The Interpolation Search is an improvement over Binary Search for instances, where the values in a sorted array are uniformly distributed. Binary Search always goes to the middle element to check. On the other hand, interpolation search may go to different locations according to the value of the key being searched. For example, if the value of the key is closer to the last element, interpolation search is likely to start search toward the end side.
The space complexity of interpolation search is O(1)
|Best case||Average case||Worst case|
the formula of interpolation search is:
pos = low + ((x – A[low]) * (high – low) // (A[high] – A[low]))
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- calculating the pos using the formula above
array[pos] == wantedElement: return pos
array[pos] > wantedElement:
high = pos - 1
array[pos] < wantedElement:
low = pos + 1
- stay repeating until the
array[pos] == wantedElementor the sub-array reduces to zero.
def InterpolationSearchAlgorithm(wantedItem: int, sortedItems: list): """ => Algorithm Name: Interpolation search => Algorithm Type: search algorithms => Time Complexity: [best case] => O(1) [average case] => O(log2(log2 n)) [worst case] => O(n) => Space Complexity => O(1) => Algorithm  => calculating the pos using the formula above  => if `array[pos] == wantedElement`: return pos  => if `array[pos] > wantedElement` : `high = pos - 1`  => if `array[pos] < wantedElement` : `low = pos + 1`  => stay repeating until the `array[pos] == wantedElement` or the sub-array reduces to zero. => params (wantedItem) => int (sortedItems) => sorted list and equally distributed. => Returns (index) if the wanted item exists in the sortedItems (False) if the wanted item doesn't exist """ low = 0 high = len(sortedItems) - 1 while (high >= low and sortedItems[high] >= wantedItem and sortedItems[low] <= wantedItem): # formula of interpolation sort pos = low + ((high - low) // (sortedItems[high] - sortedItems[low]) * (wantedItem - sortedItems[low])) if sortedItems[pos] == wantedItem: # if it match return his index (pos) return pos elif sortedItems[pos] < wantedItem: # if A[pos] is smaller than wantedItem low = pos + 1 else: # if A[pos] is larger than wantedItem high = pos - 1 return False
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