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Full Discussion: recursive function
Top Forums Programming recursive function Post 302094485 by bebop1111116 on Saturday 28th of October 2006 10:21:56 AM
Old 10-28-2006
recursive function

Hi everyone, i need your input on this. We can express a function recursivly like this
Code:
A(n) = (2                                n = 0
          5                                 n = 1
          A(n − 1) + A(n − 2) % 47 n > 1

How would i go about constructing a recursive function for this? for instance lets say i wanted to solve for A(20). And what do you think i should do to make an iterative function? Thanks.
 

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CSS::DOM::PropertyParser(3pm)				User Contributed Perl Documentation			     CSS::DOM::PropertyParser(3pm)

NAME
CSS::DOM::PropertyParser - Parser for CSS property values VERSION
Version 0.14 SYNOPSIS
use CSS::DOM::PropertyParser; $spec = new CSS::DOM::PropertyParser; # empty # OR $spec = $CSS::DOM::PropertyParser::Default->clone; $spec->add_property( overflow => { format => 'visible|hidden|scroll|auto', default => 'visible', inherit => 0, } ); $hashref = $spec->get_property('overflow'); $hashref = $spec->delete_property('overflow'); @names = $spec->property_names; DESCRIPTION
Objects of this class provide lists of supported properties for CSS::DOM style sheets. They also describe the syntax and parsing of those properties' values. Some CSS properties simply have their own values (e.g., overflow); some are abbreviated forms of several other properties (e.g., font). These are referred to in this documentation as 'simple' and 'shorthand' properties. CONSTRUCTOR
"$spec = new CSS::DOM::PropertyParser" returns an object that does not recognise any properties, to which you can add your own properties. There are two parser objects that come with this module. These are $CSS::DOM::PropertyParser::CSS21, which contains all of CSS 2.1, and $CSS::DOM::PropertyParser::Default, which is currently identical to the former, but to which parts of CSS 3 which eventually be added. If one of the default specs will do, you don't need a constructor. Simply pass it to the CSS::DOM constructor. If you want to modify it, clone it first, using the "clone" method (as shown in the "SYNOPSIS"). It is often convenient to clone the $Default spec and delete those properties that are not supported. METHODS
clone Returns a deep clone of the object. (It's deep so that you can modify the hashes/arrays inside it without modifying the original.) add_property ( $name, \%spec ) Adds the specification for the named property. See "HOW INDIVIDUAL PROPERTIES ARE SPECIFIED", below. get_property ( $name ) Returns the hashref passed to the previous method. delete_property ( $name ) Deletes the property and returns the hash ref. property_names Returns a list of the names of supported properties. subproperty_names ( $name ) Returns a list of the names of $name's sub-properties if it is a shorthand property. match Currently for internal use only. See the source code for documentation. Use at your own risk. HOW INDIVIDUAL PROPERTIES ARE SPECIFIED
Before you read this the first time, look at the "Example" below, and then come back and use this for reference. The specification for an individual property is a hash ref. There are several keys that each hash ref can have: format This is set to a string that describes the format of the property. The syntax used is based on the CSS 2.1 spec, but is not exactly the same. Unlike regular expressions, these formats are applied to properties on a token-by-token basis, not one character at a time. (This means that "100|200" cannot be written as "[1|2]00", as that would mean "1 00 | 2 00".) Whitespace is ignored in the format and in the CSS property except as a token separator. There are several metachars (in order of precedence): [...] grouping (like (?:...) ) (...) capturing group (just like a regexp) ? optional * zero or more + one or more || alternates that can come in any order and are optional, but at least one must be specified (the order will be retained if possible) | alternates, exactly one of which is required In addition, the following datatypes can be specified in angle brackets: <angle> A number with a 'deg', 'rad' or 'grad' suffix <attr> attr(...) <colour> (You can omit the 'u' if you want to.) One of CSS's predefined colour or system colour names, or a # followed by 3 or 6 hex digits, or the 'rgb(...)' format (rgba is supported, too) <counter> counter(...) <frequency> A unit of Hz or kHz <identifier> An identifier token <integer> An integer (really?!) <length> Number followed by a length unit (em, ex, px, in, cm, mm, pt, pc) <number> A number token <percentage> Number followed by % <shape> rect(...) <string> A string token <str/words> A sequence of identifiers or a single string (e.g., a font name) <time> A unit of seconds or milliseconds <url> A URL token The format for a shorthand property can contain the name of a sub-property in single ASCII quotes. All other characters are understood verbatim. It is not necessary to include the word 'inherit' in the format, since every property supports that. "<counter>" makes use of the specification for the list-style-type property. So if you modify the latter, it will affect "<counter>" as well. default The default value. This only applies to simple properties. inherit Whether the property is inherited. special_values A hash ref of values that are replaced with other values (e.g., "caption => '13px sans-serif'". The keys are lowercase identifier names. This feature only applies to single identifiers. In fact, it exists solely for the font property's use. list Set to true if the property is a list of values. The capturing parentheses in the format determine the individual values of the list. This applies to simple properties only. properties For a shorthand property, list the sub-properties here. The keys are the property names. The values are array refs. The elements within the arrays are numbers indicating which captures in the format are to be used for the sub-property's value. They are tried one after the other. Whichever is the first that matches (null matches not counting) is used. Sub-properties that are referenced in the "format" need not be listed here. serialise For shorthand properties only. Set this to a subroutine that serialises the property. It is called with a hashref of sub-properties as its sole argument. The values of the hash are blank for properties that are set to their initial values. This sub is only called when all sub-properties are set. Example our $CSS21 = new CSS::DOM::PropertyParser; my %properties = ( azimuth => { format => '<angle> | [ left-side | far-left | left | center-left | center | center-right | right | far-right | right-inside ] || behind | leftwards | rightwards', default => '0', inherit => 1, }, 'background-attachment' => { format => 'scroll | fixed', default => 'scroll', inherit => 0, }, 'background-color' => { format => '<colour>', default => 'transparent', inherit => 0, }, 'background-image' => { format => '<url> | none', default => 'none', inherit => 0, }, 'background-position' => { format => '[<percentage>|<length>|left|right] [<percentage>|<length>|top|center|bottom]? | [top|bottom] [left|center|right]? | center [<percentage>|<length>|left|right|top|bottom| center]?', default => '0% 0%', inherit => 0, }, 'background-repeat' => { format => 'repeat | repeat-x | repeat-y | no-repeat', default => 'repeat', inherit => 0, }, background => { format => "'background-color' || 'background-image' || 'background-repeat' || 'background-attachment' || 'background-position'", serialise => sub { my $p = shift; my $ret = ''; for(qw/ background-color background-image background-repeat background-attachment background-position /) { length $p->{$_} and $ret .= "$p->{$_} "; } chop $ret; length $ret ? $ret : 'none' }, }, 'border-collapse' => { format => 'collapse | separate', inherit => 1, default => 'separate', }, 'border-color' => { format => '(<colour>)[(<colour>)[(<colour>)(<colour>)?]?]?', properties => { 'border-top-color' => [1], 'border-right-color' => [2,1], 'border-bottom-color' => [3,1], 'border-left-color' => [4,2,1], }, serialise => sub { my $p = shift; my @vals = map $p->{"border-$_-color"}, qw/top right bottom left/; $vals[3] eq $vals[1] and pop @vals, $vals[2] eq $vals[0] and pop @vals, $vals[1] eq $vals[0] and pop @vals; return join " ", @vals; }, }, 'border-spacing' => { format => '<length> <length>?', default => '0', inherit => 1, }, 'border-style' => { format => "(none|hidden|dotted|dashed|solid|double|groove|ridge| inset|outset) [ (none|hidden|dotted|dashed|solid|double|groove| ridge|inset|outset) [ (none|hidden|dotted|dashed|solid|double|groove| ridge|inset|outset) (none|hidden|dotted|dashed|solid|double|groove| ridge|inset|outset)? ]? ]?", properties => { 'border-top-style' => [1], 'border-right-style' => [2,1], 'border-bottom-style' => [3,1], 'border-left-style' => [4,2,1], }, serialise => sub { my $p = shift; my @vals = map $p->{"border-$_-style"}, qw/top right bottom left/; $vals[3] eq $vals[1] and pop @vals, $vals[2] eq $vals[0] and pop @vals, $vals[1] eq $vals[0] and pop @vals; return join " ", map $_||'none', @vals; }, }, 'border-top' => { format => "'border-top-width' || 'border-top-style' || 'border-top-color'", serialise => sub { my $p = shift; my $ret = ''; for(qw/ width style color /) { length $p->{"border-top-$_"} and $ret .= $p->{"border-top-$_"}." "; } chop $ret; $ret }, }, 'border-right' => { format => "'border-right-width' || 'border-right-style' || 'border-right-color'", serialise => sub { my $p = shift; my $ret = ''; for(qw/ width style color /) { length $p->{"border-right-$_"} and $ret .= $p->{"border-right-$_"}." "; } chop $ret; $ret }, }, 'border-bottom' => { format => "'border-bottom-width' || 'border-bottom-style' || 'border-bottom-color'", serialise => sub { my $p = shift; my $ret = ''; for(qw/ width style color /) { length $p->{"border-bottom-$_"} and $ret .= $p->{"border-bottom-$_"}." "; } chop $ret; $ret }, }, 'border-left' => { format => "'border-left-width' || 'border-left-style' || 'border-left-color'", serialise => sub { my $p = shift; my $ret = ''; for(qw/ width style color /) { length $p->{"border-left-$_"} and $ret .= $p->{"border-left-$_"}." "; } chop $ret; $ret }, }, 'border-top-color' => { format => '<colour>', default => "", inherit => 0, }, 'border-right-color' => { format => '<colour>', default => "", inherit => 0, }, 'border-bottom-color' => { format => '<colour>', default => "", inherit => 0, }, 'border-left-color' => { format => '<colour>', default => "", inherit => 0, }, 'border-top-style' => { format => 'none|hidden|dotted|dashed|solid|double|groove|ridge| inset|outset', default => 'none', inherit => 0, }, 'border-right-style' => { format => 'none|hidden|dotted|dashed|solid|double|groove|ridge| inset|outset', default => 'none', inherit => 0, }, 'border-bottom-style' => { format => 'none|hidden|dotted|dashed|solid|double|groove|ridge| inset|outset', default => 'none', inherit => 0, }, 'border-left-style' => { format => 'none|hidden|dotted|dashed|solid|double|groove|ridge| inset|outset', default => 'none', inherit => 0, }, 'border-top-width' => { format => '<length>|thin|thick|medium', default => 'medium', inherit => 0, }, 'border-right-width' => { format => '<length>|thin|thick|medium', default => 'medium', inherit => 0, }, 'border-bottom-width' => { format => '<length>|thin|thick|medium', default => 'medium', inherit => 0, }, 'border-left-width' => { format => '<length>|thin|thick|medium', default => 'medium', inherit => 0, }, 'border-width' => { format => "(<length>|thin|thick|medium) [ (<length>|thin|thick|medium) [ (<length>|thin|thick|medium) (<length>|thin|thick|medium)? ]? ]?", properties => { 'border-top-width' => [1], 'border-right-width' => [2,1], 'border-bottom-width' => [3,1], 'border-left-width' => [4,2,1], }, serialise => sub { my $p = shift; my @vals = map $p->{"border-$_-width"}, qw/top right bottom left/; $vals[3] eq $vals[1] and pop @vals, $vals[2] eq $vals[0] and pop @vals, $vals[1] eq $vals[0] and pop @vals; return join " ", map length $_ ? $_ : 'medium', @vals; }, }, border => { format => "(<length>|thin|thick|medium) || (none|hidden|dotted|dashed|solid|double|groove|ridge| inset|outset) || (<colour>)", properties => { 'border-top-width' => [1], 'border-right-width' => [1], 'border-bottom-width' => [1], 'border-left-width' => [1], 'border-top-style' => [2], 'border-right-style' => [2], 'border-bottom-style' => [2], 'border-left-style' => [2], 'border-top-color' => [3], 'border-right-color' => [3], 'border-bottom-color' => [3], 'border-left-color' => [3], }, serialise => sub { my $p = shift; my $ret = ''; for(qw/ width style color /) { my $temp = $p->{"border-top-$_"}; for my $side(qw/ right bottom left /) { $temp eq $p->{"border-$side-$_"} or return ""; } length $temp and $ret .= "$temp "; } chop $ret; $ret }, }, bottom => { format => '<length>|<percentage>|auto', default => 'auto', inherit => 0, }, 'caption-side' => { format => 'top|bottom', default => 'top', inherit => 1, }, clear => { format => 'none|left|right|both', default => 'none', inherit => 0, }, clip => { format => '<shape>|auto', default => 'auto', inherit => 0, }, color => { format => '<colour>', default => 'rgba(0,0,0,1)', inherit => 1, }, content => { format => '( normal|none|open-quote|close-quote|no-open-quote| no-close-quote|<string>|<url>|<counter>|<attr> )+', default => 'normal', inherit => 0, list => 1, }, 'counter-increment' => { format => '[(<identifier>) (<integer>)? ]+ | none', default => 'none', inherit => 0, list => 1, }, 'counter-reset' => { format => '[(<identifier>) (<integer>)? ]+ | none', default => 'none', inherit => 0, list => 1, }, 'cue-after' => { format => '<url>|none', default => 'none', inherit => 0, }, 'cue-before' => { format => '<url>|none', default => 'none', inherit => 0, }, cue =>{ format => '(<url>|none) (<url>|none)?', properties => { 'cue-before' => [1], 'cue-after' => [2,1], }, serialise => sub { my $p = shift; my @vals = @$p{"cue-before", "cue-after"}; $vals[1] eq $vals[0] and pop @vals; return join " ", map length $_ ? $_ : 'none', @vals; }, }, cursor => { format => '[(<url>) ,]* (auto|crosshair|default|pointer|move|e-resize| ne-resize|nw-resize|n-resize|se-resize|sw-resize| s-resize|w-resize|text|wait|help|progress)', default => 'auto', inherit => 1, list => 1, }, direction => { format => 'ltr|rtl', default => 'ltr', inherit => 1, }, display => { format => 'inline|block|list-item|run-in|inline-block|table| inline-table|table-row-group|table-header-group| table-footer-group|table-row|table-column-group| table-column|table-cell|table-caption|none', default => 'inline', inherit => 0, }, elevation => { format => '<angle>|below|level|above|higher|lower', default => '0', inherit => 1, }, 'empty-cells' => { format => 'show|hide', default => 'show', inherit => 1, }, float => { format => 'left|right|none', default => 'none', inherit => 0, }, 'font-family' => { # aka typeface format => '(serif|sans-serif|cursive|fantasy|monospace| <str/words>) [,(serif|sans-serif|cursive|fantasy|monospace| <str/words>)]*', default => 'Times, serif', inherit => 1, list => 1, }, 'font-size' => { format => 'xx-small|x-small|small|medium|large|x-large|xx-large| larger|smaller|<length>|<percentage>', default => 'medium', inherit => 1, }, 'font-style' => { format => 'normal|italic|oblique', default => 'normal', inherit => 1, }, 'font-variant' => { format => 'normal | small-caps', default => 'normal', inherit => 1, }, 'font-weight' => { format => 'normal|bold|bolder|lighter| 100|200|300|400|500|600|700|800|900', default => 'normal', inherit => 1, }, font => { format => "[ 'font-style' || 'font-variant' || 'font-weight' ]? 'font-size' [ / 'line-height' ]? 'font-family'", special_values => { caption => '13px Lucida Grande, sans-serif', icon => '13px Lucida Grande, sans-serif', menu => '13px Lucida Grande, sans-serif', 'message-box' => '13px Lucida Grande, sans-serif', 'small-caption' => '11px Lucida Grande, sans-serif', 'status-bar' => '10px Lucida Grande, sans-serif', }, serialise => sub { my $p = shift; my $ret = ''; for(qw/ style variant weight /) { length $p->{"font-$_"} and $ret .= $p->{"font-$_"}." "; } $ret .= length $p->{'font-size'} ? $p->{'font-size'} : 'medium'; $ret .= "/$p->{'line-height'}" if length $p->{'line-height'}; $ret .= " " . ($p->{'font-family'} || "Times, serif"); $ret }, }, height => { format => '<length>|<percentage>|auto', default => 'auto', inherit => 0, }, left => { format => '<length>|<percentage>|auto', default => 'auto', inherit => 0, }, 'letter-spacing' => { # aka tracking format => 'normal|<length>', default => 'normal', inherit => 1, }, 'line-height' => { # aka leading format => 'normal|<number>|<length>|<percentage>', default => "normal", inherit => 1, }, 'list-style-image' => { format => '<url>|none', default => 'none', inherit => 1, }, 'list-style-position' => { format => 'inside|outside', default => 'outside', inherit => 1, }, 'list-style-type' => { format => 'disc|circle|square|decimal|decimal-leading-zero| lower-roman|upper-roman|lower-greek|lower-latin| upper-latin|armenian|georgian|lower-alpha| upper-alpha', default => 'disc', inherit => 1, }, 'list-style' => { format => "'list-style-type'||'list-style-position'|| 'list-style-image'", serialise => sub { my $p = shift; my $ret = ''; for(qw/ type position image /) { $p->{"list-style-$_"} and $ret .= $p->{"list-style-$_"}." "; } chop $ret; $ret || 'disc' }, }, 'margin-right' => { format => '<length>|<percentage>|auto', default => '0', inherit => 0, }, 'margin-left' => { format => '<length>|<percentage>|auto', default => '0', inherit => 0, }, 'margin-top' => { format => '<length>|<percentage>|auto', default => '0', inherit => 0, }, 'margin-bottom' => { format => '<length>|<percentage>|auto', default => '0', inherit => 0, }, margin => { format => "(<length>|<percentage>|auto) [ (<length>|<percentage>|auto) [ (<length>|<percentage>|auto) (<length>|<percentage>|auto)? ]? ]?", properties => { 'margin-top' => [1], 'margin-right' => [2,1], 'margin-bottom' => [3,1], 'margin-left' => [4,2,1], }, serialise => sub { my $p = shift; my @vals = map $p->{"margin-$_"}, qw/top right bottom left/; $vals[3] eq $vals[1] and pop @vals, $vals[2] eq $vals[0] and pop @vals, $vals[1] eq $vals[0] and pop @vals; return join " ", map $_ || 0, @vals; }, }, 'max-height' => { format => '<length>|<percentage>|none', default => 'none', inherit => 0, }, 'max-width' => { format => '<length>|<percentage>|none', default => 'none', inherit => 0, }, 'min-height' => { format => '<length>|<percentage>|none', default => 'none', inherit => 0, }, 'min-width' => { format => '<length>|<percentage>|none', default => 'none', inherit => 0, }, orphans => { format => '<integer>', default => 2, inherit => 1, }, 'outline-color' => { format => '<colour>|invert', default => 'invert', inherit => 0, }, 'outline-style' => { format => 'none|hidden|dotted|dashed|solid|double|groove|ridge| inset|outset', default => 'none', inherit => 0, }, 'outline-width' => { format => '<length>|thin|thick|medium', default => 'medium', inherit => 0, }, outline => { format => "'outline-color'||'outline-style'||'outline-width'", serialise => sub { my $p = shift; my $ret = ''; for(qw/ color style width /) { length $p->{"outline-$_"} and $ret .= $p->{"outline-$_"}." "; } chop $ret; length $ret ? $ret : 'invert'; }, }, overflow => { format => 'visible|hidden|scroll|auto', default => 'visible', inherit => 0, }, 'padding-top' => { format => '<length>|<percentage>', default => 0, inherit => 0, }, 'padding-right' => { format => '<length>|<percentage>', default => 0, inherit => 0, }, 'padding-bottom' => { format => '<length>|<percentage>', default => 0, inherit => 0, }, 'padding-left' => { format => '<length>|<percentage>', default => 0, inherit => 0, }, padding => { format => "(<length>|<percentage>) [ (<length>|<percentage>) [ (<length>|<percentage>) (<length>|<percentage>)? ]? ]?", properties => { 'padding-top' => [1], 'padding-right' => [2,1], 'padding-bottom' => [3,1], 'padding-left' => [4,2,1], }, serialise => sub { my $p = shift; my @vals = map $p->{"padding-$_"}, qw/top right bottom left/; $vals[3] eq $vals[1] and pop @vals, $vals[2] eq $vals[0] and pop @vals, $vals[1] eq $vals[0] and pop @vals; return join " ", map $_ || 0, @vals; }, }, 'page-break-after' => { format => 'auto|always|avoid|left|right', default => 'auto', inherit => 0, }, 'page-break-before' => { format => 'auto|always|avoid|left|right', default => 'auto', inherit => 0, }, 'page-break-inside' => { format => 'avoid|auto', default => 'auto', inherit => 1, }, 'pause-after' => { format => '<time>|<percentage>', default => 0, inherit => 0, }, 'pause-before' => { format => '<time>|<percentage>', default => 0, inherit => 0, }, pause => { format => '(<time>|<percentage>)(<time>|<percentage>)?', properties => { 'pause-before' => [1], 'pause-after' => [2,1], } }, 'pitch-range' => { format => '<number>', default => 50, inherit => 1, }, pitch => { format => '<frequency>|x-low|low|medium|high|x-high', default => 'medium', inherit => 1, }, 'play-during' => { format => '<url> [ mix || repeat ]? | auto | none', default => 'auto', inherit => 0, }, position => { format => 'static|relative|absolute|fixed', default => 'relative', inherit => 0, }, quotes => { format => '[(<string>)(<string>)]+|none', default => 'none', inherit => 1, list => 1, }, richness => { format => '<number>', default => 50, inherit => 1, }, right => { format => '<length>|<percentage>|auto', default => 'auto', inherit => 0, }, 'speak-header' => { format => 'once|always', default => 'once', inherit => 1, }, 'speak-numeral' => { format => 'digits|continuous', default => 'continuous', inherit => 1, }, 'speak-punctuation' => { format => 'code|none', default => 'none', inherit => 1, }, speak => { format => 'normal|none|spell-out', default => 'normal', inherit => 1, }, 'speech-rate' => { format => '<number>|x-slow|slow|medium|fast|x-fast|faster|slower', default => 'medium', inherit => 1, }, stress => { format => '<number>', default => 50, inherit => 1, }, 'table-layout' => { format => 'auto|fixed', default => 'auto', inherit => 0, }, 'text-align' => { format => 'left|right|center|justify|auto', default => 'auto', inherit => 1, }, 'text-decoration' => { format => 'none | underline||overline||line-through||blink ', default => 'none', inherit => 0, }, 'text-indent' => { format => '<length>|<percentage>', default => 0, inherit => 1, }, 'text-transform' => { format => 'capitalize|uppercase|lowercase|none', default => 'none', inherit => 1, }, top => { format => '<length>|<percentage>|auto', default => 'auto', inherit => 0, }, 'unicode-bidi' => { format => 'normal|embed|bidi-override', default => 'normal', inherit => 0, }, 'vertical-align' => { format => 'baseline|sub|super|top|text-top|middle|bottom| text-bottom|<percentage>|<length>', default => 'baseline', inherit => 0, }, visibility => { format => 'visible|hidden|collapse', default => 'visible', inherit => 1, }, 'voice-family' => { format => '(male|female|child|<str/words>) [, (male|female|child|<str/words>) ]*', default => '', inherit => 1, list => 1, }, volume => { format => '<number>|<percentage>|silent|x-soft|soft|medium|loud| x-loud', default => 'medium', inherit => 1, }, 'white-space' => { format => 'normal|pre|nowrap|pre-wrap|pre-line', default => 'normal', inherit => 1, }, widows => { format => '<integer>', default => 2, inherit => 1, }, width => { format => '<length>|<percentage>|auto', default => 'auto', inherit => 0, }, 'word-spacing' => { format => 'normal|<length>', default => 'normal', inherit => 1, }, 'z-index' => { format => 'auto|<integer>', default => 'auto', inherit => 0, }, ); $CSS21->add_property( $_ => $properties{$_} ) for keys %properties; SEE ALSO
CSS::DOM perl v5.10.1 2010-12-10 CSS::DOM::PropertyParser(3pm)
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