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- Draw the graph for sumList ( O (n)) and someLoops ( O (n^2 )) from the previous lecture.
10,000 20,000 30,000 40,000 50,000 60,
10 sec
30 sec
50 sec
20 sec
40 sec
60 sec
n
Execution Time
- Consider the following sumSomeListItems function.
import time def main(): n = eval(input("Enter size of list: ")) aList = list(range(1, n+1)) start = time.clock() sum = sumSomeListItems(aList) end = time.clock() print("Time to sum the list was %.9f seconds" % (end-start)) def sumSomeListItems(myList): """Returns the sum of some items in myList""" total = 0 index = len(myList) - 1 while index > 0: total = total + myList[index] index = index // 2 return total main()
a) What is the problem size of sumSomeListItems?
b) If we input n of 10,000 and sumSomeListItems takes 10 seconds, how long would you expect sumSomeListItems to take for n of 20,000?
(Hint: For n of 20,000, how many more times would the loop execute than for n of 10,000?)
c) What is the big-oh notation for sumSomeListItems?
d) Add the execution-time graph for sumSomeListItems to the graph.
Lecture 3 Page 1
i = 1 while i <= n: for j in range(n):
something of O(1)
end for
i = i * 2
end while
a) Analyze the above algorithm to determine its big-oh notation, O ( ).
b) If n of 10,000, takes 10 seconds, how long would you expect the above code to take for n of 20,000?
c) Add the execution-time graph for the above code to the graph.
- Most programming languages have a built-in array data structure to store a collection of same-type items. Arrays are implemented in RAM memory as a contiguous block of memory locations. Consider an array X that contains the odd integers:
a) Any array element can be accessed randomly by calculating its address. For example, address of X[5] = 4000 + 5 * 4 = 4020. What is the general formula for calculating the address of the ith element in an array?
b) What is the big-oh notation for accessing the ith element?
c) A Python list uses an array of references (pointers) to list items in their implementation of a list. For example, a list of strings containing the alphabet:
'a' 'b' 'c' 'z'
0 1 2 3 (len( )-1)
Since a Python list can contain heterogeneous data, how does storing references in the list aid implementation?
Lecture 3 Page 2
Execution flow i = 1 (^) i = 2 i = 4 (^) i = n
j = 0 to n-1 j = 0 to n-1^ j = 0 to n- loops n times loops n times loops n times
address
Memory
X[0] X[1] X[2] X[3] X[4] X[5] X[6]
