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Question 1:

Use induction to prove that radix sort works. Where does your proof need the assumption that the intermediate sort is stable?

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Please Discuss here about this assignment.Thanks

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Exercise 8.3-3
Use induction to prove that radix sort works. Where does your proof need the assumption that the intermediate sort is stable?
Basis: If , sorting on that digit sorts the array correctly.
Inductive step: Assume that RADIX-SORT sorts  digits correctly. Consider two elements  and , with their th digit  and  respectively.
(1)  and  : RADIX-SORT works correctly, because of most significant bit dominates regardless of the lower  digits.
(2)  : RADIX-SORT leaves  and  in the same order because it is stable sort. The order is correct since lower  digits sorts correctly. That's why we need that the intermediate sort must be stable.

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