Question

How does Interpolation Search work?

Answer 1

Interpolation search is a searching algorithm that improves upon binary search, particularly when the values in the array are uniformly distributed. It estimates the position of the target value by linearly interpolating it based on its relative position between the minimum and maximum values in the array. Here's how interpolation search works:

1. Initialization:

   • Given a sorted array arr, a target value target, and the array boundaries low and high.
   • Initialize low as the index of the first element in the array (0) and high as the index of the last element in the array (len(arr) - 1).

2. Interpolation Formula:

   • Calculate the probable position of the target value within the array using the interpolation formula:

     pos = low + ((target - arr[low]) * (high - low)) / (arr[high] - arr[low])
      

   • This formula estimates the position of the target value based on its relative position between the minimum and maximum values in the array.

3. Search Interval Adjustment:

   • Compare the target value with the value at index pos:
     • If target is equal to arr[pos], the target value is found at index pos, and the search ends.
     • If target is less than arr[pos], update high to pos - 1 since the target may be located in the left half of the array.
     • If target is greater than arr[pos], update low to pos + 1 since the target may be located in the right half of the array.

4. Repeat or Conclude:

   • Repeat steps 2 and 3 until the target value is found or the search interval becomes empty (low > high).

5. Target Not Found:

   • If the search interval becomes empty (low > high), conclude that the target value is not in the array.

Key Points:

• Interpolation search works best when the elements in the array are uniformly distributed.
• It narrows down the search interval faster than binary search when the distribution of elements is not uniform.
• However, it can perform poorly if the distribution is highly skewed.
• The time complexity of interpolation search is typically O(log log n) in the average case and O(n) in the worst case.

Overall, interpolation search provides a more efficient alternative to binary search in scenarios where the elements are evenly distributed, leading to faster search times.