Explain what is Interpolation SearchExplain what is Interpolation Search

Interpolation search is an algorithm used for finding a specific target value within a sorted array. It is an improvement over the traditional binary search, particularly effective when the values in the array are uniformly distributed. The key concept behind interpolation search is that it uses a formula to estimate the position of the target value, which can potentially reduce the number of comparisons needed to find the target.

How Interpolation Search Works

Interpolation search calculates the position of the target value by using a linear interpolation formula, which is derived from the formula for a line (y = mx + c). The general formula used in interpolation search to find the position pos is:

$$
\text{pos} = \text{low} + \left(\frac{(\text{high} - \text{low})}{(A[\text{high}] - A[\text{low}])}\right) \times (x - A[\text{low}])
$$

Here, low and high are the indices between which the target value x is expected to be found, and A is the array. This formula helps determine a probable position of the target value by assuming a uniform distribution of values within the array.

Steps in Interpolation Search

1. Initialize: Start by setting low as the first index of the array and high as the last index.
2. Estimate the Position: Use the interpolation formula to estimate the position pos where the target value might be located.
3. Match Check: Check if the target value is found at A[pos].
   • If A[pos] equals the target, return the position pos.
   • If the target value is greater than A[pos], adjust low to pos + 1.
   • If the target value is less than A[pos], adjust high to pos - 1.
4. Repeat: Continue the process until ...