Rosetta Code

Taxicab numbers: Difference between revisions

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Taxicab numbers (view source)

Revision as of 19:47, 11 October 2018

No change in size ,  5 years ago
m
→‎{{header|REXX}}: added more whitespace.
m (→‎{{header|Perl 6}}: Move some calculations out of hot loop, general speedup tweaks)
m (→‎{{header|REXX}}: added more whitespace.)
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Programming note:   to ensure that the taxicab numbers are in order, an extra 10% are generated.
<lang rexx>/*REXX program displays the specified first (lowest) taxicab numbers (for three ranges).*/
parse arg L.1 H.1 L.2 H.2 L.3 H.3 . /*obtain optional arguments from the CL*/
if L.1=='' | L.1=="," then L.1= 1 /*L1 is the low part of 1st range. */
if H.1=='' | H.1=="," then H.1= 25 /*H1 " " high " " " " */
Line 2,707:
if L.3=='' | L.3=="," then L.3=2000 /*L3 " " low " " 3rd " */
if H.3=='' | H.3=="," then H.3=2006 /*H3 " " high " " " " */
mx= max(L.1, H.1, LH.2, H.2,3) L.3, H.3) /*find how many taxicab numbers needed.*/
mx= mx + mx % 10 /*cushion; compensate for the triples.*/
ww= length(mx) * 3; w= ww % 2 /*widths used for formatting the output*/
numeric digits max(9, ww) /*prepare to use some larger numbers. */
@.=.; #= 0; @@. =0; @and= " ──and── " /*set some REXX vars and handy literals*/
$.= /* [↓] generate extra taxicab numbers.*/
do j=1 until #>=mx; C= j**3 /*taxicab numbers may not be in order. */
!.j= C /*use memoization for cube calculation.*/
do k=1 for j-1; s= C + !.k /*define a whole bunch of cube sums. */
if @.s==. then do; @.s= j; b.s= k /*Cube not defined? Then process it. */
iterate iterate /*define @.S and B.S≡sum of 2 cubes*/
end end /* [↑] define one cube sum at a time. */
has=@@.s /*has this number been defined before? */
if has then $.s=$.s @and U(j,' +')U(k) /* ◄─ build a display string. [↓] */
else $.s=right(s,ww) '───►' U(@.s," +")U(b.s) @and U(j,' +')U(k)
@@.s= 1 /*mark taxicab number as a sum of cubes*/
if has then iterate /*S is a triple (or sometimes better).*/
#= #+1; #.#=s s /*bump taxicab counter; define taxicab#*/
end /*k*/ /* [↑] build the cubes one─at─a─time. */
end /*j*/ /* [↑] complete with overage numbers. */
A.=
do k=1 for mx; _= #.k; A.k= $._ /*re─assign disjoint $. elements to A. */
end /*k*/
call Esort mx /*sort taxicab #s with an exchange sort*/
do grp=1 tofor 3; call tell L.grp, H.grp /*display the three grps of numbers. */
end /*grp*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
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U: return right(arg(1), w)'^3'arg(2) /*right─justify a number, append "^3" */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Esort: procedure expose A.; parse arg N; h=N N /*Esort when items have blanks.*/
do while h>1; h= h % 2
do i=1 for N-h; k=h + i; j= i
do forever; parse var A.k xk .; parse var A.j xj .; if xk>=xj then leave
_= A.j; A.j= A.k; A.k=_ _ /*swap two elements of A. array*/
if h>=j then leave; j= j - h; k= k - h
end /*forever*/
end /*i*/
end /*while h>1*/; return</lang>
{{out|output|text=&nbsp; when using the default inputinputs:}}
<pre>
1: 1729 ───► 10^3 + 9^3 ──and── 12^3 + 1^3
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