CombinatorialCase111: Difference between revisions

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* <apll>M</apll> labeled balls (1), <apll>N</apll> labeled boxes (1), any # balls per box (1)
* <apll>M</apll> labeled balls (1), <apll>N</apll> labeled boxes (1), any # balls per box (1)
* Sensitive to <apll>⎕IO</apll>
* Sensitive to <apll>⎕IO</apll>
* Allows Lexicographic order
* Counted result is an integer scalar
* Counted result is an integer scalar
* Generated result is an integer matrix.
* Generated result is an integer matrix.
Line 108: Line 109:


<pre>
<pre>
       110 1‼2 3
       111 1‼2 3 ⍝ Tuples in unspecified order
1 1
1 1
1 2
1 2
Line 118: Line 119:
3 2
3 2
3 3
3 3
      111 2‼2 3 ⍝ Tuples in Lexicographic order
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
      111 3‼2 3 ⍝ Gray Code order for Tuples not implemented as yet
NONCE ERROR
      111 3‼2 3
          ∧
       ⍝ M-tuples of N items
       ⍝ M-tuples of N items
       ⍝ Labeled balls & boxes, any # Balls per Box
       ⍝ Labeled balls & boxes, any # Balls per Box

Latest revision as of 21:47, 21 October 2017

This case produces M-Tuples of N items. That is, all length M vectors with all possibilities of N items in each position, N*M rows all together.

  • M labeled balls (1), N labeled boxes (1), any # balls per box (1)
  • Sensitive to ⎕IO
  • Allows Lexicographic order
  • Counted result is an integer scalar
  • Generated result is an integer matrix.

The count for this function is NM (↔ N*M).

For example:

If we have 2 labeled balls (❶❷) and 3 labeled boxes (123) with any # of balls per box, there are 9 (↔ 3*2) ways to meet these criteria:


       
1 2 3
 
 
   
1 2 3
 
     
1 2 3
 
 
   
1 2 3
   
   
1 2 3
     
 
1 2 3
 
     
1 2 3
     
 
1 2 3
       
1 2 3

The diagram above corresponds to

      111 1‼2 3 ⍝ Tuples in unspecified order
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
      111 2‼2 3 ⍝ Tuples in Lexicographic order
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
      111 3‼2 3 ⍝ Gray Code order for Tuples not implemented as yet
NONCE ERROR
      111 3‼2 3
           ∧
      ⍝ M-tuples of N items
      ⍝ Labeled balls & boxes, any # Balls per Box
      111 0‼3 2
8
      111 1‼3 2
1 1 1
1 1 2
1 2 1
1 2 2
2 1 1
2 1 2
2 2 1
2 2 2