KombiN is an algorithm that gives Index # of weighted combination and back, works with combinations of two finite sets ordered by sum and then by difference of combination, without generating and enumerating through possible combinations.
Let's say we have two sets:
Set A = { Apple = 0, Banana = 1, Cucumber = 2 }
Set B = { CEO = 0, CFO = 1, CSO = 2 }
Now get all possible unique combinations for both sets and sort first by sum of combination and after by difference of combination and in the end give Index # to all combinations.
In above example, both sets have zero-based index so KombiN will have output as shown in left side Table below. For example, both sets are in DataTable with Non-zero index, In that case KombiN will have output as shown in right side Table below.
In short, It provides zero and non-zero index based on type of index used in both sets.
| Index # | ai | bi | Index # | ai | bi | ||
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 1 | ||
| 1 | 0 | 1 | 2 | 1 | 2 | ||
| 2 | 1 | 0 | 3 | 2 | 1 | ||
| 3 | 0 | 2 | 4 | 1 | 3 | ||
| 4 | 1 | 1 | 5 | 2 | 2 | ||
| 5 | 2 | 0 | 6 | 3 | 1 | ||
| 6 | 1 | 2 | 7 | 2 | 3 | ||
| 7 | 2 | 1 | 8 | 3 | 2 | ||
| 8 | 2 | 2 | 9 | 3 | 3 |
You can use KombiN for
- Finding the Index # of particular combination
- Finding the Combination of particular Index #.