Combinations and Permutations
| URL | Description |
|---|---|
| Combination Formula |  |
| Efficient algorithm for generating all k-subsets of set [1,2,...n] in order | |
| Efficiently Enumerating the Subsets of a Set | The task of constructing the subsets of a set grows exponentially with the size of the set. The two most common methods of enumerating the subsets of a set, lexicographic ordering and Gray codes, in practice are sub-optimal when the sets become large. An algorithm is presented for rapidly ?nding the smallest subset Tmin µ S satisfying some condition P. The algorithm generates a sequence of all subsets of a set of n elements in which the number of elements in each subset is monotonically increasing. Time complexity of the algorithm is only slightly greater than that of lexicographic ordering. The algorithm will ?nd the smallest subset containing up to k < n items before either lexicographic ordering or a binary re?ected Gray code sequence have even looked at all n elements in the set. |
| Generating all subsets of a finite set with disjoint unions | |
| Power Set and k-Set and characteristic vector | The power set is the set of all subsets of a sest |
| What is the Difference? |
