Question

PLEASE IMPLEMENT YOUR SOLUTION RECURSIVELY IN C++. IT WOULD BE GREAT IF YOU COULD ALSO PROVIDE TEST CODE FOR IT.

5) Design a recursive function to find the immediate successor of a target integer in an array o:f sorted integers. Here the immediate successor of a target is defined as the smallest number that is no smaller than the target in this sorted array int binarySuccessor(const int anArrayl, const int first, const int last, int target); In the above function declaration, the function searches the array anArray[first] through anArrayflast] to find the smallest entry that is larger or equal to a given value target by using a binary search type of algorithm. The function returns the index of the entry that is found. When such an entry cannot be found (i.e. all entries of the array is smaller than the target), the function returns -1 You may assume the array is sorted in an ascending order of the integers and has no duplications. An example of such a sorted array without duplicated items is (-10, 2, 3, 5}. If you call binarySuccessor) to find the Successor for 4 in this array, the function returns the inde:x 3. If you call binarySuccessor0 to find the Successor for 5, the function also returns the index 3 If you call binarySuccessor) to find the Successor for 100, the function will return -1

Answer 1

The below given C++ code implements the algorithm to find the immediate successor of the entered target in the given array anArray[]. The code has been properly commented to enable the reader to understand the code better.

Explanation:

The binarySuccessor(const int anArray[], const int first, const int last, int target) takes in an array with its first and the last element's indices along with the target element that needs to be checked against the provided array to find its immediate successor.

The function first checks if the OR the element at the array's last index is smaller than the target. If either of the conditions is true then the function returns -1 because if the first element's index cannot exceed the last element's index and as the array is sorted in ascending order, the last element cannot be smaller than the target for the immediate successor for the target to exist.

" # include < bits/stdc + + . h > using namespace std: /* @ param: const int an array[]: the array in ascending order containing the elements to be tested const int first: the first index of the array const int last: the last index of the array int target: the element that needs to be tested against the array the function int binary successor() returns the index of the immediate successor of the target */ int binary successor(const int an Array[] , const int first , const int last , int target) { /* if the index of the first element is the less than the that of the last or the last element is smaller than the target then - 1 returned */ if ((first > last)

Next, the function checks if theAND the element at this index is $\geq$ target. If this case is satisfied then the function returns this index as it is this element that the search has narrowed down to and this element is also $\geq$ target.

If these above conditions are not true then the function follows the binary search algorithm to find the immediate successor.

First, the mid of the array is found and the element at mid is equated with the target element. If the element at mid target then the search space in the array shrinks to as the array is in ascending order and no other element smaller than the element at mid can be greater than or equal to the target.

If the element at mid target then the search space in the array shrinks to , as we need to find the smallest number in the array which is greater than or equal to the target element. We also include the mid element in our search space here as the mid element is also greater than the target element and can be a part of the answer.

The function by default returns -1 when no condition is satisfied.

C++ Code:

Sample output:

1.

2.

3.

4.