15.14 LAB: Binary search   Binary search can be implemented as a recursive algorithm. Each call makes a recursive call on one-half of the list the call received as an argument. Complete the recursive function BinarySearch() with the following specifications: Parameters: a target integer a vector of integers lower and upper bounds within which the recursive call will search Return value: the index within the vector where the target is located -1 if target is not found The template provides the main program and a helper function that reads a vector from input. The algorithm begins by choosing an index midway between the lower and upper bounds. If target == integers.at(index) return index If lower == upper, return -1 to indicate not found Otherwise call the function recursively on half the vector parameter: If integers.at(index) < target, search the vector from index + 1 to upper If integers.at(index) > target, search the vector from lower to index - 1 The vector must be ordered, but duplicates are allowed. Once the search algorithm works correctly, add the following to BinarySearch(): Count the number of calls to BinarySearch(). Count the number of times when the target is compared to an element of the vector. Note: lower == upper should not be counted. Hint: Use a global variable to count calls and comparisons. The input of the program consists of: the number of integers in the vector the integers in the vector the target to be located Ex: If the input is: 9 1 2 3 4 5 6 7 8 9 2 the output is: index: 1, recursions: 2, comparisons: 3 ATTENTION WHERE IT SAYS CODE HERE, IS WHERE I MUST ADD CODE. EVERYTHING ELSE CANNOT BE ALTERED #include #include #include using namespace std; // Read integers from input and store them in a vector. // Return the vector. vector ReadIntegers() {    int size;    cin >> size;    vector integers(size);    for (int i = 0; i < size; ++i) {               // Read the numbers       cin >> integers.at(i);       }    sort(integers.begin(), integers.end());    return integers; } int BinarySearch(int target, vector integers, int lower, int upper) {    /* code here. */ } int main() {    int target;    int index;    vector integers = ReadIntegers();    cin >> target;    index = BinarySearch(target, integers, 0, integers.size() - 1);    printf("index: %d, recursions: %d, comparisons: %d\n",           index, recursions, comparisons);    return 0; }

Binary search can be implemented as a recursive algorithm. Each call makes a recursive call on one-half of the list the call received as an argument.

Complete the recursive function BinarySearch() with the following specifications:

1. Parameters:
   • a target integer
   • a vector of integers
   • lower and upper bounds within which the recursive call will search
2. Return value:
   • the index within the vector where the target is located
   • -1 if target is not found

The template provides the main program and a helper function that reads a vector from input.

The algorithm begins by choosing an index midway between the lower and upper bounds.

1. If target == integers.at(index) return index
2. If lower == upper, return -1 to indicate not found
3. Otherwise call the function recursively on half the vector parameter:
   • If integers.at(index) < target, search the vector from index + 1 to upper
   • If integers.at(index) > target, search the vector from lower to index - 1

The vector must be ordered, but duplicates are allowed.

Once the search algorithm works correctly, add the following to BinarySearch():

1. Count the number of calls to BinarySearch().
2. Count the number of times when the target is compared to an element of the vector. Note: lower == upper should not be counted.

Hint: Use a global variable to count calls and comparisons.

The input of the program consists of:

1. the number of integers in the vector
2. the integers in the vector
3. the target to be located

Ex: If the input is:

the output is: