CS 502 Fundamental of Algorithms
Assignment # 02
Spring 2012 Total Marks = 20
Deadline
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Assignment Statements:
Question:
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, thereโs only one digit, so sorting on that digit sorts
the array.
Inductive step: Assuming that radix sort works for d โ 1 digits, we
will show that it works for d digits.
Radix sort sorts separately on each digit, starting from digit 1.
Thus, radix sort of d digits, which sorts on digits 1, . . . , d is
equivalent to radix sort of the low-order d โ 1 digits followed by a
sort on digit d. By our induction hypothesis, the sort of the low-
order d โ1 digits works, so just before the sort on digit d, the
elements are in order according to their low-order d โ 1 digits.
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