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- W1685302609 abstract "We show that the set Bn of balanced parenthesis strings with n left and n right parentheses can be generated by prefix shifts. If b1, b2, ..., b2n is a member of Bn, then the k-th prefix shift is the string b1, bk, b2, ..., bk-1, bk+1, ..., b2n. Prefix shift algorithms are also known for combinations, and permutations of a multiset; the combination algorithm appears in fascicles of Knuth vol 4. We show that the algorithm is closely related to the combination algorithm, and like it, has a loopless implementation, and a ranking algorithm that uses O(n) arithmetic operations. Additionally, the algorithm can be directly translated to generate all binary trees by a loopless implementation that makes a constant number of pointer changes for each successively generated tree." @default.
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- W1685302609 date "2008-01-01" @default.
- W1685302609 modified "2023-09-26" @default.
- W1685302609 title "Generating balanced parentheses and binary trees by prefix shifts" @default.
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