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 COULD YOU DEBUG THE CODE. I INCLUDED THE OUTPUT IMAGES SO YOU CAN SEE WHERE IT DIFFERES #include #include #include

Question

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

***COULD YOU DEBUG THE CODE. I INCLUDED THE OUTPUT IMAGES SO YOU CAN SEE WHERE IT DIFFERES***

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int recursions = 0;
int comparisions = 0;// Read integers from input and store them in a vector.
// Return the vector.
vector<int> ReadIntegers() {
int size;
cin >> size;
vector<int> 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<int> integers, int lower, int upper) {
recursions++;
if (lower > upper)
{
return -1;
}
int mid = (lower + upper) / 2;
if (integers[mid] == target)
{
comparisions++;
return mid;
}
else if (integers[mid] > target)
{
comparisions += 2;
return BinarySearch(target, integers, lower, mid - 1);
}
else
{
comparisions += 2;
return BinarySearch(target, integers, mid + 1, upper);
}
}

int main() {
int target;
int index;

vector<int> integers = ReadIntegers();

cin >> target;

index = BinarySearch(target, integers, 0, integers.size() - 1);
printf("index: %d, recursions: %d, comparisons: %d\n",
index, recursions, comparisions);
return 0;
}

I AM GETTING THIS ERROR WHEN THE PROGRAM RUNS(SOME ARE CORRECT AND SOME ARE NOT):

1:Compare output

Input

9 1 2 3 4 5 6 7 8 9 2

Your output

index: 1, recursions: 2, comparisons: 3

2:Compare output

0 / 2

Output differs. See highlights below.

Input

9 11 22 33 44 55 66 77 88 99 11

Your output