Describe an algorithm that takes a list of n integers a1 a2

Describe an algorithm that takes a list of n integers a1, a2, ..., an and finds the average of the largest and smallest integers in the list. Use the bubble sort algorithm discussed in class to sort 20, 64, 77, 50, 42, and 22 showing the lists obtained at each step. Use the insertion sort algorithm discussed in class to sort 20, 64, 77, 50, 42, and 22 showing the lists obtained at each step. Show how the binary search algorithm discussed in class searches for 42 in the sorted list below: 10 11 13 15 18 27 29 31 36 42 50 56 70 73 82 96

Solution

1). Describe an algorithm that takes a list of n integers a1, a2, ….., an and find the average of the largest and smallest integers in the list

Ans) .

procedure averageOfLargestAndSmallest(a1,a2,…,an: Integers)

largest: = a1

smallest: = a1

for i : = 2 to n

begin

    if ai > largest then

          largest: = ai

    if ai < smallest then

          smallest: = ai

end

average: =( largest + smallest)/2.

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2). Ans: Use the bubble sort algorithm:

20 64 77 50 42 22

Original Array: 20 64 77 50 42 22

Pass 1:

20 64 77 50 42 22    à no change if 20<64

20 64 77 50 42 22    à no change if 64<77

20 64 50 77 42 22   à if 77<50 condition fails then swap 77 and 50

20 64 50 42 77 22 à if 77<42 condition fails then swap 42 and 77

20 64 50 42 22 | 77   à if 77<22 condition fails then swap 77 and 22

Pass 2:

20 64 50 42 22 |77    à no change if 20<64

20 50 64 42 22 |77   à if 64<50 condition fails then swap 64 and 50

20 50 42 64 22 |77 è if 64<42 condition fails then swap 64 and 42

20 50 42 22 |64 77   à if 64<22 condition fails then swap 64 and 22

Pass 3:

20 50 42 22 |64 77   à no change if 20<50

20 42 50 22 |64 77 à if 50<42 condition fails then swap 42 and 50

20 42 22 |50 64 77 à if 50<22 condition fails then swap 22 and 50

Pass 4:

20 42 22 |50 64 77   à no change if 20<42

20 22 |42 50 64 77 à if 42<22 condition fails then swap 22 and 42

Pass 5:

20 22 42 50 64 77   à no change if 20<22

sorted elements After Bubble Sort:

20 22 42 50 64 77

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3Ans) Use the insertion sort algorithm:

Original Array: 20 64 77 50 42 22

20 64 77 50 42 22

20 64 77 50 42 22

20 50 64 77 42 22

20 42 50 64 77 22

20 22 42 50 64 77

sorted elements After insertion Sort:

20 22 42 50 64 77

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4Ans): Binary search Algorithm

procedure BinarysearchAlg(a1,a2,…,an: Integers)

key:=42

low := 1;

   high := n;

    do

   

        mid := (low + high) / 2;

        if (key< array[mid])

            high := mid - 1;

        else if (key > a[mid])

            low = mid + 1;

    } while (key!= a[mid] && low <= high);

    if (key == a[mid])

    {

        print(\"SEARCH SUCCESSFUL \");

    }

    else

    {

        print(\"SEARCH FAILED \");

    }

Search element:

Step1:

key:=42

List : 10 11 13 15 18 27 29 31 36 42 50 56 70 73 82 96

Low=1

High=16

Step2:

List: 10 11 13 15 18 27 29 31 36 42 50 56 70 73 82 96

Mid=(1+16)/2 =8

If( 36<key) then low=mid+1

Step3:

List: 10 11 13 15 18 27 29 31 36 42 50 56 70 73 82 96

Mid=(9+16)/2 =12

If(70>key) then high=mid-1

Step4:

List: 10 11 13 15 18 27 29 31 36 42 50 56 70 73 82 96

Mid=(9+12)/2 =10

If(50>key) then high=mid-1

Step5:

List: 10 11 13 15 18 27 29 31 36 42 50 56 70 73 82 96

Mid=(9+9)/2 =9

If(42==key) then

42 is found in the list