Ramsey's theorem: Difference between revisions
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m (→{{header|REXX}}: added whitespace, change comments, used a better method of showing a negative result.) |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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Mainline programming was borrowed from '''C'''. |
Mainline programming was borrowed from '''C'''. |
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<lang rexx>/*REXX program finds |
<lang rexx>/*REXX program finds & displays a 17 node graph such that any four nodes are neither ···*/ |
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/* |
/*────────────────────────────────────────── totally connected nor totally unconnected. */ |
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@.=0; #=17 /*initialize the node graph to zero. */ |
@.=0; #=17 /*initialize the node graph to zero. */ |
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do d=0 for #; @.d.d=2 |
do d=0 for #; @.d.d= 2 /*set the diagonal elements to 2 (two).*/ |
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end /*d*/ |
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do k=1 by 0 while k<=8 /*K is doubled each time through loop.*/ |
do k=1 by 0 while k<=8 /*K is doubled each time through loop.*/ |
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do i=0 for #; |
do i=0 for #; j= (i+k) // # /*set a row,column and column,row. */ |
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@.i.j=1; |
@.i.j= 1; @.j.i= 1 /*set two array elements to unity (1). */ |
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end /*i*/ |
end /*i*/ |
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k=k+k |
k= k + k /*double the value of K for each loop. */ |
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end /*k*/ |
end /*k*/ |
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/* [↓] display a connection grid. */ |
/* [↓] display a connection grid. */ |
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do r=0 for #; _=; do c=0 for # /*build rows; build column by column. */ |
do r=0 for #; _=; do c=0 for # /*build rows; build column by column. */ |
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_=_ @.r.c |
_= _ @.r.c /*add (append) the column to the row.*/ |
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end /*c*/ |
end /*c*/ |
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say left('', 9) translate(_, " |
say left('', 9) translate(_, "─", 2) /*display (indented) constructed row.*/ |
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end /*r*/ |
end /*r*/ |
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!.= 0 /*verify the sub─graphs connections. */ |
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ok= 1 /*Ramsey's connections; OK (so far).*/ |
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do v=0 for # /*check the sub─graphs # of connections*/ |
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do v=0 for # /*check the sub-graphs # of connections*/ |
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do h=0 for # /*check column connections to the rows.*/ |
do h=0 for # /*check column connections to the rows.*/ |
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if @.v.h==1 then !._v.v= !._v.v + 1 /*if connected, then bump the counter.*/ |
if @.v.h==1 then !._v.v= !._v.v + 1 /*if connected, then bump the counter.*/ |
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end /*h*/ /* [↑] |
end /*h*/ /* [↑] Note: we're counting each ··· */ |
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ok=ok & !._v.v==# % 2 |
ok= ok & !._v.v==# % 2 /* connection twice, so ··· */ |
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end /*v*/ /* the total by two. |
end /*v*/ /* divide the total by two. */ |
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/* [↓] check col. with row connections*/ |
/* [↓] check col. with row connections*/ |
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do h=0 for # /*check the |
do h=0 for # /*check the sub─graphs # of connections*/ |
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do v=0 for # /*check the row connection to a column.*/ |
do v=0 for # /*check the row connection to a column.*/ |
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if @.h.v==1 then !._h.h= !._h.h + 1 /*if connected, then bump the counter.*/ |
if @.h.v==1 then !._h.h= !._h.h + 1 /*if connected, then bump the counter.*/ |
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end /*v*/ /* [↑] |
end /*v*/ /* [↑] Note: we're counting each ··· */ |
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ok=ok & !._h.h==# % 2 |
ok= ok & !._h.h==# % 2 /* connection twice, so ··· */ |
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end /*h*/ /* the total by two. |
end /*h*/ /* divide the total by two. */ |
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say /*stick a fork in it, we're all done. */ |
say /*stick a fork in it, we're all done. */ |
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say space("Ramsey's condition is" |
say space("Ramsey's condition is"word("'nt", 1+ok) 'satisfied.') /*show yea─or─nay.*/</lang> |
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{{out|output|text= ('''17x17''' connectivity matrix):}} |
{{out|output|text= ('''17x17''' connectivity matrix):}} |
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<pre> |
<pre> |
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─ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 |
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1 |
1 ─ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 |
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1 1 |
1 1 ─ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 |
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0 1 1 |
0 1 1 ─ 1 1 0 1 0 0 0 1 1 0 0 0 1 |
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1 0 1 1 |
1 0 1 1 ─ 1 1 0 1 0 0 0 1 1 0 0 0 |
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0 1 0 1 1 |
0 1 0 1 1 ─ 1 1 0 1 0 0 0 1 1 0 0 |
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0 0 1 0 1 1 |
0 0 1 0 1 1 ─ 1 1 0 1 0 0 0 1 1 0 |
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0 0 0 1 0 1 1 |
0 0 0 1 0 1 1 ─ 1 1 0 1 0 0 0 1 1 |
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1 0 0 0 1 0 1 1 |
1 0 0 0 1 0 1 1 ─ 1 1 0 1 0 0 0 1 |
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1 1 0 0 0 1 0 1 1 |
1 1 0 0 0 1 0 1 1 ─ 1 1 0 1 0 0 0 |
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0 1 1 0 0 0 1 0 1 1 |
0 1 1 0 0 0 1 0 1 1 ─ 1 1 0 1 0 0 |
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0 0 1 1 0 0 0 1 0 1 1 |
0 0 1 1 0 0 0 1 0 1 1 ─ 1 1 0 1 0 |
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0 0 0 1 1 0 0 0 1 0 1 1 |
0 0 0 1 1 0 0 0 1 0 1 1 ─ 1 1 0 1 |
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1 0 0 0 1 1 0 0 0 1 0 1 1 |
1 0 0 0 1 1 0 0 0 1 0 1 1 ─ 1 1 0 |
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0 1 0 0 0 1 1 0 0 0 1 0 1 1 |
0 1 0 0 0 1 1 0 0 0 1 0 1 1 ─ 1 1 |
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1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 |
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 ─ 1 |
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1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 |
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 ─ |
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Ramsey's condition is satisfied. |
Ramsey's condition is satisfied. |
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