Knuth Algorithm

Answers and Replies

  • #2
[STRIKE]bump[/STRIKE]

plus why at the level 1 the branch containing "D" (i.e. containing 0, 1, 1, 1 in columns 2, 3, 5 & 6) was terminated unsuccessfully?
 
Last edited:
  • #3
188
1
Hi all, at http://en.wikipedia.org/wiki/Knuth's_Algorithm_X in the example I don't understand that why not "A" is in the final solution & only B, D & F are in the final solution whereas "A" was selected at Level 1
[STRIKE]bump[/STRIKE]

plus why at the level 1 the branch containing "D" (i.e. containing 0, 1, 1, 1 in columns 2, 3, 5 & 6) was terminated unsuccessfully?
The intent, as far as I understand it, is to find a combination of rows that include every number from 1 to 7 but where each number only occurs in at most one row.

The algorithm seems to work by picking the row (A) that has the most numbers in it and then trying to find a combination of the other rows that have the numbers that aren't in A.

Having selected A (in this case), it proceeds by removing any sets that have a number in common with A (in this case, B,C,E and F). This is because any combination of B,C,E or F with A will have at least one multiple of '1', '4' or '7'. This only leaves row D as a possible match for A.

However, row D doesn't contain a '2' and neither does A, so the combination of A and D is not an exact cover, hence the algorithm terminates and goes to test for another combination.

NR
 
  • #4
The intent, as far as I understand it, is to find a combination of rows that include every number from 1 to 7 but where each number only occurs in at most one row.

The algorithm seems to work by picking the row (A) that has the most numbers in it and then trying to find a combination of the other rows that have the numbers that aren't in A.

Having selected A (in this case), it proceeds by removing any sets that have a number in common with A (in this case, B,C,E and F). This is because any combination of B,C,E or F with A will have at least one multiple of '1', '4' or '7'. This only leaves row D as a possible match for A.

However, row D doesn't contain a '2' and neither does A, so the combination of A and D is not an exact cover, hence the algorithm terminates and goes to test for another combination.

NR
thank you sooooooooooo much, you really helped me in understanding it.
 

Related Threads on Knuth Algorithm

  • Last Post
Replies
22
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
2
Replies
25
Views
10K
  • Last Post
Replies
2
Views
18K
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
17
Views
8K
  • Last Post
Replies
11
Views
749
Top