H put
+dup 73 /I put
+dup 74 /J put
+dup 75 /K put
+dup 76 /L put
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+98.288544 26.595190 98.205208 26.450851 98.205208 26.258402 ct
+98.205208 26.065952 98.288544 25.921614 98.455208 25.825390 ct
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+104.532669 22.432442 104.449333 22.288103 104.449333 22.095654 ct
+104.449333 21.903204 104.532669 21.758865 104.699333 21.662642 ct
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+[1.000000 0.000000 0.000000 1.000000 45.605740 21.360535] concat
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+68.683624 20.719139 mt 69.091812 20.359570 69.530602 20.119856 70.000000 20.000000 ct
+69.530602 19.880144 69.091812 19.640430 68.683624 19.280861 ct
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+68.683624 20.719139 mt 69.091812 20.359570 69.530602 20.119856 70.000000 20.000000 ct
+69.530602 19.880144 69.091812 19.640430 68.683624 19.280861 ct
+69.078537 20.000000 lt
+68.683624 20.719139 lt
+cp
+st
+gr
+showpage
+
+%%Trailer
+%%DocumentSuppliedResources: procset VrrEPSProcSet
+%%+ font CMMI10 CMSY7 CMR10
+end restore
+%%EOF
-- 
2.39.2