Chapter 8, Problem 5P

(a)

Program Plan Intro

To explain that an array to be 1-sorted.

(b)

Program Plan Intro

To give a permutation of the number $1,2,3,\mathrm{......},10$ that is 2-sorted but not sorted.

(c)

Program Plan Intro

To prove that an n -element array is k -sorted if $A[i]\le A[i+k]$ for all $i=1,2,\mathrm{3....},n-k.$

(d)

Program Plan Intro

To give an algorithm that k -sorted an n -element array in $O(n\lg (n/k))$ time.

(e)

Program Plan Intro

To show that sorting a k -sort array of length n in $O(n\lg k)$ time.

(f)

Program Plan Intro

To show that k -sorting an n -element array requires $\Omega (n\lg n)$ time.