Week 6: Thursday
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Q1. (30)

Write a function to recursively compute the harmonic mean of an array of
numbers.

In the main function, create an array of size 10. Input integers from the user
till a negative integer is input or the 10 elements have been filled up. Save
the number of valid entries of the array in a variable. Find the harmonic mean
of the elemnts of this array.

Q2. (70)

In the main function, input a sorted array of 10 integers. You can assume that
the user will input distinct integers in an increasing order. Now input another
integer q from the user.

Write a recursive function search that checks whether q is present in the
array. If q is present, it returns the index where q occurs in the array;
otherwise, it returns -1. Note that you must implement the function search as a
recursive function:
int search(int[] a, int q, int start, int end)
where start and end denote the starting and ending indexes of the array where
the search will be conducted.

Since the array is sorted, a new way of searching will be used. First, the
element to be searched q is compared with the middle element of the array. The
middle elemnt is at the index mid = (start + end) / 2. Now there are three
possibilities:

(a) a[mid] is q. Return mid.
(b) a[mid] < q. Since the array is sorted, q cannot lie on the left side of the
array. So the part of the array now needs to be searched is from mid + 1 to
end.
(c) a[mid] > q. Since the array is sorted, q cannot lie on the right side of
the array. So the part of the array now needs to be searched is from start to
mid - 1.

Take care of the base cases, i.e., when the array contains one element or no
elements.

Example:

Input is 2 4 6 8 9 10 12 13 14 15

(i) Search for q = 13

Compare with middle element 9. Then search right side, i.e., from 10 to 15.
Again, compare with middle element, i.e., 13. Return the index 7.

(ii) Search for q = 6

Compare with middle element 9. Then search left side, i.e., from 2 to 8.
Again, compare with middle element, i.e., 4. Then search right side, i.e., from
6 to 8. Now, compare with middle element, i.e., 6. Return the index 2.

(iii) Search for q = 5

Compare with middle element 9. Then search left side, i.e., from 2 to 8.
Again, compare with middle element, i.e., 4. Then search right side, i.e., from
6 to 8. Now, compare with middle element, i.e., 6. Next, search the left side.
Since the left side is empty, return -1.