Consider the C function given below. Assume that the array listA contains n ($> 0$) elements, sorted in ascending order.int ProcessArray(int *listA, int x, int n) { int i, j, k; i = 0; j = n-1; do { k = (i+j)/2; if (x <= listA[k]) j = k-1; if (listA[k] <= x) i = k+1; }while (i <= j); if (listA[k] == x) return(k); else return -1; }Which one of the following statements about the function ProcessArray is CORRECT?

Let us trace the do-while loop in ProcessArray:

1. At each iteration, $k = \lfloor(i+j)/2\rfloor$.

2. If $x < \text{listA}[k]$:

   • if (x <= listA[k]) is true $\implies j = k - 1$.

   • if (listA[k] <= x) is false $\implies i$ remains unchanged.

   • The search space shrinks to the left half $[i, k-1]$.

3. If $x > \text{listA}[k]$:

   • if (x <= listA[k]) is false $\implies j$ remains unchanged.

   • if (listA[k] <= x) is true $\implies i = k + 1$.

   • The search space shrinks to the right half $[k+1, j]$.

4. If $x == \text{listA}[k]$:

   • Both conditions x <= listA[k] and listA[k] <= x are true.

   • $j$ becomes $k - 1$ and $i$ becomes $k + 1$.

   • Since $i = k+1 > k-1 = j$, the loop condition $(i \le j)$ becomes false immediately and the loop terminates.

   • Outside the loop, $k$ still holds the index where $\text{listA}[k] == x$, so return(k) correctly returns the index $k$.

5. If $x$ is not in listA, the search interval $[i, j]$ eventually becomes empty ($i > j$), loop terminates, and since $\text{listA}[k] \neq x$, it returns $-1$.

Therefore, the function is a valid implementation of binary search (Option B).