% CHANGES TO VOLUME 1 OF THE ART OF COMPUTER PROGRAMMING
%
% Copyright (C) 2011 Donald E. Knuth
% This file may be freely copied provided that no modifications are made.
% All other rights are reserved.
%
% Three levels of changes to the books are distinguished here:
%
% "\bugonpage" introduces the correction of an error;
% "\amendpage" introduces new material for future editions;
% "\improvepage" introduces ameliorations of lesser importance.
%
% (Changes introduced by \improvepage do not appear in the hardcopy listing.)
%
% Also, "\planforpage" introduces some of the author's half-baked intentions.
%

% NOTE: TO PUT THE INDEX ON A SEPARATE PAGE, RUN THIS WITH THE COMMAND LINE
%   tex "\let\indexeject+ \input err1"

\newif\ifall % \alltrue means show the trivial items too
\relax % hook

\def\vertical{|}
\def\inref#1 #{\expandafter\def\csname\vertical#1\endcsname}
\catcode`|=\active
\let|\inref \input \jobname.ref
\catcode`|=12

\input taocpmac % use the format for TAOCP, with modifications below

\def\becomes{\ifmmode\ \hbox\fi{\manfnt y}\ } % wiggly arrow indicates a change

\def\bugonpage#1.#2 #3 (#4) {
  \medbreak\defaultpointsize
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   {\bf Page #2}\enspace #3
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  \line{\kern-5pt{\bf Page #2}\enspace #3
   \leaders\hrule\hfill\ \eightrm\date#4.}
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  \medbreak\ninepoint
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   \leaders\hrule\hfill\ \eightrm\date#4.}
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  \nobreak\smallskip\begingroup\let\endchange=\endgroup\sl\noindent}
\let\endchange=\fi
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\def\hangit{\hangindent2em}
\def\cutpar{{\parfillskip=0pt\par}}

\def\date#1.#2.#3.{% convert "yy.mm.dd." to "dd Mon 19yy"
  #3
  \ifcase#2\or Jan\or Feb\or Mar\or Apr\or May\or Jun\or
               Jul\or Aug\or Sep\or Oct\or Nov\or Dec\fi
  \ \ifnum #1<97 \hundred#1\else19#1\fi}
\def\hundred{20} % the "century" for dates before '97

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%%%%%%%%%%%%%% opening remarks %%%%%%%%%%%%%%%%%%%%%%%%

\def\lhead{INTRODUCTION}
\let\rhead=\lhead
\titlepage
\volheadline{THE ART OF COMPUTER PROGRAMMING}
\bigskip
\volheadline{ERRATA TO VOLUME 1 (after 2010)}
\bigskip

\noindent This document is a transcript of the notes that I have been making
in my personal copy of {\sl The Art of Computer Programming}, Volume~1 (third
edition, 27th printing), since it was first printed in 2011.
Previous errata are recorded in another file `{\tt all1-pre.ps}'.

\ifall Four levels of updates\dash---``errors,'' ``amendments,'' ``plans,''
   and ``improvements''\dash---appear, indicated by four
\else Three levels of updates\dash---``errors,'' ``amendments,'' and
   ``plans''\dash---appear, indicated by three \fi
different typographic conventions:
\begingroup\def\hundred{17}

\bugonpage 0.666 line 1 (76.07.04)
Technical or typographical errors (aka bugs) are the most critical items, so
they are flagged with a `\thinspace{\manfnt x}\thinspace' preceding the page
number. The date on which I first was told about the bug is shown; this is the
effective date on which I paid the finder's fee. The necessary
corrections are indicated in
a straightforward way. If,~for example, the book says
`$n$' where it should have said `$n+1$', the change is shown thus:
\smallskip
$n$ \becomes $n+1$
\endchange

\amendpage 0.666 line 2 (89.07.14)
Amendments to the text appear in the same format as bugs, but without
the~`\thinspace{\manfnt x}\thinspace'. These are things I wish I had known
about or thought of when I wrote the original text, so I added them later.
The date is the date I drafted the new text.
\endchange

\def\hundred{19}

\planforpage 0.666 line 3 (17.11.20)
Plans for the future represent a third kind of item. In such notes I~sketched
my intentions about things that I wasn't ready to flesh out further when
I~wrote them down. You can identify these items because they're written in
slanted type, and preceded by a bunch of dots
`\hbox to 6em{\leaders\hbox to 5pt{\hss.\hss}\hfill}' leading to the date on
which I recorded the plan in my files.
\endchange

\improvepage 0.666 line 4 (38.01.10)
The fourth and final category\dash---indicated by page and line number in
smaller, slanted type\dash---consists of minor corrections or improvements
that most readers don't want to know about, because they are so trivial.
You wouldn't even
be seeing these items if you hadn't specifically chosen to print the complete
errata list in all its gory details.
Are you sure you wanted to do that?
\endchange

\endgroup
\ifall\else\medskip\ninepoint
My personal file of updates also includes a fourth category of items, not
shown in this list. They are miscellaneous minor corrections or improvements
that most readers don't want to know about, because they are so trivial.
If you really want to see all of the gory details,
you can download the full list from Internet webpage
$$\.{http://www-cs-faculty.stanford.edu/\char`\~knuth/taocp.html}$$
by selecting the ``long form'' of the errata.
\fi

\medskip
\tenpoint
My shelves at home are
bursting with preprints and reprints of significant research results that I
want to digest and summarize, where appropriate, in the ultimate edition of
Volume~1. I didn't do that in the third edition because I would surely have to do
it over again later: New results continue to pour forth at a great rate, and I
will have time to rewrite that volume only~once. Volumes 4 and~5 need to be
finished first. So I've put most of my effort so far into writing up
those parts of the total picture that seem to have converged to their
near-final form. It follows, somewhat paradoxically, that the updates in this
document are most current in the areas where there has been least activity.

On the other hand I do believe that the changes listed here bring Volume~1
completely up to date in two respects: (1)~All of the research problems in the
previous edition\dash---i.e., all exercises that were rated 46 and
above\dash---have received new ratings of 45 or less whenever I learned of a
solution; and in such cases, the answer now refers to that solution.
(2)~All of the historical information about pioneering developments has been
amended whenever new details have come to my attention.

\beginconstruction
The ultimate, glorious, 100\% perfect editions of Volumes 1--4A are works in progress.
Please let me know of any improvements that you think I ought to make.
Send your comments either by snail mail to D.~E. Knuth, Computer
Science, Gates Building 4B, Stanford University, Stanford CA~94305-9045,
or by email to
{\tt taocp{\char`\@}cs.stanford.edu}. (Use email for book suggestions
only, please\dash---all
other correspondence is returned unread to the sender, or discarded,
because I have no time to
read ordinary email.) Although I'm working full time on
Volume~4B these days, I~will try to reply to all such messages
within a year of receipt. Current news about {\sl The Art of Computer
Programming\/} is posted on
$$\.{http://www-cs-faculty.stanford.edu/\char`~knuth/taocp.html}$$
and updated regularly.
\par\endconstruction
\rightline{\dash---Don Knuth, January 2011}

\bigskip
\bigskip
{\quoteformat
What happened?
The subject took the bit in its teeth and ran away with it,
that's what happened.
I know now how Sir James Frazer felt when,
after setting out to dash off a brief monograph
on a single obscure rite, he found himself
in the embarrassing possession of
the 12 volumes of ``The Golden Bough.''
\author WAVERLEY ROOT (1974)
% International Herald Tribune, 22 May 1974, p8
\vfill\eject
}

\def\today{\number\day\space\ifcase\month\or
  January\or February\or March\or April\or May\or June\or
  July\or August\or September\or October\or November\or December\fi
  \space\number\year}

%%%%%%%%%%%%%%% CHANGES FOR VOLUME 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\lhead{CHANGES TO VOLUME 1: FUNDAMENTAL ALGORITHMS}
\let\rhead=\lhead
\titlepage
\volheadline{FUNDAMENTAL ALGORITHMS}
\bigskip
\rightline{Copyright \copyright\ 2011 Addison\with Wesley; all rights reserved}
\rightline{Last updated \today}
\bigskip
\rightline{\sl Most of these corrections have already been made in
                  recent printings.}
\smallskip
\let\defaultpointsize=\tenpoint

\amendpage 1.xvi line 16 (11.06.16)
a {\it 45\/} rating \becomes
a {\it 40\/} rating
\endchange

\bugonpage 1.27 line 1 (11.07.22)
\ninepoint $n>1$ \becomes $n>1$ and $n\ne e$.
\endchange % actually I've also changed $n$ to $x$ in this exercise

\amendpage 1.144 line 2 (11.11.29)
\ninepoint to zero. \becomes to zero,
and the overflow toggle is cleared.
\endchange

\amendpage 1.151 line $-11$ (11.11.29)
{\sl set to zero\/} \becomes {\sl set to positive zero\/}
\endchange

\bugonpage 1.229 line 11 (11.02.06)
{\sl Mechanization\/} \becomes {\sl Mechanisation}
\endchange

\amendpage 1.303 in the line before {\eq(13)} (11.08.29)
transformation: \becomes
transformation (see M.~H. Doolittle,
{\sl Report of the Superintendent of the U.~S. Coast and Geodetic Survey\/}
(1878), 115--120):
\endchange

\bugonpage 1.339 replacement for line 17 (11.03.14)
$$D(y)=3\bigl( 1/(x+1)\bigr) -\bigl(-(a(2x))/(x^2)^2\bigr),\eqno(21)$$
\endchange

\let\defaultpointsize=\ninepoint % get ready for answer pages

\improvepage 1.470 in step E1 of answer 28 (11.10.28)
If $1-\epsilon$ \dots $k\gets1$. \becomes
Set $x\gets1-\epsilon-x$, $y\gets y_0$,
and $k\gets1$, where $1-\epsilon$ is the largest possible value
of~$x$, and $y_0$ is the nearest approximation to $b^{1-\epsilon}$.
\endchange

\amendpage 1.472 new copy for end of answer 31 (11.10.20)
Consequently we have $\bigl(\sum_{j=1}^n u_j\bigr)\bigl(\sum_{j=1}^n v_j\bigr)
\le n\sum_{j=1}^n u_jv_j$ when $u_1\le u_2\le\cdots\le u_n$ and
$v_1\le v_2\le\cdots\le v_n$, a result known as {\it Chebyshev}'s
monotonic inequality. [See {\sl Soobshch.\ mat.\ obshch.\ Khar'kovskom
Univ.\ \bf4},\thinspace2 (1882), 93--98.]
\endchange

\amendpage 1.474 lines 3--5 of answer 43 (11.11.26)
as in exercise 44 \dots\ $(x_i-1)\bigr)$. \becomes
by setting $x=1$ in exercise~40 and obtaining
${\prod_{k\ne i}(x_k-1)/x_i\prod_{k\ne i}(x_k-x_i)}$. After multiplying
numerator and denominator by $x_i-1$, we can sum on $i$
by applying exercise~33 with $r=0$ to the $n+2$ numbers
$\{0,1,x_1,\ldots,x_n\}$.
\endchange

\let\defaultpointsize=\tenpoint % begin appendices

\amendpage 1.628 new entries for Appendix C (11.04.17)
\ninepoint\noindent
Program 1.2.10M, 145, 186.\nl
Program 1.4.3.1M, 204--211, 530.\nl
Program 2.1A, 236.\nl
Program 2.1B, 535.\nl
Program 2.3.1S, 325.
\endchange

\bugonpage 1.629 in Appendix C (11.04.17)
\ninepoint\noindent
Algorithm 2.4B$'$, 606. \becomes
Algorithm 2.4B$'$, 605. Algorithm 2.4B$''$, 606.\nl
Algorithm 2.5G, 613. \becomes Algorithm 2.5G, 613--614.
\endchange

\expandafter\ifx\csname indexeject\endcsname\relax\else\vfill\eject\fi
\amendpage 1.630 and following (11.01.01)
Miscellaneous changes to the existing index of Volume~1 are collected here,
including corrections and amendments to the old entries as well as new entries
that are occasioned by the new material. Thus, the lines of the full index
that have changed serve also as an index to the present document. However,
when a correction or amendment has caused an old index entry to be deleted,
the deletion is usually not indicated.

\input exotic
\begindoublecolumns
\indexformat
\gdef\Uni1.08:{\bitmap24:1.08:}
\hangindent 2em
Chebyshev, Pafnutii Lvovich ({\rus Chebyshev, Pafnutii0 Lp1vovich}), inequalities, 98, 104, 472. % 29th
Doolittle, Myrick Hascall, 303. % 29th
GO button of \MIX, 126, 139, 143--144, 211. % 29th
Overflow toggle of \MIX, 126, 131, 134, 142, 144, 208, 214, 228. % 29th
Staver, Tor B{\o}hm, 582. % 28th

\vfill
\enddoublecolumns
\endchange

\bye

[The next printing will be the 30th.]
Not mentioned above:
page 76, line 2 after (8), slightly better positioning below the \sum signs
page 384, slightly better wording, 3 and 5 lines after (4)
page 394, different style for the reference in statement of Theorem R
page 459, middle, better spacing in "Comp. J."
page 471, answer 30 is now "x" not "n"
page 621, larger $n$ in caption

ARTICLES "TO APPEAR" THAT ARE STILL PENDING: