![]() ![]() Looking at the diagram on the Wikipedia page might help. You can prove that both of these facts are true using induction, although that doesn't provide any intuition as to why it's true. Whereas if the vector is of odd length, it will be simply swap the first and last elements: → Given a vector of even length, a full iteration of Heap's algorithm will rearrange the elements according to the rule → To see how Heap's algorithm works, you need to look at what a full iteration of the loop does to the vector, in both even and odd cases. See for the correct algorithm (at least, it's correct today) or see the discussion at Heap's algorithm permutation generator In either case, it does unnecessary work. Reverse the part of the permutation to the right of where that element was.īoth steps (1) and (3) are worst-case O(n), but it is easy to prove that the average time for those steps is O(1).Īn indication of how tricky Heap's algorithm is (in the details) is that your expression of it is slightly wrong because it does one extra swap the extra swap is a no-op if n is even, but significantly changes the order of permutations generated when n is odd. Swap that element with the smallest element to its right which is larger than it. ![]() Given some permutation, find the next one by:įinding the rightmost element which is smaller than the element to its right. The lexicographic order algorithm is extremely simple to describe. There is a much more intuitive algorithm which will produce permutations in lexicographical order although it is amortized O(1) (per permutation) instead of O(1), it is not noticeably slower in practice, and it is much easier to derive on the fly. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are e.g.Heap's algorithm is probably not the answer to any reasonable interview question.How many different words can be formed using all of the letters in the word CONNAUGHTON ? If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are e.g.If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are.4 objects all different A B C D A B D C A C B D A C D B A D B C A D C B B A C D B A D C B C A D B C D A B D A C B D A B 2 same A A B C A A C B A B A C A B C A A C A B A C B A B A A C B A C A B C A A C A A B C A B A C B A A 3 same A A A B A A B A A B A A B A A A C B A D C B D A C A B D C A D B C D B A C D A B D A C B D A B C D C A B D C B A D B A C D B A B 4 same A A A A.4 objects all different A B C D A B D C A C B D A C D B A D B C A D C B B A C D B A D C B C A D B C D A B D A C B D A B 2 same A A B C A A C B A B A C A B C A A C A B A C B A B A A C B A C A B C A A C A A B C A B A C B A A 3 same A A A B A A B A A B A A B A A A C B A D C B D A C A B D C A D B C D B A C D A B D A C B D A B C D C A B D C B A D B A C D B A B.4 objects all different A B C D A B D C A C B D A C D B A D B C A D C B B A C D B A D C B C A D B C D A B D A C B D A B 2 same A A B C A A C B A B A C A B C A A C A B A C B A B A A C B A C A B C A A C A A B C A B A C B A A C B A D C B D A C A B D C A D B C D B A C D A B D A C B D A B C D C A B D C B A D B A C D B A B.4 objects all different A B C D A B D C A C B D A C D B A D B C A D C B B A C D B A D C B C A D B C D A B D A C B D A B C B A D C B D A C A B D C A D B C D B A C D A B D A C B D A B C D C A B D C B A D B A C D B A B.some of the objects are the same) 2 objects all different A B B A 2 same A A 3 objects all different A B C A C B B A C B C A C A B C B A 2 same A A B A B A B A A 3 same A A A Permutations Case 3: Ordered Sets of n Objects, Not All Different (i.e.some of the objects are the same) 2 objects all different A B B A 2 same A A 3 objects all different A B C A C B B A C B C A C A B C B A 2 same A A B A B A B A A Permutations ![]() some of the objects are the same) 2 objects all different A B B A 2 same A A 3 objects all different A B C A C B B A C B C A C A B C B A Permutations some of the objects are the same) 2 objects all different A B B A 2 same A A 3 objects Permutations some of the objects are the same) 2 objects all different A B B A 2 same A A Permutations some of the objects are the same) 2 objects all different A B B A Permutations some of the objects are the same) 2 objects Permutations some of the objects are the same) Permutations Case 3: Ordered Sets of n Objects, Not All Different Permutations. ![]()
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