added 2.1-1,2,3
1. added insertion-sort pseudocode and code,unittest 2. added 2.1-1 and 2.1-2 3. part of 2.1-3
This commit is contained in:
pezy_mbp
3
.gitignore
vendored
3
.gitignore
vendored
@@ -1,2 +1,5 @@
|
||||
#mac-os
|
||||
.DS_Store
|
||||
|
||||
#tex
|
||||
.texpadtmp/
|
||||
|
||||
@@ -73,3 +73,32 @@ for n in range(1, 100):
|
||||
|
||||
check and run [calc.py](calc.py)
|
||||
see [P1-1.pdf](P1-1.pdf)
|
||||
|
||||
### 2.1-1
|
||||
> Using Figure 2.2 as a model, illustrate the operation of `INSERTION-SORT` on the array `A = <31, 41, 59, 26, 41, 58>.`
|
||||
|
||||
```
|
||||
31 [41] 59 26 41 58
|
||||
31 41 [59] 26 41 58
|
||||
31 41 59 [26] 41 58
|
||||
26 31 41 59 [41] 58
|
||||
26 31 41 41 59 [58]
|
||||
26 31 41 41 58 59
|
||||
```
|
||||
|
||||
### 2.1-2
|
||||
> Rewrite the `INSERTION-SORT` procedure to sort into nonincreasing instead of non- decreasing order.
|
||||
|
||||
[procedure](nonincreasing-insertion-sort.pdf) |
|
||||
[code](insertion_sort.py) |
|
||||
[unittest](insertion_sort_unittest.py)
|
||||
|
||||
### 2.1-3
|
||||
> Consider the searching problem:
|
||||
|
||||
> **Input**: A sequence of n numbers `A = <a1, a2,...,an>` and a value v.
|
||||
|
||||
> **Output**: An index i such that `v = A[i]` or the special value NIL if v does not
|
||||
appear in A.
|
||||
|
||||
> Write pseudocode for linear search, which scans through the sequence, looking for v. Using a loop invariant, prove that your algorithm is correct. Make sure that your loop invariant fulfills the three necessary properties.
|
||||
|
||||
343
Foundations/overview/clrscode3e.sty
Normal file
343
Foundations/overview/clrscode3e.sty
Normal file
@@ -0,0 +1,343 @@
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
% clrscode3e.sty
|
||||
|
||||
% See the document "Using the clrscode3e Package in LaTeX 2e" for
|
||||
% examples.
|
||||
|
||||
% Package for producing pseudocode in the style of Cormen, Leiserson,
|
||||
% Rivest, and Stein, Introduction to Algorithms, Third edition.
|
||||
|
||||
% LIMITATION: This package works only if each procedure has at most 99
|
||||
% numbered lines of code.
|
||||
|
||||
% Each pseudocode procedure is typeset within a codebox environment,
|
||||
% \begin{codebox}...\end{codebox}.
|
||||
|
||||
% Normally, the first line within the codebox environment is a \Procname
|
||||
% command. The argument of the \Procname command is a math-mode
|
||||
% expression consisting of the procedure name and its parameters. The
|
||||
% name of the procedure itself goes within a \proc command. Example:
|
||||
% \Procname{$\proc{Matrix-Multiply}(A,B)$}
|
||||
% The \Procname command is optional.
|
||||
|
||||
% To typeset the name of a procedure (e.g., Matrix-Multiply) in small
|
||||
% caps, use the \proc command:
|
||||
% \proc{Matrix-Multiply}
|
||||
|
||||
% To typeset the name of a constant (e.g., nil) in small caps, use the
|
||||
% \const command:
|
||||
% \const{nil}
|
||||
|
||||
% To typeset the name of an identifier (e.g., rank) in regular italics,
|
||||
% use the \id command:
|
||||
% \id{rank}
|
||||
|
||||
% To typeset the name of a fixed function (e.g., sin) in roman, use the
|
||||
% \func command:
|
||||
% \func{sin}
|
||||
% (Note that several fixed functions, like sin, are already built into
|
||||
% LaTeX.)
|
||||
|
||||
% The \proc, \const, \id, and \func commands not only use the correct
|
||||
% font, they also perform the important service of interpreting a dash
|
||||
% as a hyphen, rather than as a minus sign. These commands may be used
|
||||
% either in or out of math mode.
|
||||
|
||||
% For attributes, use the various forms of the \attrib commands.
|
||||
|
||||
% Other than the \Procname line, all lines begin with either \li (for a
|
||||
% numbered line) or \zi (for an unnumbered line). The following
|
||||
% commands are provided for typesetting keywords and handling automatic
|
||||
% indentation:
|
||||
|
||||
% Loops: \For, \To, \By, \Downto, \Do, \While, \Repeat, \Until
|
||||
% Selection: \If, \Then, \Else, \ElseIf, \ElseNoIf
|
||||
% Jumps: \Return, \Error, \Goto
|
||||
% Multithreading: \Spawn, \Sync, \Parfor
|
||||
% Comments: \Comment, \RComment, \CommentSymbol
|
||||
% Indentation: \Indentmore, \Startalign, \Stopalign
|
||||
|
||||
% \label commands appearing in or after the first numbered line in a
|
||||
% codebox resolve to the number of the most recent numbered line.
|
||||
|
||||
% \twodots produces the ".." notation used for subarrays.
|
||||
|
||||
% Written for general distribution by Thomas H. Cormen, March 2009.
|
||||
|
||||
% The author grants permission for anyone to use this macro package and
|
||||
% to distribute it unchanged without further restriction. If you choose
|
||||
% to modify this package, you must indicate that you have modified it
|
||||
% prior to your distributing it. I don't want to get bug reports about
|
||||
% changes that *you* have made!
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
\ProvidesPackage{clrscode3e}
|
||||
\RequirePackage{graphics} % needed for \scalebox command
|
||||
|
||||
% The \useregularv command is because we used a different lowercase v
|
||||
% in math mode in the book. Most users of the clrscode3e package will
|
||||
% use the standard lowercase v in math mode, and so the \useregularv
|
||||
% command is a no-op for them.
|
||||
\ifdefined\useregularv\else\newcommand{\useregularv}{}\fi
|
||||
|
||||
% Commands for typesetting constants, procedure names, identifiers, and
|
||||
% fixed functions.
|
||||
\newcommand{\const}[1]{\textnormal{\scshape#1}}
|
||||
\newcommand{\proc}[1]{\textnormal{\scshape#1}}
|
||||
\newcommand{\text@hyphens}{\mathcode`\-=`\-\relax}
|
||||
\newcommand{\func}[1]{%
|
||||
\ensuremath{{\useregularv\mathop{\text@hyphens\operator@font#1}\nolimits}}}
|
||||
\newcommand{\id}[1]{%
|
||||
\ensuremath{\mathit{\text@hyphens#1}}}
|
||||
|
||||
% Commands for typesetting object attributes. All of these commands
|
||||
% may be used either in or out of math mode.
|
||||
|
||||
% Definitions:
|
||||
% An i-string is a string that you would use in an \id command,
|
||||
% typically one or more non-Greek letters, numerals, or dashes.
|
||||
% An x-string is a string that you would not use in an \id command,
|
||||
% typically because it has a subscript or one or more Greek letters.
|
||||
% A single non-Greek letter can be either an i-string or an x-string.
|
||||
|
||||
% Most of the time, we use the \attrib command, which assumes that its
|
||||
% first argument, the object name, is an x-string and its second
|
||||
% argument, the attribute name, is an i-string. Examples of the
|
||||
% \attrib command: \attrib{A}{length}, \attrib{x}{next},
|
||||
% \attrib{\rho}{next-item}. \attrib is just a direct call to the
|
||||
% \attribxi macro.
|
||||
|
||||
% The four macros \attribxi, \attribxx, \attribix, and \attribii each
|
||||
% take two arguments. The two letters at the end of the macro name
|
||||
% determine, in order, how each argument is treated. x indicates that
|
||||
% the argument should be an x-string, and i indicates that the
|
||||
% argument should be an i-string.
|
||||
|
||||
% Because we use a single letter to indicate most objects and a string
|
||||
% of one or more letters to indicate most attribute names, \attribxi
|
||||
% is the most common macro we use. That's why \attrib is just a
|
||||
% direct call to \attribxi.
|
||||
|
||||
% Use \attribxx when the object name is an x-string and the object
|
||||
% name is also an x-string, for example, when the attribute name has a
|
||||
% subscript: \attribxx{x}{c_i} or \attrib{x}{\id{key}_i}. Another
|
||||
% time you would use \attribxx is when the attribute name is a Greek
|
||||
% letter: \attrib{v}{\pi}.
|
||||
|
||||
% When the object name has more than one letter, it is usually an
|
||||
% i-string. In this case, use \attribii or \attribix, depending on
|
||||
% the attribute name: \attribii{item}{key}, \attribii{prev-item}{np},
|
||||
% \attribix{item}{\pi}.
|
||||
|
||||
% The \attribb, \attribbb, \attribbbb, and \attribbxxi macros are for
|
||||
% cascading attributes. They just call the appropriate \attribxi and
|
||||
% \attribxx commands. For one level of cascading, use \attribb:
|
||||
% \attribb{x}{left}{size}. For two levels, use \attribbb:
|
||||
% \attribbb{y}{p}{left}{size}. For three levels, use \attribbbb (but
|
||||
% no examples in the book use this macro). The \attribbxxi macro is
|
||||
% for one level of cascading where the first attribute given is an
|
||||
% x-string: \attribbxxi{x}{c_i}{n}.
|
||||
|
||||
% When the object is an edge of a graph, specified by two vertices,
|
||||
% use \attribe or \attribex: \attribe{u}{v}{f}, \attribex{u}{v}{c'}.
|
||||
|
||||
\newcommand{\attribxi}[2]{\ensuremath{#1.\hspace*{1pt}\id{#2}}}
|
||||
\newcommand{\attribxx}[2]{\ensuremath{#1.\hspace*{1pt}#2}}
|
||||
\newcommand{\attribix}[2]{\ensuremath{\id{#1}\hspace*{1pt}.#2}}
|
||||
\newcommand{\attribii}[2]{\ensuremath{\id{#1}\hspace*{1pt}.\hspace*{1pt}\id{#2}}}
|
||||
\newcommand{\attrib}[2]{\attribxi{#1}{#2}}
|
||||
\newcommand{\attribe}[3]{\attribxi{(#1,#2)}{#3}}
|
||||
\newcommand{\attribex}[3]{\attribxx{(#1,#2)}{#3}}
|
||||
\newcommand{\attribb}[3]{\attribxi{\attribxi{#1}{#2}}{#3}}
|
||||
\newcommand{\attribbb}[4]{\attribxi{\attribb{#1}{#2}{#3}}{#4}}
|
||||
\newcommand{\attribbbb}[5]{\attribxi{\attribbb{#1}{#2}{#3}{#4}}{#5}}
|
||||
\newcommand{\attribbxxi}[3]{\attribxi{\attribxx{#1}{#2}}{#3}}
|
||||
|
||||
% Command for typesetting subarray ranges.
|
||||
\newcommand{\twodots}{\mathinner{\ldotp\ldotp}}
|
||||
|
||||
% The codelinenumber counter counts the current line number.
|
||||
\newcounter{codelinenumber}
|
||||
|
||||
% The indent counter keeps track of the current indentation level.
|
||||
\newcounter{indent}
|
||||
|
||||
% The \iffirstcodeline command tells us whether we are about to
|
||||
% produce the first line other than the procedure declaration.
|
||||
\newif\iffirstcodeline\firstcodelinetrue
|
||||
|
||||
% The \zeroli command makes it so that we're about to produce the
|
||||
% first line other than the procedure declaration.
|
||||
\newcommand{\zeroli}{\setcounter{codelinenumber}{0}%
|
||||
\setcounter{indent}{0}%
|
||||
\firstcodelinetrue}
|
||||
|
||||
% \digitwidth gives the width of a single digit. All digits are the
|
||||
% same width. We'll need this amount to do the right thing for line
|
||||
% numbers.
|
||||
\newlength{\digitwidth}
|
||||
\settowidth{\digitwidth}{0}
|
||||
|
||||
% The \li command bumps the counter, outputs it, and skips some space
|
||||
% A \label cmd for a given numbered line is allowed to appear after the
|
||||
% \\, as in
|
||||
% \li $x\gets y$ \label{li:assign-x}
|
||||
% But if \li merely set \@currentlabel in the usual way via
|
||||
% \refstepcounter, the value of \@currentlabel does not persist outside
|
||||
% the current cell. Solution: use an additional, global variable
|
||||
% \@lilabel.
|
||||
|
||||
% THC: This next command is magic to me. I didn't write it.
|
||||
\def\@startline{\global\@curtabmar\@nxttabmar\relax
|
||||
\global\@curtab\@curtabmar\setbox\@curline\hbox
|
||||
{}\@startfield\strut}
|
||||
|
||||
% \code@init is run at the beginning of a codebox environment.
|
||||
\def\code@init{%
|
||||
\zeroli% producing the first line
|
||||
\setlength{\tabbingsep}{1em}% distance between numbers and code
|
||||
% Initialize \@lilabel to allow a pageref \label cmd at the beginning
|
||||
% of the codebox
|
||||
\global\let\@lilabel\@currentlabel
|
||||
\def\@currentlabel{\@lilabel}%
|
||||
}
|
||||
|
||||
% When we make a codebox, we save the code part into a box before
|
||||
% printing it. We do not actually print the code until we know how many
|
||||
% line numbers there are.
|
||||
\newsavebox{\savecode}
|
||||
|
||||
% The \ifprocname command tells us whether this procedure has been
|
||||
% given a name yet.
|
||||
\newif\ifprocname\procnamefalse
|
||||
|
||||
% Assume that the width of the codebox is the width of the text, minus
|
||||
% the width of 2 digits. We'll correct for that later.
|
||||
\newlength{\codeboxwidth}
|
||||
\setlength{\codeboxwidth}{\linewidth} % Thanks, David Etherington!
|
||||
\addtolength{\codeboxwidth}{-2\digitwidth}
|
||||
|
||||
% The "codebox" environment produces an unbreakable section of code
|
||||
\newenvironment{codebox}{%
|
||||
\global\procnamefalse% this proc hasn't been given a name yet
|
||||
\code@init% set up for first line
|
||||
\begin{lrbox}{\savecode}% save the code into a box
|
||||
\begin{minipage}[t]{\codeboxwidth}% it'll be a minipage
|
||||
% Set up the tab stops
|
||||
\def\codeindent{\textbf{else} }%
|
||||
\begin{tabbing}%
|
||||
99\=\codeindent\=\codeindent\=\codeindent\=\codeindent\=\codeindent\=\codeindent\=\codeindent\=codeindent\=codeindent\=\+\kill%
|
||||
}{%
|
||||
% Here's what's run at the end of a codebox environment. Start by
|
||||
% making sure that we have ended at indent level 0. Otherwise, print a
|
||||
% warning.
|
||||
\ifnum\value{indent}=0\else\typeout{Warning: Indentation ends at level \theindent\space in codebox on page \thepage.}\fi%
|
||||
\end{tabbing}\end{minipage}\end{lrbox}%
|
||||
\addtolength{\topsep}{0.5ex}% for the following trivlist
|
||||
\begin{trivlist}\item\parindent=0pt%
|
||||
% If there was a procedure name given, print it now but with a little
|
||||
% space below, and disallow a page break after the procedure name.
|
||||
\@nobreaktrue%
|
||||
\ifprocname\saveprocname\rule[-1.25ex]{0pt}{0pt}\\ \fi%
|
||||
% Put in the right amount of space, depending on whether we reached
|
||||
% double digits in the line numbers.
|
||||
\ifnum\value{codelinenumber}>9\hspace*{2\digitwidth}\else\hspace*{1\digitwidth}\fi%
|
||||
% Now print the code
|
||||
\usebox{\savecode}\end{trivlist}%
|
||||
\addtolength{\topsep}{-0.5ex}\global\procnamefalse}
|
||||
|
||||
% Use the \Procname macro to give the name of the procedure.
|
||||
\newcommand{\Procname}[1]{\global\def\saveprocname{#1}\global\procnametrue}
|
||||
|
||||
\newcounter{thisindent} % counter for recursive indenting code
|
||||
\newcommand{\Indent}{\setcounter{thisindent}{\value{indent}}\putindents}
|
||||
% \putindents is a recursive macro that indents a number of times given
|
||||
% by the counter thisindent.
|
||||
\newcommand{\putindents}{\ifnum\value{thisindent}>0\>\addtocounter{thisindent}{-1}\putindents\fi}
|
||||
|
||||
% For typesetting any keyword in the main text.
|
||||
\newcommand{\kw}[1]{\textbf{#1}}
|
||||
|
||||
% Override the 'gets' symbol.
|
||||
\def\gets{\mathrel{\hspace{1pt}=\hspace{1pt}}}
|
||||
\newcommand{\isequal}{\mathrel{\scalebox{0.8}[1]{=}\hspace*{1pt}\scalebox{0.8}[1]{=}}}
|
||||
|
||||
% All of our favorite keywords.
|
||||
\newcommand{\For}{\textbf{for} }
|
||||
\newcommand{\To}{\ifmmode\ \textrm{\textbf{to}}\ \else\textbf{to}\ \fi}
|
||||
\newcommand{\By}{\ifmmode\ \textrm{\textbf{by}}\ \else\textbf{by}\ \fi}
|
||||
\newcommand{\Downto}{\ifmmode\ \textrm{\textbf{downto}}\ \else\textbf{downto}\ \fi}
|
||||
\newcommand{\While}{\textbf{while} }
|
||||
\newcommand{\Repeat}{\textbf{repeat}\>\addtocounter{indent}{1}}
|
||||
\newcommand{\Until}{\kill\addtocounter{indent}{-1}\liprint\textbf{until} }
|
||||
\newcommand{\If}{\textbf{if} }
|
||||
\newcommand{\Then}{\>\addtocounter{indent}{1}}
|
||||
\newcommand{\Else}{\kill\addtocounter{indent}{-1}\liprint\textbf{else}\>\addtocounter{indent}{1}}
|
||||
\newcommand{\End}{\addtocounter{indent}{-1}}
|
||||
\newcommand{\ElseIf}{\kill\addtocounter{indent}{-1}\liprint\textbf{elseif} }
|
||||
\newcommand{\ElseNoIf}{\kill\addtocounter{indent}{-1}\liprint\textbf{else} \addtocounter{indent}{1}}
|
||||
\newcommand{\Do}{\>\addtocounter{indent}{1}}
|
||||
\newcommand{\Return}{\textbf{return} }
|
||||
\newcommand{\CommentSymbol}{\texttt{\textbf{/\hspace*{-0.3em}/}}}
|
||||
\newcommand{\Comment}{\CommentSymbol\ }
|
||||
\newcommand{\RComment}{\`\CommentSymbol\ }
|
||||
\newcommand{\Goto}{\textbf{goto} }
|
||||
\newcommand{\Error}{\textbf{error} } % optionally followed by string argument
|
||||
\newcommand{\EndTest}{\textbf{:}}
|
||||
\newcommand{\Spawn}{\ifmmode\textbf{spawn}\ \else\textbf{spawn} \fi}
|
||||
\newcommand{\Sync}{\textbf{sync}}
|
||||
\newcommand{\Parfor}{\textbf{parallel for} }
|
||||
|
||||
% Indent the next line one level more
|
||||
\newcommand{\Indentmore}{\addtocounter{indent}{1}}
|
||||
|
||||
\newif\ifnumberedline
|
||||
\numberedlinetrue
|
||||
|
||||
% The \li command starts a new numbered line.
|
||||
\newcommand{\li}{\global\numberedlinetrue%
|
||||
\iffirstcodeline\global\firstcodelinefalse\else\\ \fi
|
||||
\stepcounter{codelinenumber}%
|
||||
\liprint}
|
||||
|
||||
% The \lispace command starts a new numbered line with a little extra
|
||||
% space above, given by the argument.
|
||||
\newcommand{\lispace}[1]{\iffirstcodeline\global\firstcodelinefalse\else\\[#1] \fi
|
||||
\stepcounter{codelinenumber}%
|
||||
\liprint}
|
||||
|
||||
% \liprint actually prints the line number and sets up the indentation.
|
||||
\newcommand{\liprint}{\protected@xdef\@lilabel{\thecodelinenumber}%
|
||||
\ifnumberedline\thecodelinenumber\fi\'\Indent%
|
||||
}
|
||||
|
||||
\providecommand{\numref}[1]{%
|
||||
\@ifundefined{r@#1}{000}{%
|
||||
\expandafter\expandafter\expandafter\@firstoftwo
|
||||
\csname r@#1\endcsname
|
||||
}%
|
||||
}
|
||||
|
||||
% \setlinenumber sets the line number to its argument
|
||||
\newcommand{\setlinenumber}[1]{\setcounter{codelinenumber}{\numref{#1}}%
|
||||
\addtocounter{codelinenumber}{-1}}
|
||||
% \setlinenumberplus sets the line number to its first argument plus its
|
||||
% second argument.
|
||||
\newcommand{\setlinenumberplus}[2]{\setcounter{codelinenumber}{\numref{#1}}%
|
||||
\addtocounter{codelinenumber}{-1}\addtocounter{codelinenumber}{#2}}
|
||||
|
||||
% The \zi command starts a new unnumbered line.
|
||||
\newcommand{\zi}{\global\numberedlinefalse%
|
||||
\iffirstcodeline\global\firstcodelinefalse\else\\ \fi
|
||||
\liprint}
|
||||
|
||||
% Temporarily make all lines indented so that they start at the end of
|
||||
% a given text.
|
||||
\newcommand{\Startalign}[1]{\\ \pushtabs\FakeIndent#1\=\kill}
|
||||
\newcommand{\Stopalign}{\poptabs}
|
||||
\newcommand{\FakeIndent}{\setcounter{thisindent}{\value{indent}}\putfakeindents}
|
||||
\newcommand{\putfakeindents}{\ifnum\value{thisindent}>0\textbf{else }\addtocounter{thisindent}{-1}\putfakeindents\fi}
|
||||
|
||||
\endinput
|
||||
23
Foundations/overview/insertion_sort.py
Normal file
23
Foundations/overview/insertion_sort.py
Normal file
@@ -0,0 +1,23 @@
|
||||
__author__ = 'pezy'
|
||||
|
||||
|
||||
def insertion_sort(lst):
|
||||
for j in range(1, len(lst)):
|
||||
key = lst[j]
|
||||
i = j - 1
|
||||
while i >= 0 and lst[i] > key:
|
||||
lst[i + 1] = lst[i]
|
||||
i -= 1
|
||||
lst[i + 1] = key
|
||||
return lst
|
||||
|
||||
|
||||
def insertion_sort_non_increasing(lst):
|
||||
for j in range(1, len(lst)):
|
||||
key = lst[j]
|
||||
i = j - 1
|
||||
while i >= 0 and lst[i] < key:
|
||||
lst[i + 1] = lst[i]
|
||||
i -= 1
|
||||
lst[i + 1] = key
|
||||
return lst
|
||||
21
Foundations/overview/insertion_sort_unittest.py
Normal file
21
Foundations/overview/insertion_sort_unittest.py
Normal file
@@ -0,0 +1,21 @@
|
||||
__author__ = 'pezy'
|
||||
|
||||
import unittest
|
||||
from insertion_sort import *
|
||||
|
||||
|
||||
# case from @Mooophy
|
||||
class InsertionSortTest(unittest.TestCase):
|
||||
def test_insertion_sort(self):
|
||||
self.assertEqual(insertion_sort([5, 2, 4, 6, 1, 3]), [1, 2, 3, 4, 5, 6])
|
||||
self.assertEqual(insertion_sort([5]), [5])
|
||||
self.assertEqual(insertion_sort([]), [])
|
||||
self.assertEqual(insertion_sort([1, 5, 2, 1, 6]), [1, 1, 2, 5, 6])
|
||||
|
||||
def test_insertion_sort_non_increasing(self):
|
||||
self.assertEqual(insertion_sort_non_increasing([1, 5, 2, 1, 6]), [6, 5, 2, 1, 1])
|
||||
self.assertEqual(insertion_sort_non_increasing([]), [])
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
BIN
Foundations/overview/linear-search.pdf
Normal file
BIN
Foundations/overview/linear-search.pdf
Normal file
Binary file not shown.
17
Foundations/overview/linear-search.tex
Normal file
17
Foundations/overview/linear-search.tex
Normal file
@@ -0,0 +1,17 @@
|
||||
\documentclass{article}
|
||||
\usepackage{clrscode3e}
|
||||
\begin{document}
|
||||
\title{2.1-3}
|
||||
\author{pezy}
|
||||
\maketitle
|
||||
\begin{codebox}
|
||||
\Procname{$\proc{Linear-Search}(A, v)$}
|
||||
\li \For $j \gets 1$ \To $\attrib{A}{length}$
|
||||
\li \Do
|
||||
\If $A[j] \isequal v$
|
||||
\li \Then \Return $j$
|
||||
\li \Else
|
||||
\Return \const{nil}
|
||||
\End
|
||||
\end{codebox}
|
||||
\end{document}
|
||||
BIN
Foundations/overview/nonincreasing-insertion-sort.pdf
Normal file
BIN
Foundations/overview/nonincreasing-insertion-sort.pdf
Normal file
Binary file not shown.
24
Foundations/overview/nonincreasing-insertion-sort.tex
Normal file
24
Foundations/overview/nonincreasing-insertion-sort.tex
Normal file
@@ -0,0 +1,24 @@
|
||||
\documentclass{article}
|
||||
\usepackage{clrscode3e}
|
||||
\begin{document}
|
||||
\title{2.1-2}
|
||||
\author{pezy}
|
||||
\maketitle
|
||||
\begin{codebox}
|
||||
\Procname{$\proc{Nonincreasing-Insertion-Sort}(A)$}
|
||||
\li \For $j \gets 2$ \To $\attrib{A}{length}$
|
||||
\li \Do
|
||||
$\id{key} \gets A[j]$
|
||||
\li \Comment Insert $A[j]$ into the sorted sequence $A[1 \twodots j-1]$.
|
||||
\li $i \gets j-1$
|
||||
\li \While $i > 0$ and $A[i] < \id{key}$
|
||||
\li \Do
|
||||
$A[i+1] \gets A[i]$
|
||||
\li $i \gets i-1$
|
||||
\End
|
||||
\li $A[i+1] \gets \id{key}$
|
||||
\End
|
||||
\end{codebox}
|
||||
\end{document}
|
||||
|
||||
|
||||
Reference in New Issue
Block a user