Answers for 3, 4, 5, 6

Sections 7.1 and 7.2 1. Implement the Insertion Sort algorithm (Algorithm 7.1), run it on your sys- tem, and study its best-case, average-case, and worst-case time complexities using several problem instances. 2. Show that the maximum number of comparisons performed by the Inser- tion Sort algorithm (Algorithm 7.1) is achieved when the keys are input in nonincreasing order. 3. Show that the worst-case and average-case time complexities for the num- ber of assignments of records performed by the Insertion Sort algorithm (Algorithm 7.1) are given by W (n) = (n + 4)(n-1) and A( 22 2 2 4 4. Show that the worst-case and average-case time complexities for the num- ber of assignments of records performed by the Exchange Sort algorithm (Algorithm 1.3) are given by 3n (n-1) and A(n) = 3n (n - 7) 2 4 5. Compare the best-case time complexities of Exchange Sort (Algorithm 1.3) and Insertion Sort (Algorithm 7.1). W (1) Sections 7.1 and 7.2 1. Implement the Insertion Sort algorithm (Algorithm 7.1), run it on your sys- tem, and study its best-case, average-case, and worst-case time complexities using several problem instances. 2. Show that the maximum number of comparisons performed by the Inser- tion Sort algorithm (Algorithm 7.1) is achieved when the keys are input in nonincreasing order. 3. Show that the worst-case and average-case time complexities for the num- ber of assignments of records performed by the Insertion Sort algorithm (Algorithm 7.1) are given by W (n) = (n + 4)(n-1) and A( 22 2 2 4 4. Show that the worst-case and average-case time complexities for the num- ber of assignments of records performed by the Exchange Sort algorithm (Algorithm 1.3) are given by 3n (n-1) and A(n) = 3n (n - 7) 2 4 5. Compare the best-case time complexities of Exchange Sort (Algorithm 1.3) and Insertion Sort (Algorithm 7.1). W (1)