I have a sorted array of 5000 integers. How fast can I tell if a random integer is a member of the array? An answer in general, C and Ruby would be nice.

The array values are of the form

```
c * c + 1
```

where `c`

can be any integer from 1 to 5000.

For example:

```
[2, 5, 10, 17, 26, 37, 50 ...]
```

## Best Solution

Binary search, as others have mentioned, is O(log2N), and can be coded either recursively:

or iteratively:

However, if you're looking for the fastest possible way, you can set up a look up table based on the

`sqrt(N-1)`

of your numbers. With just 5,000 words of memory you can achieve O(1) lookups this way.Explanation:

Since all your numbers are of the form N^2 + 1 for an integer N from 1 to N, you can create a table of N elements. The element at position i will specify if i^2 + 1 is in your array or not. The table can be implemented with a simple array of length N. It will take O(N) to build, and N words of space. But once you have the table, all lookups are O(1).

Example:

Here's sample code in Python, which reads like pseudocode, as always :-)

Building the table takes up O(N) at most, and lookups are O(1).