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Exercises

1. [15] If a worm crawls around the binary tree (4), how could it easily reconstruct the parentheses of (1)?

2. [20] (S. Zaks, 1980.) Modify Algorithm P so that it produces the combinations z1 z2 . . . zn of (8) instead of the parenthesis strings a1 a2 . . . a2n.

3. [23] Prove that (11) converts z1 z2 . . . zn to the inversion table c1 c2 . . . cn.

4. [20] True or false: If the strings a1 . . . a2n are generated in lexicographic order, so are the corresponding strings d1 . . . dn, z1 . . . zn, p1 . . . pn, and c1 . . . cn.

5. [15] What tables d1 . . . dn, z1 . . . zn, p1 . . . pn, and c1 . . . cn correspond to the nested parenthesis ...

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