11 Questions
What is the purpose of the constant K in the interpolation search algorithm?
To narrow the search space
What is the time complexity of the interpolation search algorithm in the worst case?
O(n)
What is the auxiliary space complexity of the interpolation search algorithm?
O(1)
What is the formula for finding the probe position in the interpolation search algorithm?
K = data - low / high - low
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
What time complexity does Jump Search have?
O(?n)
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]
What is the assumption behind linear interpolation?
That we have two data points (x1,y1) and (x2,y2)
What is the time complexity of Binary Search?
O(log n)
What is the advantage of Interpolation Search over Binary Search?
It takes advantage of the uniform distribution of elements
What is the process of creating new data points within the range of a discrete set of known data points called?
Interpolation
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])] -
lois the starting index,hiis the ending index,xis the element to be searched, andarris 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
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.
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