28 august 2009
- Wide cut
Sometimes one needs to cut a bit more than the actual delimiter shows. An example will explain.
Suppose the array 0 1 1 1 0 1 0 0 2 2 2 1 2 2 0 2 1 1 2 1 0 2 0 1 2 0 0 is to be boxed after a 2 including the next zeroes with a max of 2 and after a 1 including the next zero, if possible. The output should be
+---+-+---+---+---+-+-+-+-+---+-+-+-+-+---+---+-+-----+ |0 1|1|1 0|1 0|0 2|2|2|1|2|2 0|2|1|1|2|1 0|2 0|1|2 0 0| +---+-+---+---+---+-+-+-+-+---+-+-+-+-+---+---+-+-----+
To do this a technique is used applied by Hui in Hui 2008July.
Translating the requirements in a more concise form we get the following cases to be considered
- 1 0 - NB. - can be everything, so 0 1 2 - 2 0 * NB. * is unequal to 0, so 1 2 2 0 0 - - - 1 * - - 2 *
Notice that we have to look at 4 positions since a decision cannot be made after 2 0 or after 1 or after 2 .
If we apply 3&#. to the 4 numbers, these conditions become
- 1 0 - 9 10 11 e.~ 27 | 3 #. ] - 2 0 * 19 20 e.~ 27 | 3 #. ] 2 0 0 - 54 55 56 e.~ 3 #. ] - - 1 * 4 5 e.~ 9 | 3 #. ] - - 2 * 7 8 e.~ 9 | 3 #. ] NB. So together ((9 10 11 19 20 e.~ 27 | ]) +. (4 5 7 8 e.~ 9 |] ) +. 54 55 56 e.~ ]) 3 #. ]
Since we replace the third position of every infix of 4, the argument has to be preceded by 0 0 and followed by 2 or 1 .
So the verb to produce the wide cut becomes
wicu=: 3 : 'y <;.2~ ((9 10 11 19 20 e.~ 27 | ]) +. (4 5 7 8 e.~ 9 |] ) +. 54 55 56 e.~ ]) 3 #. 4[\0 0 , y , 2' wicu 0 1 1 1 0 1 0 0 2 2 2 1 2 2 0 2 1 1 2 1 0 2 0 1 2 0 0 +---+-+---+---+---+-+-+-+-+---+-+-+-+-+---+---+-+-----+ |0 1|1|1 0|1 0|0 2|2|2|1|2|2 0|2|1|1|2|1 0|2 0|1|2 0 0| +---+-+---+---+---+-+-+-+-+---+-+-+-+-+---+---+-+-----+