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?

<p>K = data - low / high - low (A)</p>
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What is the purpose of the loop in the iteration approach of the interpolation search algorithm?

<p>To repeat the calculation of the probe position until a match is found (B)</p>
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What time complexity does Jump Search have?

<p>O(?n) (A)</p>
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What is the main idea behind Interpolation Search's formula?

<p>To return a higher value of pos when the element is closer to arr[hi] (D)</p>
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What is the assumption behind linear interpolation?

<p>That we have two data points (x1,y1) and (x2,y2) (D)</p>
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What is the time complexity of Binary Search?

<p>O(log n) (D)</p>
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What is the advantage of Interpolation Search over Binary Search?

<p>It takes advantage of the uniform distribution of elements (C)</p>
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What is the process of creating new data points within the range of a discrete set of known data points called?

<p>Interpolation (A)</p>
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Study Notes

  • 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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