Create and implement a mergesort variant that yields an int[] array perm instead of rearranging the array's entries, with perm[i] being the index of the array's i th smallest element.

Make and implement a mergesort variation that gives an int[] array perm, where perm[i] is the index of the array's i th smallest element, rather than rearranges the array's elements.

TODO 9 Using the dummy_array given below, complete the following indexing/slicing TODOs. Index/slice the first (index 0), third (index 2), and last (index 4 or -1) columns of the array dummy_array. Store the output into the variable column_slice. Hint: The output shape should be a (2, 3)! Index ONLY the first row (think about the corresponding index value) of dummy_array. Store the output into the variable row_slice. Index ONLY the second row and first two columns of dummy_array. Store the output into the variable slice_array. dummy_array = np.arange(10).reshape(2, -1)print(f"dummy_array output: \n {dummy_array}")print(f"dummy_array shape: {dummy_array.shape}")   # TODO 9.1column_slice =  print(f"column_slice output: \n {column_slice}")print(f"column_slice shape: {column_slice.shape}") todo_check([    (column_slice.shape == (2, 3), 'column_slice did not return the correct shape of (2, 3)'),    (np.all(column_slice == np.array([[0, 2, 4], [5, 7, 9]])), 'column_slice did not return…

Write a program to compute the exact value of the number of array accesses usedby top-down mergesort and by bottom-up mergesort. Use your program to plot the values for N from 1 to 512, and to compare the exact values with the upper bound 6N lg N.