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CS502 Assignment No 2 Solution & Discussion Due Date: 02-05-2012

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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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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?
solution:
Basis: If $d = 1$, sorting on that digit sorts the array correctly.
Inductive step: Assume that RADIX-SORT sorts $d-1$ digits correctly. Consider two elements $a$ and $b$, with their $d$th digit $a_d$ and $b_d$ respectively.
(1) $a_d > b_d$ and $b_d > a_d$ : RADIX-SORT works correctly, because of most significant bit dominates regardless of the lower $d-1$ digits.
(2) $a_d = b_d$ : RADIX-SORT leaves $a$ and $b$ in the same order because it is stable sort. The order is correct since lower $d-1$ digits sorts correctly. That's why we need that the intermediate sort must be stable.

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