CSC108H Fall 2022 Worksheet: Insertion Sort Analysis
1. Insertion Sort: Worst Case
(a) In the list below, 4 passes of the insertion sort algorithm have been completed, and the double bar
separates the sorted part of the list from the unsorted part. The item at index i is missing. Fill in
the missing item with a value that will cause insert(L, i) to perform the most number of steps.
(As a reminder, this is called the worst case.)
i
L 3 4 6 6 3 1 5
(b) When insert(L, i) is executed on the example list, how many times does the while loop iterate?
(c) When insert(L, i) is called on the example list, how many assignment statements are executed?
(d) In general, in the worst case, on pass i of insertion sort, how many times does the while loop iterate?
(Your answer should be a formula that involves i.)
(e) In general, in the worst case, on pass i of insertion sort, how many assignment statements are
executed? (Again, your answer should be a formula that involves i.)
(f) In terms of i, in the worst case, does function insert have constant running time, linear running
time, quadratic running time, or some other running time?
(a) constant (b) linear (c) quadratic (d) something else
(g) In function insertion_sort, the first time that function insert is called, i is 0; the second time, i
is 1; and so on. What value does i have the last time that function insert is called?
(h) For the call insertion_sort(L), in the worst case, write a formula expressing how many compar-
isons are made during all the calls to insert.
(i) In the worst case, does insertion_sort have constant running time, linear running time, quadratic
running time, or some other running time?
(a) constant (b) linear (c) quadratic (d) something else
1. Insertion Sort: Worst Case
(a) In the list below, 4 passes of the insertion sort algorithm have been completed, and the double bar
separates the sorted part of the list from the unsorted part. The item at index i is missing. Fill in
the missing item with a value that will cause insert(L, i) to perform the most number of steps.
(As a reminder, this is called the worst case.)
i
L 3 4 6 6 3 1 5
(b) When insert(L, i) is executed on the example list, how many times does the while loop iterate?
(c) When insert(L, i) is called on the example list, how many assignment statements are executed?
(d) In general, in the worst case, on pass i of insertion sort, how many times does the while loop iterate?
(Your answer should be a formula that involves i.)
(e) In general, in the worst case, on pass i of insertion sort, how many assignment statements are
executed? (Again, your answer should be a formula that involves i.)
(f) In terms of i, in the worst case, does function insert have constant running time, linear running
time, quadratic running time, or some other running time?
(a) constant (b) linear (c) quadratic (d) something else
(g) In function insertion_sort, the first time that function insert is called, i is 0; the second time, i
is 1; and so on. What value does i have the last time that function insert is called?
(h) For the call insertion_sort(L), in the worst case, write a formula expressing how many compar-
isons are made during all the calls to insert.
(i) In the worst case, does insertion_sort have constant running time, linear running time, quadratic
running time, or some other running time?
(a) constant (b) linear (c) quadratic (d) something else
