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Partition function P: Difference between revisions
→{{header|REXX}}: added a faster 2nd version.
(→{{header|REXX}}: added a faster 2nd version.) |
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=={{header|REXX}}==
=== version 1 ===
<lang rexx>/*REXX program calculates and displays a specific value (or a range of) partitionsP(N).*/
numeric digits 1000 /*able to handle some ginormous numbers*/
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if hi=='' | hi=="," then hi= lo /* " " " " " " */
@.= 0; @.0= 1; @.1= 1; @.2= 2; @.3= 3; @.4= 5 /*assign default value and low values. */
!.= @.; !.1= 1; !.3= 1; !.5= 1; !.7= 1; !.9= 1 /*assign default value and even digits.*/
w= length( commas(hi) ) /*W: is used for aligning the index. */
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commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
partP: procedure expose @. !.; parse arg n
if @.n\==0 then return @.n /*Is it already computed? Return it. */
#= 0 /*initialize part P number.*/
do k=1 for n; z= n - (k*3 - 1) * k % 2
if z<0 then leave /*Is Z negative? Then leave.*/
if @.z==0 then x= partP(z) /*use recursion if not known.*/
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else #= # - (x + y) /*Even? " subtract " " " */
end /*k*/
@.n= #;
{{out|output|text= when using the input of: <tt> 6666 </tt>}}
<pre>
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66,666 931,283,431,869,095,717,238,416,063,534,148,471,363,928,685,651,267,074,563,360,050,977,549,251,436,058,076,515,262,033,789,845,457,356,081,278,451,246,751,375,974,038,318,319,810,923,102,769,109,446,980,055,567,090,089,060,954,748,065,131,666,952,830,623,286,286,824,837,240,058,805,177,319,865,230,913,417,587,625,830,803,675,380,262,765,598,632,742,903,192,085,254,824,621
</pre>
=== version 2 ===
This REXX version is about '''25%''' faster than REXX version 1.
The biggest part of the improvement was using the expression '''k+k+k''' instead of '''k*3'''.
<lang rexx>/*REXX program calculates and displays a specific value (or a range of) partitionsP(N).*/
numeric digits 1000 /*able to handle some ginormous numbers*/
parse arg lo hi . /*obtain optional arguments from the CL*/
if lo=='' | lo=="," then lo= 0 /*Not specified? Then use the default.*/
if hi=='' | hi=="," then hi= lo /* " " " " " " */
@.= 0; @.0= 1; @.1= 1; @.2= 2; @.3= 3; @.4= 5 /*default values for some low numbers. */
!.= @.; !.1= 1; !.3= 1; !.5= 1; !.7= 1; !.9= 1 /* " " " all the 1─digit #s*/
w= length( commas(hi) ) /*W: is used for aligning the index. */
do j=lo to hi /*compute a range of partitionsP. */
say right( commas(j), w) ' ' commas( partP(j) )
end /*j*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
partP: procedure expose @. !.; parse arg n /*obtain number (index) for computation*/
if @.n\==0 then return @.n /*Is it already computed? Return it. */
#= 0 /*initialize part P number.*/
do k=1 for n; z= n - (k+k+k - 1) * k % 2 /*compute the partition P num*/
if z<0 then leave /*Is Z negative? Then leave.*/
if @.z==0 then x= partP(z) /*use recursion if not known.*/
else x= @.z /*use the pre─computed number*/
z= z - k /*subtract index (K) from Z. */
if z<0 then y= 0 /*Is Z negative? Then set Y=0*/
else if @.z==0 then y= partP(z) /*use recursion if not known.*/
else y= @.z /*use the pre─computed number*/
parse var k '' -1 _ /*obtain K's last decimal dig*/
if !._ then #= # + x + y /*Odd? Then sum X and Y.*/
else #= # - (x + y) /*Even? " subtract " " " */
end /*k*/
@.n= #; return # /*define and return partitionsP of N. */</lang>
{{out|output|text= is identical to the 1<sup>st</sup> REXX version.}} <br><br>
=={{header|Rust}}==
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