2016 Update

This commit is contained in:
Tina Müller 2016-12-05 22:15:40 +01:00
parent 948b86eafa
commit dcf5d15da3
7965 changed files with 139854 additions and 31002 deletions

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[[wp:Floyd's triangle|Floyd's triangle]] lists the natural numbers in a right triangle aligned to the left where
* the first row is just 1
[[wp:Floyd's triangle|Floyd's triangle]]   lists the natural numbers in a right triangle aligned to the left where
* the first row is   '''1'''     (unity)
* successive rows start towards the left with the next number followed by successive naturals listing one more number than the line above.
The first few lines of a Floyd triangle looks like this:
<pre> 1
<pre>
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15</pre>
11 12 13 14 15
</pre>
The task is to:
# Write a program to generate and display here the first n lines of a Floyd triangle.<br>(Use n=5 and n=14 rows).
# Ensure that when displayed in a monospace font, the numbers line up in vertical columns as shown and that only one space separates numbers of the last row.
;Task:
:# Write a program to generate and display here the first &nbsp; n &nbsp; lines of a Floyd triangle. <br>(Use &nbsp; n=5 &nbsp; and &nbsp; n=14 &nbsp; rows).
:# Ensure that when displayed in a mono-space font, the numbers line up in vertical columns as shown and that only one space separates numbers of the last row.
<br><br>

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triangle = (array) -> for n in array
console.log "#{n} rows:"
printMe = 1
printed = 0
row = 1
to_print = ""
while row <= n
cols = Math.ceil(Math.log10(n * (n - 1) / 2 + printed + 2.0))
p = ("" + printMe).length
while p++ <= cols
to_print += ' '
to_print += printMe + ' '
if ++printed == row
console.log to_print
to_print = ""
row++
printed = 0
printMe++
triangle [5, 14]

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fun main(args: Array<String>) = args.forEach { Triangle(it.toInt()) }
internal class Triangle(n: Int) {
init {
println("$n rows:")
var printMe = 1
var printed = 0
var row = 1
while (row <= n) {
val cols = Math.ceil(Math.log10(n * (n - 1) / 2 + printed + 2.0)).toInt()
print("%${cols}d ".format(printMe))
if (++printed == row) { println(); row++; printed = 0 }
printMe++
}
}
}

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floyd := proc(rows)
local num, numRows, numInRow, i, digits;
digits := Array([]);
for i to 2 do
num := 1;
numRows := 1;
numInRow := 1;
while numRows <= rows do
if i = 2 then
printf(cat("%", digits[numInRow], "a "), num);
end if;
num := num + 1;
if i = 1 and numRows = rows then
digits(numInRow) := StringTools[Length](convert(num-1, string));
end if;
if numInRow >= numRows then
if i = 2 then
printf("\n");
end if;
numInRow := 1;
numRows := numRows + 1;
else
numInRow := numInRow +1;
end if;
end do;
end do;
return NULL;
end proc:
floyd(5);
floyd(14);

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options replace format comments java crossref symbols binary
/*REXX program constructs & displays Floyd's triangle for any number of rows.*/
parse arg numRows .
if numRows == '' then numRows = 1 -- assume 1 row is not given
if numRows == '' then numRows = 1 -- assume 1 row if not given
maxVal = numRows * (numRows + 1) % 2 -- calculate the max value.
say 'displaying a' numRows "row Floyd's triangle:"
say

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constant @floyd = (1..*).rotor(1..*);

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constant @floyd = gather for 1..* -> $s { take [++$ xx $s] }

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constant @floyd = gather for 1..* -> $s { take [++$ xx $s] }
sub say-floyd($n) {
my @formats = @floyd[$n-1].map: {"%{.chars}s"}

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/*REXX pgm constructs & displays Floyd's triangle for any number of rows*/
parse arg rows .; if rows=='' then rows=5 /*Not specified? Use default*/
maxV = rows * (rows+1) % 2 /*calculate the max value. */
say 'displaying a' rows "row Floyd's triangle:"; say /*show header*/
#=1; do r=1 for rows; i=0; _= /*row by row.*/
do #=# for r; i=i+1 /*start a row*/
_ = _ right(#, length(maxV-rows+i)) /*build a row*/
end /*#*/ /*row is done*/
say substr(_,2) /*suppress the 1st leading blank,*/
end /*r*/ /* [↑] introduced by 1st abutt.*/
/*stick a fork in it, we're done.*/
/*REXX program constructs & displays Floyd's triangle for any number of specified rows.*/
parse arg rows .; if rows=='' then rows=5 /*Not specified? Then use the default.*/
mx=rows * (rows+1) % 2 /*calculate maximum value of any value.*/
say 'displaying a ' rows " row Floyd's triangle:" /*show header for the triangle.*/
say
#=1; do r=1 for rows; i=0; _= /*construct Floyd's triangle row by row*/
do #=# for r; i=i+1 /*start to construct a row of triangle.*/
_=_ right(#, length(mx-rows+i)) /*build a row of the Floyd's triangle. */
end /*#*/
say substr(_,2) /*remove 1st leading blank in the line,*/
end /*r*/ /* [↑] introduced by first abutment. */
/*stick a fork in it, we're all done. */

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/*REXX pgm displays Floyd's triangle for any number of rows in base 16.*/
parse arg rows .; if rows=='' then rows=6 /*Not specified? Use default*/
maxV = rows * (rows+1) % 2 /*calculate the max value. */
say 'displaying a' rows "row Floyd's triangle in base 16:"; say /*hdr*/
#=1; do r=1 for rows; i=0; _= /*row by row.*/
do #=# for r; i=i+1 /*start a row*/
_ = _ right(d2x(#), length(d2x(maxV - rows + i)))
end /*#*/ /* [↑] the triangle row is done.*/
say substr(_,2) /*suppress the 1st leading blank,*/
end /*r*/ /* [↑] introduced by 1st abutt.*/
/*stick a fork in it, we're done.*/
/*REXX program constructs & displays Floyd's triangle for any number of rows in base 16.*/
parse arg rows .; if rows=='' then rows=6 /*Not specified? Then use the default.*/
mx=rows * (rows+1) % 2 /*calculate maximum value of any value.*/
say 'displaying a ' rows " row Floyd's triangle in base 16:"; say /*show triangle hdr*/
#=1
do r=1 for rows; i=0; _= /*construct Floyd's triangle row by row*/
do #=# for r; i=i+1 /*start to construct a row of triangle.*/
_=_ right(d2x(#),length(d2x(mx-rows+i))) /*build a row of the Floyd's triangle. */
end /*#*/
say substr(_,2) /*remove 1st leading blank in the line,*/
end /*r*/ /* [↑] introduced by first abutment. */
/*stick a fork in it, we're all done. */

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/*REXX pgm displays Floyd's triangle for any # of rows up to base 90.*/
parse arg rows b .; if rows=='' then rows=5 /*Not given? Use default.*/
if b=='' then b=10 /*use base 10 if not given.*/
maxV = rows * (rows+1) % 2 /*calculate the max value. */
say 'displaying a' rows "row Floyd's triangle in base" b':'; say
#=1; do r=1 for rows; i=0; _= /*row by row.*/
do #=# for r; i=i+1 /*start a row*/
_ = _ right(base(#, b), length(base(maxV-rows+i, b)))
end /*#*/ /*row is done*/
say substr(_,2) /*suppress the 1st leading blank,*/
end /*r*/ /* [↑] introduced by 1st abutt.*/
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────BASE subroutine─────────────────────*/
base: procedure; parse arg x 1 ox,toB,inB /*get number, toBase, inBase*/
@abc='abcdefghijklmnopqrstuvwxyz' /*lowercase Latin alphabet. */
@abcU=@abc; upper @abcU /*go whole hog and extend 'em. */
@@@='0123456789'@abc || @abcU /*prefix 'em with numeric digits.*/
@@@=@@@'<>[]{}()?~!@#$%^&*_=|\/;:¢¬' /*add some special chars as well.*/
/*handles up to base 90, special chars must be viewable.*/
numeric digits 1000 /*what the hey, support gihugeics*/
maxB=length(@@@) /*max base (radix) supported here*/
if toB=='' | toB==',' then toB=10 /*if skipped, assume default (10)*/
if inB=='' | inB==',' then inB=10 /* " " " " " */
if inB<2 | inb>maxB then call erb 'inBase',inB /*bad boy inBase.*/
if toB<2 | tob>maxB then call erb 'toBase',toB /* " " toBase.*/
if x=='' then call erm /* " " number.*/
sigX=left(x,1); if pos(sigX,"-+")\==0 then x=substr(x,2) /*X has sign?*/
else sigX= /*no sign. */
#=0; do j=1 for length(x) /*convert X, base inB ──► base 10*/
_=substr(x, j, 1) /*pick off a numeral from X. */
v=pos(_, @@@) /*get the value of this "digit". */
if v==0 | v>inB then call erd x,j,inB /*illegal "digit"? */
#=#*inB+v-1 /*construct new num, dig by dig. */
end /*j*/
y=
do while #>=toB /*convert #, base 10 ──► base toB*/
y=substr(@@@, (#//toB)+1, 1)y /*construct the number for output*/
#=#%toB /*··· and whittle # down also. */
end /*while #≥toB*/
/*REXX program constructs/shows Floyd's triangle for any number of rows in any base ≤90.*/
parse arg rows radx . /*obtain optional arguments from the CL*/
if rows=='' | rows=="," then rows= 5 /*Not specified? Then use the default.*/
if radx=='' | radx=="," then radx=10 /* " " " " " " */
mx=rows * (rows+1) % 2 /*calculate maximum value of any value.*/
say 'displaying a ' rows " row Floyd's triangle in base" radx':'; say /*display hdr*/
#=1
do r=1 for rows; i=0; _= /*construct Floyd's triangle row by row*/
do #=# for r; i=i+1 /*start to construct a row of triangle.*/
_=_ right(base(#, radx), length(base(mx-rows+i, radx))) /*build triangle row*/
end /*#*/
say substr(_,2) /*remove 1st leading blank in the line,*/
end /*r*/ /* [↑] introduced by first abutment. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
base: procedure; parse arg x 1 ox,toB,inB /*obtain number, toBase, inBase. */
@abc='abcdefghijklmnopqrstuvwxyz' /*lowercase Latin alphabet. */
@abcU=@abc; upper @abcU /*go whole hog and extend 'em. */
@@@='0123456789'@abc || @abcU /*prefix 'em with numeric digits.*/
@@@=@@@'<>[]{}()?~!@#$%^&*_=|\/;:¢¬' /*add some special chars as well.*/
/*handles up to base 90, all chars must be viewable.*/
numeric digits 1000 /*what the hey, support gihugeics*/
mxB=length(@@@) /*max base (radix) supported here*/
if toB=='' | toB=="," then toB=10 /*if skipped, assume default (10)*/
if inB=='' | inB=="," then inB=10 /* " " " " " */
if inB<2 | inb>mxB then call erb 'inBase',inB /*invalid/illegal arg: inBase. */
if toB<2 | tob>mxB then call erb 'toBase',toB /* " " " toBase. */
if x=='' then call erm /* " " " number. */
sigX=left(x,1)
if pos(sigX,'-+')\==0 then x=substr(x,2) /*X number has a leading sign? */
else sigX= /* ··· no leading sign.*/
#=0; do j=1 for length(x) /*convert X, base inB ──► base 10*/
_=substr(x, j, 1) /*pick off a numeral from X. */
v=pos(_, @@@) /*get the value of this "digit". */
if v==0 | v>inB then call erd x,j,inB /*is this an illegal "numeral" ? */
#=#*inB+v-1 /*construct new num, dig by dig. */
end /*j*/
y=
do while # >= toB /*convert #, base 10 ──► base toB*/
y=substr(@@@, (#//toB)+1, 1)y /*construct the number for output*/
#=#%toB /* ··· and whittle # down also.*/
end /*while*/
y=sigX || substr(@@@, #+1, 1)y /*prepend the sign if it existed.*/
return y /*rturn the number in base toB. */
/*──────────────────────────────────error subroutines───────────────────*/
erb: call ser 'illegal' arg(2) "base:" arg(1) "must be in range: 2──►" maxB
erd: call ser 'illegal "digit" in' x":" _
erm: call ser 'no argument specified.'
ser: say; say '*** error! ***'; say arg(1); say; exit 13
y=sigX || substr(@@@, #+1, 1)y /*prepend the sign if it existed.*/
return y /*return the number in base toB.*/
/*───────────────────────────────────────────────────────────────────────────────────────*/
erb: call ser 'illegal' arg(2) "base:" arg(1) "must be in range: 2──►" mxB
erd: call ser 'illegal "digit" in' x":" _
erm: call ser 'no argument specified.'
ser: say; say '*** error! ***'; say arg(1); say; exit 13

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input " Number of rows:"; rows
html "<table>"
for r = 1 to rows ' r = rows
html "<TR align=right>"
for c = 1 to r ' c = columns
j = j + 1
html "<TD> ";j;"</TD>"
next c
next r
input "Number of rows: "; rows
dim colSize(rows)
for col=1 to rows
colSize(col) = len(str$(col + rows * (rows-1)/2))
next
thisNum = 1
for r = 1 to rows
for col = 1 to r
print right$( " "+str$(thisNum), colSize(col)); " ";
thisNum = thisNum + 1
next
print
next

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10 LET n=10: LET j=1: LET col=1
20 FOR r=1 TO n
30 FOR j=j TO j+r-1
40 PRINT TAB (col);j;
50 LET col=col+3
60 NEXT j
70 PRINT
80 LET col=1
90 NEXT r