Ramsey's theorem: Difference between revisions

<lang rexx>/*REXX programsprogram finds and displays a 17 node graph such that any four nodes are neither */

/*────── nodes are neither ─────────────────────────────────────────── totally connected nor totally unconnected.*/

@.=0; #=17 /*initialize the node graph to zero. */

do d=0 for #; @.d.d=2; end /*d*/ /*set the diagonal elements to 2two. */

do do k=1 by 0 while k<=8 /*K is doubled each time through loop.*/

do i=0 for # /*process each column in the array. */

j= (i+k) // # /*set a row,colcolumn and colcolumn,row. */

@.i.j=1; @.j.i=1 /*set two array elements to unity. */

k=k+k /*double the value of K for each loop*/

end /*while k≤8*/

/* [↓] display a connection grid. */

do r=0 for #; _=; do c=0 for # /*show each row, build colcolumn by colcolumn*/

_=_ @.r.c /*add this (append) the column to the row. */

end /*c*/

say left('', 9) translate(_,' "-'", 2) /*display the constructed row. */

end /*r*/

/*verify the sub-graphs connections. */

!.=0; ok=1 /*Ramsey's connections; OK (so far).*/

/* [↓] check columncol. with row connconnections*/

do v=0 for # /*check sub-graphs #number connections. */

do h=0 for # /*check column connectionconnections to rowthe rows.*/

if @.v.h==1 then !._v.v=!._v.v+1 /*if connected, then bump the counter.*/

end /*h*/ /* [↑] Note: we're counting each */

ok=ok & !._v.v==#%2 /* each connection twice, so divide */

end /*v*/ /* so dividethe total by two. */

/* [↓] check columncol. with row connconnections*/

do h=0 for # /*check the sub-graphs # of connections.*/

do v=0 for # /*check the row connection to a column.*/

if @.h.v==1 then !._h.h=!._h.h+1 /*if connected, then bump the counter.*/

end /*v*/ /* [↑] Note: we're counting each */

ok=ok & !._h.h==#%2 /* each connection twice, so divide */

end /*h*/ /* so dividethe total by two. */

say /* [↓] a yea─or─nay message. */

say; say space("Ramsey's condition" word('not', 1+ok) ' "satisfied.'")

/*stick a fork in it, we're all done. */</lang>