# Cpt S 450 Homework 2 solution

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## Description

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1. (easy) Write psuedo-code for partition(A, p, q).

2. (standard) Consider insertsort. Suppose that the input array A has 1%
probability to be monotonically decreasing. Show that, in this case, the
average-case complexity of insertsort is Θ(n
2
).

3. (not hard) Let iqsort(A, 1, n) be an algorithm that sorts an array A with
n integers. It works as follows:
iqsort(A, p, q){
if p ≥ q, return;
r=partition(A, p, q);
//run quick sort on the low part
quicksort(A, p, r − 1);
//run insert sort on the high part
insertsort(A, r + 1, q);
}
Compute the best-case, worst-case, and average-case complexities of iqsort.

4. (hard) Let mixsort(A, 1, n) be an algorithm that sorts an array A with n
integers. It works as follows:
mixsort(A, p, q){
if p ≥ q, return;
r=partition(A, p, q);
//run mixsort on the low part
mixsort(A, p, r − 1);
//run insert sort on the high part
insertsort(A, r + 1, q);
}
Compute the best-case, worst-case, and average-case complexities of mixsort.