Given an item and a sequence, tell whether the item is in the sequence or not.

Use recursion.

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Find the length of a given sequence.

Use recursion.

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Given a possibly nested sequence and an item, count the occurrences of the item in the sequence.

For instance given,

[1, [2, 3], 4, [5, [6, 4]]]

you should be able to count 2 occurrences of 4.

Use recursion.

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Map a possibly nested sequence to its flattend version, which comprises only the ground element. For example, the sequence

[1, [2, 3], 4, [5, [6, 7]]]

should be mapped to

[1, 2, 3, 4, 5, 6, 7]

Use recursion.

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Write a function that takes an object and a sequence and returns the index of the item in the sequence, starting from 0. If the item does not occur in the sequence, return -1.

Use recursion.

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Given a set of items provided as a list, write a function that returns the power set of the given set.

Use recursion.

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Compute the permutations of a list or string.

Use recursion.

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Given a possibly nested list, compute the deepest level of embedding in the list. The ground level counts as 0 depth. For example, the list T

[1, [2, 3], 4, [5, [6, 7]]]

should return 2.

Use recursion.

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