Question

In: Computer Science

def sequentialSearch(theList, item): #**** to be changed: # counts the iterations of the while...

def sequentialSearch(theList, item):
    #**** to be changed:
    # counts the iterations of the while loop and returns this value
    found = False
    index = 0
    while index < len(theList) and not found:
        if theList[index] == item:
            found = True
        index = index + 1
    return found

def binarySearch(theList, item):
    #**** to be changed:
    # counts the iterations of the while loop and returns this value
    startIndex = 0
    endIndex = len(theList)- 1
    found = False
    while startIndex <= endIndex and not found:
        middleIndex = (startIndex + endIndex)//2
        if item == theList[middleIndex]:
            found = True
        elif item > theList[middleIndex]:
            startIndex = middleIndex + 1
        else:
            endIndex = middleIndex - 1
    return found

# program for testing the search algorithms
dataSet = [-200, -190, -180, -170, -160, -110, -105, -74, -30, -17, -12, -1, 4, 5, 13, 26, 37, 42, 62, 96, 100, 110, 120,130]

print("\nSuccessful sequential search - all elements of the data set")
totalComparisons = 0
#**** to be completed:
#     list traversal on the dataSet list:
#     for each item: perform a sequential search and
#                    display the number of comparisons,
#     count the total number of comparisons
print("Average number of comparisons: "+str(totalComparisons/len(dataSet)))

print("\nUn-successful sequential search")
target = 196                 # target not in the dataSet
comparisons = 0 #**** to be changed: perform a sequential search for target
print ("target " + str(target), "\t comparisons used " + str(comparisons))

print("\nSuccessful binary search - all elements of the data set")
totalComparisons = 0
#**** to be completed:
#     list traversal on the dataSet list:
#     for each item: perform a binary search and
#                    display the number of comparisons,
#     count the total number of comparisons
print("Average number of comparisons: "+str(totalComparisons/len(dataSet)))

print("\nUn-successful binary search")
target = 196 # target not in the dataSet
comparisons = 0 #**** to be changed: perform a binary search for target
print ("target " + str(target), "\t comparisons used " + str(comparisons))

make some change to the python according to the comment line and complete the following question.

Sequential Search Algorithm		Binary Search Algorithm
Successful searches		Successful searches
Average number of comparisons		Average number of comparisons
Maximum number of comparisons found at index _____________		Maximum number of comparisons found at index _____________
Minimum number of comparisons found at index____________		Minimum number of comparisons found at index____________
Un-Successful search		Un-Successful search
Number of comparisons		Number of comparisons

What is the size n of the data set used?
What is the worst case for sequential search?
What is the best case for sequential search?
Is the worst case for sequential search O(n)?

What is the best case for binary search?

What is the worst case for binary search?

Is the worst case for binary search O(log n)?

Expert Solution

Sequential Search Algorithm		Binary Search Algorithm
Successful searches	24	Successful searches	24
Average number of comparisons	12.5	Average number of comparisons	3.9166666666666665
Maximum number of comparisons found at index (assuming index starts at 1) 24	24	Maximum number of comparisons found at index (assuming index starts at 1) 2,5,8,11,14,17,20,22,24	5
Minimum number of comparisons found at index______1______	1	Minimum number of comparisons found at index (assuming index starts at 1) 12	1
Un-Successful search	1	Un-Successful search	1
Number of comparisons	24	Number of comparisons	5

What is the size n of the data set used? -> 24
What is the worst case for sequential search? ->O(n) (for the above case O(24))
What is the best case for sequential search? ->O(1)
Is the worst case for sequential search O(n)? ->Yes

What is the best case for binary search? -> O(1)

What is the worst case for binary search? -> O(log n) (with base 2)

Is the worst case for binary search O(log n)? ->Yes

Below is the modified program to get the number of comparisons in each case as required.

def sequentialSearch(theList, item):
    #**** to be changed:
    # counts the iterations of the while loop and returns this value
    found = False
    index = 0
    compare_count=0
    while index < len(theList) and not found:
        compare_count+=1
        if theList[index] == item:
            found = True
        index = index + 1
    return compare_count

def binarySearch(theList, item):
    #**** to be changed:
    # counts the iterations of the while loop and returns this value
    startIndex = 0
    endIndex = len(theList)- 1
    found = False
    compare_count=0
    while startIndex <= endIndex and not found:
        middleIndex = (startIndex + endIndex)//2
        compare_count+=1
        if item == theList[middleIndex]:
            found = True
        elif item > theList[middleIndex]:
            startIndex = middleIndex + 1
        else:
            endIndex = middleIndex - 1
    return compare_count

# program for testing the search algorithms
dataSet = [-200, -190, -180, -170, -160, -110, -105, -74, -30, -17, -12, -1, 4, 5, 13, 26, 37, 42, 62, 96, 100, 110, 120,130]

print("\nSuccessful sequential search - all elements of the data set")
totalComparisons = 0
#**** to be completed:
#     list traversal on the dataSet list:
#     for each item: perform a sequential search and
#                    display the number of comparisons,

for num in dataSet:
    comparisons = sequentialSearch(dataSet,num)
    print("target " + str(num), "\t comparisons used " + str(comparisons))
#     count the total number of comparisons
    totalComparisons= totalComparisons + comparisons

print("Average number of comparisons: "+str(totalComparisons/len(dataSet)))

print("\nUn-successful sequential search")
target = 196 # target not in the dataSet
comparisons = 0 #**** to be changed: perform a sequential search for target
comparisons= sequentialSearch(dataSet, target)
print ("target " + str(target), "\t comparisons used " + str(comparisons))

print("\nSuccessful binary search - all elements of the data set")

totalComparisons = 0
#**** to be completed:
#     list traversal on the dataSet list:
#     for each item: perform a binary search and
#                    display the number of comparisons,

for num in dataSet:
    comparisons = binarySearch(dataSet,num)
    print("target " + str(num), "\t comparisons used " + str(comparisons))
#     count the total number of comparisons
    totalComparisons= totalComparisons + comparisons

print("Average number of comparisons: "+str(totalComparisons/len(dataSet)))

print("\nUn-successful binary search")
target = 196 # target not in the dataSet
comparisons = 0 #**** to be changed: perform a binary search for target
comparisons= binarySearch(dataSet, target)
print ("target " + str(target), "\t comparisons used " + str(comparisons))

Please find below attached the schreeshot of the program and console output.

venereology answered 1 month ago

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