Question

The code is in python. The file does not have to be the data set from HW2. What I need is a code combing selection sort and merge sort. The 2-1 is what the problem in refers to as Q1.

d) [10 points] Write a code combining both selection sort and mergesort algorithms (NOT insertion and merge sorts) as described in Q1) to find out the most optimal k minimizing time efficiency of your algorithms using 1 M data set from HW2. You may use the time efficiency program you wrote in the previous home work. Please collect and display some performance data proving your k is the most optimal as shown below: k-10: 11.42 seconds k-5: 11.07 seconds k: 10.55 seconds k+5: 10.59 seconds. k+10: 11.02 seconds Please note that the efficiency data above are all made up by me for this homework purpose only. They are not actual simulation results.

Answer 1

# Code combining merge sort and selection sort. Here, I am using merge sort on the whole array and using selection sort for arrays with length smaller than a threshold.

def selectionSort(X, l, r):

   for i in range(l,r+1):

     min_index = i

     for j in range(i+1, r+1):

       if X[min_index] > X[j]:

         min_index = j

     X[i], X[min_index] = X[min_index], X[i]

   return X

def merge(arr, l, m, r):

    n1 = m - l + 1

    n2 = r- m

  

    # creating temporary arrays and copying data in them

    temp1 = [0] * (n1)

    temp2 = [0] * (n2)

  

    for i in range(0 , n1):

        temp1[i] = arr[l + i]

  

    for j in range(0 , n2):

        temp2[j] = arr[m + 1 + j]

  

    # Merge the temp arrays back into arr[l..r]

    i = 0     # for first subarray

    j = 0     # for second subarray

    k = l     # for merged subarray

  

    while i < n1 and j < n2 :

        if temp1[i] <= temp2[j]:

            arr[k] = temp1[i]

            i += 1

        else:

            arr[k] = temp2[j]

            j += 1

        k += 1

  

    # Copy the remaining elements of L

    while i < n1:

        arr[k] = temp1[i]

        i += 1

        k += 1

  

    # Copy the remaining elements of R

    while j < n2:

        arr[k] = temp2[j]

        j += 1

        k += 1

k = 4 # threshold length, arrays smaller than this will be sorted using selection sort

def mergeSelectionSort(X, l, r):

    if (r - l <= k):

        selectionSort(X, l, r);

    else:

        mid = int((l + r)/2);

        mergeSelectionSort(X, l, mid);

        mergeSelectionSort(X, mid+1, r);

        merge(X, l, mid, r);

arr = [9,8,7,6,5,4,3,2,1]# array to be sorted

mergeSelectionSort(arr, 0, len(arr)-1)

print(arr)