September 2017 Update
This commit is contained in:
Ingy döt Net
parent
bba7bfd280
commit
ba8067c3b7
14570 changed files with 153136 additions and 63871 deletions
|
|
@ -1,45 +1,46 @@
|
|||
/*REXX program cuts rectangles into two symmetric pieces, the rectangles are */
|
||||
/*────────────────────────────── cut along unit dimensions and may be rotated.*/
|
||||
numeric digits 20 /*be able to handle some big integers. */
|
||||
parse arg N .; if N=='' then N=10 /*N not specified? Then use default.*/
|
||||
dir.=0; dir.0.1=-1; dir.1.0=-1; dir.2.1=1; dir.3.0=1 /*4 directions.*/
|
||||
/*REXX program cuts rectangles into two symmetric pieces, the rectangles are cut along */
|
||||
/*────────────────────────────────────────────────── unit dimensions and may be rotated.*/
|
||||
numeric digits 20 /*be able to handle some big integers. */
|
||||
parse arg N .; if N=='' | N=="," then N=10 /*N not specified? Then use default.*/
|
||||
dir.=0; dir.0.1=-1; dir.1.0=-1; dir.2.1=1; dir.3.0=1 /*the four directions.*/
|
||||
|
||||
do y=2 to N; say /*calculate rectangles up to size NxN.*/
|
||||
do x=1 for y; if x//2 & y//2 then iterate /*not if both X&Y odd.*/
|
||||
_=solve(y,x,1); _=right(_,max(10,length(_))) /*align the output. */
|
||||
say right(y,9) "x" right(x,2) 'rectangle can be cut' _ "way"s(_)'.'
|
||||
do y=2 to N; say /*calculate rectangles up to size NxN.*/
|
||||
do x=1 for y; if x//2 & y//2 then iterate /*not if both X&Y odd.*/
|
||||
z=solve(y,x,1); _=comma(z); _=right(_, max(14, length(_))) /*align the output. */
|
||||
say right(y,9) "x" right(x,2) 'rectangle can be cut' _ "way"s(z).
|
||||
end /*x*/
|
||||
end /*y*/
|
||||
exit /*stick a fork in it, we're all done. */
|
||||
/*────────────────────────────────────────────────────────────────────────────*/
|
||||
s: if arg(1)=1 then return arg(3); return word(arg(2) 's',1) /*pluralizer*/
|
||||
/*────────────────────────────────────────────────────────────────────────────*/
|
||||
solve: procedure expose # dir. @. h len next. w; @.=0 /*zero rect. coördinates*/
|
||||
parse arg hh 1 h,ww 1 w,recur /*obtain the values for some arguments.*/
|
||||
if h//2 then do; t=w; w=h; h=t; if h//2 then return 0
|
||||
exit /*stick a fork in it, we're all done. */
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
comma: procedure; arg _; do k=length(_)-3 to 1 by -3; _=insert(',',_,k); end; return _
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
s: if arg(1)=1 then return arg(3); return word(arg(2) 's', 1) /*pluralizer.*/
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
solve: procedure expose # dir. @. h len next. w; @.=0 /*zero rectangle coördinates.*/
|
||||
parse arg h,w,recur /*get values for some args. */
|
||||
if h//2 then do; t=w; w=h; h=t; if h//2 then return 0
|
||||
end
|
||||
if w==1 then return 1
|
||||
if w==2 then return h
|
||||
if h==2 then return w /* % is REXX's integer division. */
|
||||
cy = h%2; cx=w%2 /*cut the [XY] rectangle in half. */
|
||||
len = (h+1) * (w+1) - 1 /*extend the area of the rectangle. */
|
||||
next.0=-1; next.1=-w-1; next.2=1; next.3=w+1 /*direction & distance*/
|
||||
if h==2 then return w /* [↓] % is REXX's integer division.*/
|
||||
cy=h % 2; cx=w % 2; wp=w + 1 /*cut the [XY] rectangle in half. */
|
||||
len=(h+1) * wp - 1 /*extend the area of the rectangle. */
|
||||
next.0=-1; next.1=-wp; next.2=1; next.3=wp /*direction & distance.*/
|
||||
if recur then #=0
|
||||
do x=cx+1 to w-1; t=x+cy*(w+1)
|
||||
@.t=1; _=len-t; @._=1; call walk cy-1,x
|
||||
end /*x*/
|
||||
do x=cx+1 to w-1; t=x + cy*wp; @.t=1; _=len - t; @._=1
|
||||
call walk cy-1, x
|
||||
end /*x*/
|
||||
#=#+1
|
||||
if h==w then #=#+# /*double the count of rectangle cuts. */
|
||||
else if w//2==0 & recur then call solve w,h,0
|
||||
if h==w then #=# + # /*double the count of rectangle cuts. */
|
||||
else if w//2==0 & recur then call solve w, h, 0
|
||||
return #
|
||||
/*────────────────────────────────────────────────────────────────────────────*/
|
||||
walk: procedure expose # dir. @. h len next. w; parse arg y,x
|
||||
if y==h | x==0 | x==w | y==0 then do; #=#=2; return; end
|
||||
t=x + y*(w+1); @.t=@.t+1; _=len-t
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
walk: procedure expose # dir. @. h len next. w wp; parse arg y,x
|
||||
if y==h | x==0 | x==w | y==0 then do; #= #+2; return; end
|
||||
t=x + y*wp; @.t=@.t + 1; _=len - t
|
||||
@._=@._+1
|
||||
do j=0 for 4; _ = t+next.j /*try four directions.*/
|
||||
if @._==0 then call walk y+dir.j.0, x+dir.j.1
|
||||
do j=0 for 4; _=t + next.j /*try each of four directions.*/
|
||||
if @._==0 then call walk y + dir.j.0, x + dir.j.1
|
||||
end /*j*/
|
||||
@.t=@.t-1
|
||||
_=len-t; @._=@._-1
|
||||
return
|
||||
@.t=@.t - 1
|
||||
_=len - t; @._=@._ - 1; return
|
||||
|
|
|
|||
|
|
@ -1,55 +1,55 @@
|
|||
/*REXX program cuts rectangles into two symmetric pieces, the rectangles are */
|
||||
/*────────────────────────────── cut along unit dimensions and may be rotated.*/
|
||||
numeric digits 20 /*be able to handle some big integers. */
|
||||
parse arg N .; if N=='' then N=10 /*N not specified? Then use default.*/
|
||||
dir.=0; dir.0.1=-1; dir.1.0=-1; dir.2.1=1; dir.3.0=1 /*4 directions.*/
|
||||
/*REXX program cuts rectangles into two symmetric pieces, the rectangles are cut along */
|
||||
/*────────────────────────────────────────────────── unit dimensions and may be rotated.*/
|
||||
numeric digits 20 /*be able to handle some big integers. */
|
||||
parse arg N .; if N=='' | N=="," then N=10 /*N not specified? Then use default.*/
|
||||
dir.=0; dir.0.1=-1; dir.1.0=-1; dir.2.1=1; dir.3.0=1 /*the four directions.*/
|
||||
|
||||
do y=2 to N; say /*calculate rectangles up to size NxN.*/
|
||||
do x=1 for y; if x//2 & y//2 then iterate /*not if both X&Y odd.*/
|
||||
_=solve(y,x,1); _=right(_,max(10,length(_))) /*align the output. */
|
||||
say right(y,9) "x" right(x,2) 'rectangle can be cut' _ "way"s(_)'.'
|
||||
do y=2 to N; say /*calculate rectangles up to size NxN.*/
|
||||
do x=1 for y; if x//2 & y//2 then iterate /*not if both X&Y odd.*/
|
||||
z=solve(y,x,1); _=comma(z); _=right(_, max(14, length(_))) /*align the output. */
|
||||
say right(y,9) "x" right(x,2) 'rectangle can be cut' _ "way"s(z).
|
||||
end /*x*/
|
||||
end /*y*/
|
||||
exit /*stick a fork in it, we're all done. */
|
||||
/*────────────────────────────────────────────────────────────────────────────*/
|
||||
s: if arg(1)=1 then return arg(3); return word(arg(2) 's',1) /*pluralizer*/
|
||||
/*────────────────────────────────────────────────────────────────────────────*/
|
||||
solve: procedure expose # dir. @. h len next. w; @.=0 /*zero rect. coördinates*/
|
||||
parse arg hh 1 h,ww 1 w,recur /*obtain the values for some arguments.*/
|
||||
if h//2 then do; parse value w h w with t w h; if h//2 then return 0
|
||||
exit /*stick a fork in it, we're all done. */
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
comma: procedure; arg _; do k=length(_)-3 to 1 by -3; _=insert(',',_,k); end; return _
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
s: if arg(1)=1 then return arg(3); return word(arg(2) 's', 1) /*pluralizer.*/
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
solve: procedure expose # dir. @. h len next. w; @.=0 /*zero rectangle coördinates.*/
|
||||
parse arg h,w,recur /*get values for some args. */
|
||||
if h//2 then do; t=w; w=h; h=t; if h//2 then return 0
|
||||
end
|
||||
if w==1 then return 1
|
||||
if w==2 then return h
|
||||
if h==2 then return w /* % is REXX's integer division. */
|
||||
cy = h%2; cx=w%2 /*cut the [XY] rectangle in half. */
|
||||
len = (h+1) * (w+1) - 1 /*extend the area of the rectangle. */
|
||||
next.0=-1; next.1=-w-1; next.2=1; next.3=w+1 /*direction & distance*/
|
||||
if h==2 then return w /* [↓] % is REXX's integer division.*/
|
||||
cy=h % 2; cx=w % 2; wp=w + 1 /*cut the [XY] rectangle in half. */
|
||||
len=(h+1) * wp - 1 /*extend the area of the rectangle. */
|
||||
next.0=-1; next.1=-wp; next.2=1; next.3=wp /*direction & distance.*/
|
||||
if recur then #=0
|
||||
do x=cx+1 to w-1; t=x+cy*(w+1)
|
||||
@.t=1; _=len-t; @._=1; call walk cy-1,x
|
||||
end /*x*/
|
||||
do x=cx+1 to w-1; t=x + cy*wp; @.t=1; _=len - t; @._=1
|
||||
call walk cy-1, x
|
||||
end /*x*/
|
||||
#=#+1
|
||||
if h==w then #=#+# /*double the count of rectangle cuts. */
|
||||
else if w//2==0 & recur then call solve w,h,0
|
||||
if h==w then #=# + # /*double the count of rectangle cuts. */
|
||||
else if w//2==0 & recur then call solve w, h, 0
|
||||
return #
|
||||
/*────────────────────────────────────────────────────────────────────────────*/
|
||||
walk: procedure expose # dir. @. h len next. w; parse arg y,x
|
||||
if y==h then do; #=#+2; return; end /*◄──┐ REXX short circuit. */
|
||||
if x==0 then do; #=#+2; return; end /*◄──┤ " " " */
|
||||
if x==w then do; #=#+2; return; end /*◄──┤ " " " */
|
||||
if y==0 then do; #=#+2; return; end /*◄──┤ " " " */
|
||||
t=x + y*(w+1); @.t=@.t+1; _=len-t /* │ordered by most likely ►──┐*/
|
||||
@._=@._+1 /* └──────────────────────────┘*/
|
||||
do j=0 for 4; _ = t+next.j /*try 4 directions.*/
|
||||
if @._==0 then do
|
||||
yn=y+dir.j.0; xn=x+dir.j.1
|
||||
if yn==h then do; #=#+2; iterate; end
|
||||
if xn==0 then do; #=#+2; iterate; end
|
||||
if xn==w then do; #=#+2; iterate; end
|
||||
if yn==0 then do; #=#+2; iterate; end
|
||||
call walk yn, xn
|
||||
end
|
||||
end /*j*/
|
||||
@.t=@.t-1
|
||||
_=len-t; @._=@._-1
|
||||
return
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
walk: procedure expose # dir. @. h len next. w wp; parse arg y,x
|
||||
if y==h then do; #=#+2; return; end /* ◄──┐ REXX short circuit. */
|
||||
if x==0 then do; #=#+2; return; end /* ◄──┤ " " " */
|
||||
if x==w then do; #=#+2; return; end /* ◄──┤ " " " */
|
||||
if y==0 then do; #=#+2; return; end /* ◄──┤ " " " */
|
||||
t=x + y*wp; @.t=@.t + 1; _=len - t /* │ordered by most likely ►──┐*/
|
||||
@._=@._+1 /* └──────────────────────────┘*/
|
||||
do j=0 for 4; _=t + next.j /*try each of the four directions.*/
|
||||
if @._==0 then do; yn=y + dir.j.0; xn=x + dir.j.1
|
||||
if yn==h then do; #=#+2; iterate; end
|
||||
if xn==0 then do; #=#+2; iterate; end
|
||||
if xn==w then do; #=#+2; iterate; end
|
||||
if yn==0 then do; #=#+2; iterate; end
|
||||
call walk yn, xn
|
||||
end
|
||||
end /*j*/
|
||||
@.t=@.t - 1
|
||||
_=len - t; @._=@._ - 1; return
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue