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Interpolation Search Algorithm

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Questions and Answers

What is the purpose of the constant K in the interpolation search algorithm?

To widen the search space

To narrow the search space (correct)

To skip the binary search step

To compare with the binary search result

What is the time complexity of the interpolation search algorithm in the worst case?

O(log2 n)

O(n^2)

O(log2(log2 n))

O(n) (correct)

What is the auxiliary space complexity of the interpolation search algorithm?

O(1) (correct)

O(n)

O(n^2)

O(log n)

What is the formula for finding the probe position in the interpolation search algorithm?

K = data - low / high - low Signup and view all the answers

What is the purpose of the loop in the iteration approach of the interpolation search algorithm?

To repeat the calculation of the probe position until a match is found Signup and view all the answers

What time complexity does Jump Search have?

O(?n) Signup and view all the answers

What is the main idea behind Interpolation Search's formula?

To return a higher value of pos when the element is closer to arr[hi] Signup and view all the answers

What is the assumption behind linear interpolation?

That we have two data points (x1,y1) and (x2,y2) Signup and view all the answers

What is the time complexity of Binary Search?

O(log n) Signup and view all the answers

What is the advantage of Interpolation Search over Binary Search?

It takes advantage of the uniform distribution of elements Signup and view all the answers

What is the process of creating new data points within the range of a discrete set of known data points called?

Interpolation Signup and view all the answers

Study Notes

Interpolation Search

A search algorithm that improves upon Binary Search for uniformly distributed values in a sorted array
Time complexity: O(log2(log2 n)) for average case, O(n) for worst case
Auxiliary Space Complexity: O(1)

Interpolation Formula

Calculates the position to be searched: pos = lo + [(x-arr[lo]) * (hi-lo) / (arr[hi]-arr[lo])]
lo is the starting index, hi is the ending index, x is the element to be searched, and arr is the array

Linear Interpolation

A type of interpolation method that takes two data points (x1, y1) and (x2, y2)
Formula: y = y1 + [(x-x1) * (y2-y1) / (x2-x1)]

Interpolation Search Algorithm

Iterative approach:
- Calculate the value of "pos" using the probe position formula
- If it's a match, return the index of the item and exit
- If the item is less than arr[pos], calculate the probe position in the left sub-array
- Otherwise, calculate the same in the right sub-array
- Repeat until a match is found or the sub-array reduces to zero

Comparison with Other Search Algorithms

Linear Search: O(n) time
Jump Search: O(√n) time
Binary Search: O(log n) time

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Description

Understand the interpolation search algorithm, its formula, and time complexity. Compare it with binary search and learn how to implement it using an iterative approach.