# CodeStepByStep ## binarySearch3

Language/Type: C++ binary search searching

Suppose we are performing a binary search on a sorted vector initialized as follows:

```            // index   0   1   2   3   4   5   6   7   8   9  10  11  12  13
vector<int> numbers {-23, -5,  9, 14, 15, 18, 23, 24, 25, 29, 34, 62, 85, 87};
int index = binarySearch(numbers, 25);
```

Write the indexes of the elements that would be examined by the binary search (the `mid` values in our algorithm's code) and write the value that would be returned from the search.

Now suppose we are performing both an iterative (loop-based) sequential search and then a recursive binary search on the same list. The sequential search is a standard version that does not take any advantage of the sortedness of the list, simply looking each element in order from the start to the end of the list.

Suppose we are searching the list for the value `25`. Also suppose that we are operating on a special computer where reading an element's value in the list (such as examining the value of `numbers`) costs 7 units of time; calling any function costs 10 units of time; and all other operations are essentially 0 cost. (Keep in mind that even in a non-recursive search, the cost of making the one and only call to `binarySearch` still counts in your total.) What is the total "cost" of running a sequential search and recursive binary search over this list of data, searching for the value `25`?

 `indexes examined` `value returned` `sequential search cost` `binary search cost`